ASTRONOMY COACHES HANDBOOKTABLE OF CONTENTS Part I Rationale and Correlation to National Standards…………………….3-4 Introduction to Astronomy Teaching Guide.………………………….. 5 Part II Deep Sky Objects (DSOs) How to Search and Organize Images and Information………………... 6 How and What to Study ………………………………………………. 7 Practice Questions with Answers……………………………………… 7 Materials on CD-ROM and Additional Internet Resources…………… 8 Multiwavelength Images How and What to Study……………………………………………..... 9 Practice Questions with Answers………………………………………10 Materials on CD-ROM and Additional Internet Resources……………11 Spectroscopy & Spectra Electromagnetic Radiation……………………………………...… 12-13 Black Body Radiation & the Radiation Laws…………………..… 13-14 Spectral Classifications & Spectra………………………...……….14-16 Stellar Bar Code Classification Activity…………………………...17-21 Practice Questions with Answers…………………………………….. 21 A Stellar Classification Activity……………………………………22-36 Materials on CD-ROM and Additional Internet Resources…………... 37 Stellar Evolution Introduction to Stellar Evolution & the H-R Diagram………..…....38-42 Proto-stars and T-Tauri Stars…………………………………….. 43-44 Brown Dwarfs and Low Mass Stars……………………………… 44-45 Mid-Size Stars, Planetary Nebulae & White Dwarfs…………….. 45-46 White Dwarfs & Type Ia Supernovae……………………………..46-47 Massive Stars & Type II Supernovae…………………………….. 47-50 Neutron Stars, Pulsars, Magnetars & Black Holes………………...50-53 Chandra X-Ray Observatory and Stellar Evolution……………….54-58 How and What to Study……………………………………………… 59 Practice Questions with Answers………………………………… 60-62 Materials on CD-ROM and Additional Internet Resources………….. 63 Variable Stars & Light Curves Cepheid Variable Stars……………………………………………….. 64 Light Curve Plots of Magnitude & Julian Day …………………….64-66 RR Lyrae & Mira Variable Stars………………………………….. 66-67 Cataclysmic Variable Stars…………………………………………….67 Eclipsing Binary Stars & Phase Diagrams….…………………….. 68-69 How and What to Study………………………………………………. 70 Practice Questions with Answers…………………………………..71-79 Materials on CD-ROM and Additional Internet Resources…….….80-81 1 AAVSO Citizen Sky Project……………………………………..82-86 H-R Diagrams Introduction to the H-R Diagram………………………………… 87-89 Stellar Evolution on the H-R Diagram…………………………… 89-91 Spectra and the H-R Diagram…………………………………………92 Globular Clusters, Luminosity and the H-R Diagram………….....93-94 How and What to Study………………………………………..... 95-97 Practice Questions with Answers……………………………….. 98-108 Materials on CD-ROM and Additional Internet Resources………….109 Cosmological Distances Parallax………………………………………………………...……. 110 Spectroscopic Parallax…………………………………………..110-111 RR Lyrae and Cepheid Variables (The Distance Modulus)……. 111-112 Type Ia Supernovae…………………………………………………..113 Tully-Fisher Relationship………………………………………. 113-114 Hubble's Law…………………………………………………….……114 How and What to Study……………………………………….....115-116 Practice Questions with Answers……………………………...…116-118 Materials on CD-ROM and Additional Internet Resources………..…119 Part III Mathematical Equations & Relationships Important Equations…………………………………………….. 120-121 Derivations and Sample Problems…………………………….. 122-131 Part IV DS9 Image Analysis Software DS9 Tutorial ……………..…………………………………....…132-143 DS9 Investigations – 3-Color Composites……………………….144-147 DS9 Investigations – Star Formation & U/HLXs ………………..148-155 DS9 Investigations – Estimating Ages of Supernova Remnants…156-166 DS9 Investigations – Supernova Remnants & Spectroscopy..…...167-192 DS9 Investigations –Analyzing Two Pulsating X-ray Sources…..193-204 Part V Resources……………………………………………………………. 205 Permission is granted by the Chandra X-Ray Center (CXC), the American Association of Variable Star Observers (AAVSO), and Donna L Young for the use of the activities and materials included in this Coaches Handbook. ASTRONOMY COACHES HANDBOOK Written by Donna L Young, Chandra E/PO Office, SAO, Cambridge, MA National Astronomy Event Supervisor
[email protected] ds9 Activities written by Pamela Perry, Lewiston HS, Lewiston, ME
[email protected] Derivations and Sample Problems contributed by Dustin Schroeder, Co-National Astronomy Event Supervisor
[email protected] 2 Rationale: Approximately 15 billion years ago the space and time we call the universe came into existence, along with hydrogen, helium, and lithium. During the first 10 billion years galaxies were formed and stars were born. Many generations of massive stars underwent catastrophic core collapse and left behind supernovae remnants, neutron stars, pulsars and black holes. Elements heavier than lithium were synthesized during this process. Before the final collapse, these massive stars fused hydrogen to helium to carbon, oxygen, silicon, sulfur and iron. Elements heavier than iron were produced in the outer envelopes of the stars during the supernovae explosions and the resulting shock waves from the core collapse. The shockwaves traveled through the remnants, carrying the heavier elements from the interior of the star into the surrounding interstellar medium, enriching the medium with the newly created elements. The interstellar medium - the gas and dust between the stars - provided the raw materials for the formation of a new generation of stars. Some five billion years ago, the shockwave from a local galactic neighborhood supernova event triggered the beginning of the collapse of a cloud of gas and dust into the stellar nursery that gave birth to our Sun and the Solar System. Supernovae explosions, white dwarfs, neutron stars, black holes and all celestial events are governed by the same laws of physics that describe motions on Earth, and through nucleosynthesis create the elements that we study in chemistry. The residue of the maelstrom of stellar cycles of life and death is incorporated into the molecular structure of every life form on this planet. The ground we walk on, the objects we touch, everything we see - contains elements that were created during the death of massive stars. Astronomy is the study of physics, chemistry, biology, and Earth science over immense scales of space and time. A major focus of the NASA enterprise is the study of the structure and evolution of the universe. The goals for the program include forecasting our cosmic destiny, understanding when and where elements are created, exploring the cycles of matter and energy in the evolving universe, and examining the limits of extreme gravity and energy. These goals are supported by the National Research Council science education standards and the Benchmarks for Science Literacy. Unifying concepts and processes supported by these standards include how we use technology to observe and measure evolution and cycles in both small-scale and large-scale systems. More specifically, high school students should have some understanding of current theories of the origin and evolution of the Earth system and the universe. This event is constructed so students can gain an understanding of the life cycles of stars, and an appreciation of the evolutionary processes that are shaping this breathtakingly elegant universe that we call home. Benchmarks for Science Literacy: The Physical Setting: Grades 9 through 12 Benchmarks states that this is the time when concepts from physics, chemistry, mathematical ways of thinking, and ideas about the role of technology in exploring the universe should contribute to an understanding of the character of the universe. The role of gravity in forming and maintaining planets, stars, and the solar system should become clear, as well as large numbers and distances - and why light is used to measure cosmological distances. Specifically, students should know: 3 ●Stars differ from each other in size, temperature, and age; however are composed of the same elements and behave according to the same physical principles. ●The universe, consisting of all energy, matter and time, expanded explosively into existence ~15 billions years ago. Stars condensed by gravity and the fusion of lighter elements into heavier elements began, releasing enormous amounts of energy. Eventually stars exploded and collapsed, producing heavy elements that later allowed other stars, planets, and life to form. The process of star formation and destruction is an endlessly repeating cycle. ●Increasingly sophisticated technology is used to learn about the universe. Optical, radio, ultraviolet, infrared, x-ray and gamma telescopes and observatories collect information from the entire electromagnetic spectrum. Computers and image analysis software have become increasingly efficient in interpreting and transforming information from photons to images and information about the chemistry and physics of stars. National Research Council National Science Education Standards: Grades 9-12 Students should have an understanding of the fundamental concepts and principles of: Content Standard B: ●The structure of atoms and elements and the nuclear forces that hold them together. ●The enormous release of energy from fusion at high pressures and temperatures. ●Chemical reactions are either endothermic (absorb energy) or exothermic (release energy). ●Gravitation is a universal force between two masses that is directly proportional to the two masses and inversely proportional to the distance between them. Electrical forces have the same relationship of proportionality as gravity. ●Electromagnetic radiation in the form of photons is comprised of alternating electric and magnetic fields which self-propagate through the near vacuum of space, contain energy, and transfer that energy when they interact with matter. ●Electromagnetic waves result when electrons change motion or move from higher to lower energy levels within an atom. The energy of the radiation produced is inversely proportional to the wavelength. Electromagnetic waves include radio, microwave, infrared, optical, ultraviolet, x-rays, and gamma rays. Content Standard D: ●How the universe evolved from the Big Bang to its present day structure. ●How the early elements hydrogen and helium became clumped together by gravitation to form trillions of stars, and billions of gravitationally bound stars became bound into galaxies which now contain most of the visible mass of the universe. ●The fusion of hydrogen and helium in stars produce the nuclear energy which leads to the formation of all other elements. Content Standard E: ●Many scientific investigations require the contributions of individuals from different disciplines, including engineering. New disciplines, such as astrobiology, often emerge at the interface of two old disciplines. ●Science advances with new technologies. New technology often expands scientific understanding and leads to new areas of research. 4 INTRODUCTION TO ASTRONOMY The Study Guide Format: The content has been organized into different topics with a specific focus so the content can be studied one section at a time. The topics include: Deep Sky Objects (DSO's): How to search, save and organize the DSO images, what information about the images is important to know, and how to study the images. Multiwavelength Images: Why images of the deep sky objects should be studied in several wavelengths, and what stellar processes are responsible for producing the different wavelengths of radio, infrared, optical, ultraviolet, and x-ray. Stellar Evolution: The stages of evolution from birth through death for the different types of stars, including brown dwarfs, red dwarfs, mid-sized stars, massive and super- massive stars - and their end products, including white dwarfs, planetary nebulae, red giants, red supergiants, supernovae remnants, pulsars, neutron stars, and black holes. Variable Stars & Light Curves: The different types of variable stars, including eclipsing binaries, Cepheids, RR Lyrae and Mira periodic variables, and cataclysmic variables - and the signature light curves produced by each type of variable star. AAVSO Citizen Sky Project: Resource materials, activities, and software to participate in a public observing campaign for the intriguing variable Epsilon Aurigae; the American Association of Variable Star Observers and amateur observations. Spectroscopy & Spectra: The origin of electromagnetic radiation, and how the analysis of the resulting stellar spectra and the radiation laws - Planck's law and blackbody radiation, Wien's law, and Stefan-Boltzmann's law - are used to classify stars and determine physical properties. H-R Diagrams: How to use the graphical plot of absolute magnitude versus stellar classification to determine the mass, age, chemical composition, temperature, and evolutionary stage of individual stellar objects - as well as the age, type, and evolutionary history of open clusters and globular clusters. Cosmological Distances: The specific methods of measuring distances of near-by stars and deep sky objects - including stars, globular clusters, galaxies, and quasars - with parallax, spectroscopic parallax, the distance modulus, planetary nebulae, Type Ia supernovae, the Tully-Fisher relationship and Hubble's law. Mathematical Equations & Relationships: The important equations and relationships, including derivations and re-arranging of variables, and the types of problems and situations that use each type of equation. DS9 Image Analysis Software: Activities and tutorials on how to access, download and learn to use the DS9 image analysis software; access the Chandra X-ray archive for variable stars, supernova remnants, galaxies; develop research projects. Folders: Folders located on the CD-ROM include image sets from selected topic areas and past national and state Astronomy C events to use as study materials. 5 Deep Sky Objects (DSOs) The selection of DSO's represents a variety of stages of stellar evolution. Students should have a good knowledge of where each object fits into the stellar cycle, and what the image looks like in several wavelengths, i.e. radio, infrared (IR), ultraviolet (UV), optical and X-ray. Using Cas A as an example, the best way to gather the necessary information about the deep sky objects is as follows: 1) Go to the Astronomy Picture of the Day (APOD) website: http://antwrp.gsfc.nasa.gov/apod/astropix.html At the bottom of the page click on search and when the search page comes up enter the word Cas A and hit return. The following page opens up: http://antwrp.gsfc.nasa.gov/cgi-bin/apod/apod_search?CAS+A This page contains only two different images of Cas A. Each image has a brief description with many links highlighted. In reading through the information, it can be determined that Cas A is a shortened form of the complete name of the object – Cassiopeia A. Anytime there is more than one nomenclature for an object search for that name also. At the bottom of the page click return to search page. Enter the word Cassiopeia A and another page opens up with more images of Cas A. 2) Create a desktop folder for DSO Images. Right click on each image of Cas A and save them to the folder. Name each image for the wavelength it was observed in, i.e. Cas A radio, Cas A X-ray. Read the descriptions on the APOD website, and follow the links to other sites. List the most important information about Cas A, which should include: ●Cas A is the result of the catastrophic core collapse of a massive star ●Cas A is a type II supernova remnant with a neutron star in its center. ●the remnant is located in the constellation of Cassiopeia ●Cas A is a strong radio source Additional Images of Cas A, including composite images: ●images of Cas A in many wavelengths. The images saved from APOD are x-ray and optical - go to http://chandra.harvard.edu/ and click on Photo Album at the top of the page. This categorizes all Chandra images by type. Click on supernovas & SNR (SNR is an abbreviation for SuperNova Remnant.) Scroll down until you get to the first image of Cassiopeia A. Click on the image. At the bottom of the page there are two headings labeled More Information on Cas A and Related Chandra Images. This will give you more images of Cas A. Save images in radio, infrared, optical and X-ray. 3) The DSO Image folder now contains several multiwavelength images of Cas A. Create a subfolder called Cas A and move all the saved Cas A images to the subfolder. Create a different subfolder for each DSO listed in the Astronomy event description in the Science Olympiad Student Manual for the current national competition year. Follow the same procedure described above to search and save a variety of images and information. 6 4) Knowing the DSO's is important - the answers relating to identification and knowledge about these objects carries the highest weight and are used for breaking ties. Learn one deep sky object at a time. Make up a set of study cards for the Cas A images. Either electronically arrange them all in a word document or PowerPoint slides, or print them out and paste them onto index cards. On the back of each image list the following information: name, location, wavelength, and type. For Cas A the information would be: Cas A, Cassiopeia, wavelength varies by image (i.e. optical, x-ray, radio etc.), Type II supernova. Practice with Cas A until you feel familiar with the object and comfortable about recognizing it. HINT: rotate the images so you can recognize them in any orientation. A sample flash card set for Cas A in PowerPoint format is included on the CD-ROM. If you are not familiar with the constellation of Cassiopeia, you can include images of the constellation also as part of the flash cards. Constellations that are easily recognizable do not include the lines; difficult to recognize constellations always have the lines drawn in for national competition. A good website which has real constellation images is listed below under Additional Internet Resources. The constellations can be displayed either with or without lines. 5) Some sample identification questions involving the Cas A image are presented. It is difficult to devise questions on a single image - especially when they are black and white and not in color - this is only meant to give a general idea of the types of questions that are asked. More comprehensive sets of questions are provided in the Additional Examples of Previous State and National Events section. 1 2 3 4 5 6 7 8 9 10 Using the image set above, answer the following questions: Image 10 is Cas A. 1. What type of object is it? ______ 2. Cas A is strongest in what wavelength? ______ 3. Which image shows Cas A in this wavelength? ______ 4. Which image shows the location of Cas A? ______ 5. Which image shows an object that represents the evolutionary stage prior to Cas A? ______ 6. What type of stellar end product is in the Cas A remnant? ______ [Answers: 1. __Type II supernova remnant; 2. __radio; 3. __image 9; 4. __image 4; 5. __image 8; 6. __neutron star] 7 Additional materials and resources: ●Cas A Image Set: This is a representative set of multiwavelength images of Cas A and its location in the constellation of Cassiopeia. It is easier to learn one DSO at a time. You should be able to recognize the DSO's in different wavelengths and orientations - remember there is no "up" or "down" in space. As you learn to recognize the images, also learn what type of object it is. The images can be used to create a set of flash/study cards. The image set is in a folder on this CD. ●Cassiopeia A Story: http://chandra.harvard.edu/edu/formal/casa_timeline/ A cultural and societal history of the discovery and evolution of Cas A. ●Video Clips: Animation of the Cas A supernova event in two formats, MPEG and QuickTime. If you have Windows Media Player, open it and drag the Cas A Supernova Explosion MPEG clip to the player; same procedure for QuickTime format. http://chandra.harvard.edu/resources/animations/snr.html ●Stellar Scenes: http://www.ne.jp/asahi/stellar/scenes/english/ This site has excellent images of the constellations. The images can be viewed and saved both with and without the lines. This is the only site you need to study constellations. ●Messier Deep Space (Sky) Objects: http://www.seds.org/messier/objects.html This is the SEDS (Students for the Exploration of Space) website which lists all DSO's with a Messier catalog number (110 objects.) The Andromeda Galaxy for example is also M31. The objects on this site can be viewed by either number or type. A wealth of detailed information is available for each object. This site and the APOD site (http://antwrp.gsfc.nasa.gov/apod/astropix.html) with the provided links will give you more than enough information for the DSO's. If you still want to research further, the following SEDS URL lists several good sites to explore - http://www.seds.org/messier/deep-l.html ●Chandra PhotoAlbum: http://chandra.harvard.edu/photo/category_list.html Contains all objects imaged by the Chandra X-Ray Observatory by category. Many of the images have comparison images in other wavelengths. ●The Hubble Space Telescope News Archive: http://hubblesite.org/newscenter/archive/ This Hubble website displays all images that have been released, arranged by category. For example, the first subcategory under Exotic is Black Hole. Click on Black Hole and a list of all 88 objects in this category opens up, from the most recent (2009) to the earliest (1990); Click on any of the 88 titles, and public release images appear with a brief summary of the article. Above the image is a link to any related images, and links to additional information. 8 Multiwavelength Images The multiwavelength image set of Cen A below is an example of the wavelengths that should be studied and why. The descriptions explain the type of phenomena that each of the images represents. NOTE: Cen A [NGC 5128] is an active spiral galaxy. Cen A Optical Cen A Infrared Cen A X-ray Cen A Radio Cen A Optical: Optical images show that NGC5128 is an elliptical galaxy with huge dust lanes across the middle of the galaxy. Astronomers speculate that Cen A was the site of a merger between a small spiral galaxy and a large elliptical galaxy several hundred million years ago. The optical radiation is primarily from stars. Cen A Infrared: The infrared image gives a better view of the dust lanes, as well as the brilliance of the central source. The infrared radiation is produced by cool stars with temperatures of "only" a few thousand degrees Celsius, and by dust that has been heated to a few hundred to a thousand degrees. Cen A X-ray: The Chandra X-ray image of Cen A shows a bright source in the nucleus of the galaxy, which is probably due to a supermassive black hole. The bright jet extending out from the nucleus to the upper left is due to explosive or highly energetic activity around the black hole which ejects matter at high speeds from the vicinity of the black hole. A faint "counter jet" extending to the lower right can also be seen. This jet is probably pointing away from us. Numerous point-like sources of X rays are also apparent. These are probably due to neutron stars or black holes that are accreting matter from nearby companion stars. Cen A Radio: The radio image shows striking jet-like structures that flare out from the center of the galaxy. These structures have been traced well beyond the galaxy out to distances of 600,000 light years. The total length of the radio jet shown here is about ten arc minutes, or about 30,000 light years in length. The radio emission is produced by the synchrotron process, in which high-energy electrons radiate as they spiral around the magnetic field of the galaxy. To understand how a living organism functions, you cannot study only the respiratory system, circulatory system, digestive system, or nervous system; you need to study all of the individual systems and how they exchange energy and materials with each other. The Cen A galaxy requires the same type of analysis – you have to study the dust (infrared), stars (optical), activity within the nucleus (X-rays), and the magnetic fields (x-ray and radio) to understand the physical processes that contribute to this energetic spiral galaxy. The following sample is a typical question set using multiwavelength images of a DSO. Access http://chandra.harvard.edu/photo/0099/index.html to study the Eta Carinae images and descriptions and then answer the sample question set below: 9 Eta Carinae (Eta Car) is the most luminous star known in our galaxy. Observations indicate that Eta Carinae is an unstable star that is rapidly boiling matter off its surface and could explode as a supernova any time! Use the multiwavelength image set of Eta Carinae below to answer the sample questions involving different wavelengths images. 1 2 3 4 5 Look at images 1 and 2. Image 5 shows that image 1 is much smaller than image 2 and is located in the center of image 2. 1. Which of these two images is an x-ray image? _____ 2. Which one is an optical image? _____ 3. Image 3 shows Eta Car in the infrared. What feature(s) does this image show? _____ 4. Eta Car in radio is shown in image 4. It has the same overall structure as the optical. Why is it so bright in the center? _____ 5. Images 3 and 4 are the same scale. What is the predominate wavelength from Eta Car? _____ 6. Which wavelength is showing the structures with the highest energy? _____ 7. The highest temperature? _____ 8. What features does the X-ray image show? _____ [Answers: 1. __image 2; 2. __image 1; 3. __dust; 4. __it must have had an outburst and is a strong radio source; 5. __infrared; 6. __image 2 (X-ray); 7. __image 2 (X-ray); 8. __the central star and the shock waves.] NOTE: The section on Spectroscopy & Spectra discusses the origin and basic properties of the different bandwidths of electromagnetic radiation. That information will give you more details on how to analyze multiwavelength images. Basic facts to keep in mind when answering questions about these images are: ●Optical images "look" like optical images and should be easily recognizable. ●X-ray images show only phenomena in the millions of degree range so only the most energetic features are seen, such as the central star and shockwave features in Eta Car. ●Infrared is radiated by dust and shows areas where dust is concentrated - such as materials ejected from stars, or areas of star-forming activity since stars are born from condensing clouds of dust and gas. The infrared image of Eta Car above shows a huge diffuse region of dust with concentrated areas near the center where large amounts of material are being ejected from the highly unstable star. ●Radio frequencies associated with magnetic field lines have the same orientation as the X-ray frequencies, such as in the Cen A galaxy images on the previous page. In Cen A they are both oriented 90 degrees from the optical and infrared emitting areas of the galaxy. The stars and dust are in the plane of the galaxy, and the high energy jets of material being ejected from the black hole at the center of the galaxy follow the magnetic field lines that lie along the axis of rotation. In the Eta Car images, the radio is more diffuse, however is brightest at the center - exactly where the x-ray image shows the location of the star. 10 Additional materials and resources: ● Cen A Images: Contains several images of Cen A that can be used to put together to create a set of flash/study cards. The image set is in a folder on this CD. ● Eta Carinae Images: Contains several images that can be put together to create a set of flash/study cards. The image set is in a folder on this CD. ● Cas A and Crab Overlay Sets: Each of these same-scale image sets shows the Cassiopeia A and Crab supernova remnants in a different wavelength. For each set, each image will print on one overhead transparency. The purpose is to show the differences in the information conveyed by the image in each wavelength. The transparencies are designed to be superimposed as overlays. Each image is surrounded by small symbols (squares, triangles and circles) that when matched, will orient and align the images to superimpose accurately. These overlays allow superimposition of all four wave lengths simultaneously to give a complete picture of all the processes that determine the present structure of Cas A and the Crab. These overlays are in a folder on this CD and the location URLs are listed below. ● Multiwavelength animation of the Milky Way Galactic Center: http://chandra.harvard.edu/photo/2002/gcenter/animations.html ● Cassiopeia A Composite Image Gallery: This page allows you to view specific combinations of different wavelengths of the Cas A supernova remnant. http://chandra.harvard.edu/edu/formal/composites/casa_composite.html ● Cassiopeia A Overlays: This page shows thumbnails of the images and gives information about each wavelength. PDF files of images are on the CD-ROM. As listed above. http://chandra.harvard.edu/edu/formal/composites/casa_overlays.html ● Crab Nebula and Pulsar Composite Image Gallery: This page allows you to view specific combinations of different wavelengths of the Crab supernova remnant. http://chandra.harvard.edu/edu/formal/composites/crab_composite.html ● Crab Nebula Overlays: This page shows thumbnails of the images and gives information about each wavelength. PDF files of images are on the CD-ROM. http://chandra.harvard.edu/edu/formal/composites/crab_overlays.html ● Multiwavelength Composites: This page shows multiwavelength composites for several DSO's imaged by the Chandra X-ray Observatory. http://chandra.harvard.edu/resources/illustrations/composites/index.html ● The MultiWavelength Milky Way Homepage: These pages bring together many different data sets to present and explain how data across the electromagnetic spectrum are used to learn about the Milky Way's shape, size, and composition. http://mwmw.gsfc.nasa.gov/ Within this site the page http://mwmw.gsfc.nasa.gov/mmw_sci.html shows the galactic plane in ten different wavelengths. A complete description of each wavelength is provided. This site provides highly technical information. ● Cool Cosmos: This site provides a basic tutorial on multiwavelength astronomy and has a good gallery of images - click on Multiwavelength: http://coolcosmos.ipac.caltech.edu/ ● Cen A and Eta Carinae Animations: http://chandra.harvard.edu/photo/2008/cena/animations.html http://chandra.harvard.edu/photo/2007/etacar/animations.html ● Cen A Composite Image Gallery: This page allows you to view specific Combinations of different wavelengths of the Cen A galaxy: http://chandra.harvard.edu/edu/formal/composites/cena_composite.html ● DS9 Multi-Wavelength Investigations in this manual on pages 144 – 155. 11 Spectroscopy & Spectra The Electromagnetic Spectrum (EMS) Optical light is only a small part of the electromagnetic spectrum, which includes everything from radio waves to gamma rays. The range of wavelengths for the various classifications of electromagnetic radiation (EMR) is so large we have to use powers of ten to describe them. The wavelengths of radio EMR are actually macroscopic--typically anywhere from centimeters to 10's of meters in length. Wavelengths of optical light are so small that several thousand of them could fit in one millimeter! And gamma rays have wavelengths that are smaller still by a factor of 10,000. The violet and red "ends" of the optical spectrum are not really "ends" at all, but rather simply the limits to the portion of the EM spectrum to which our eyes are sensitive. Beyond red light lies the region known as the infrared, which is also referred to as heat radiation. The longest wavelength infrared radiation blends into the shortest wavelength radio waves, and the radio region extends out to the longest wavelengths we are able to measure. Beyond the violet of the optical spectrum lies a broad region known as the ultraviolet, which blends into the X-ray region, followed by the shortest wavelength radiation known, the gamma rays. Again, there is no edge or "end" of the spectrum at shortest wavelengths, although we reach a practical limit as to what can be measured. There are no hard boundaries to each spectral region - they are a continuum of smoothly changing wavelengths. Even the boundaries themselves are ill-defined. The spectral regions are just convenient definitions that are used for reference, and can be modified. For example, sometimes it is convenient to define a range of wavelengths between infrared and radio - the microwave region - by revising the assumed boundaries for the infrared and radio regions and inserting this newly defined region in between. Scientists also find it convenient at times to refer to smaller "sub-regions" of these major spectral regions. However, these sub-regions are not always well-defined, and different conventions are sometimes followed. For instance, the infrared (IR) region is sometimes broken into the "near-infrared" (closest to the red optical spectrum) and the "far-infrared" (closest to the microwave or radio region). The ultraviolet (UV) spectral band is sub- divided into the near-ultraviolet (closest to violet optical light), the far-ultraviolet (the middle of the UV band), and finally the extreme-ultraviolet (closest to the X-ray region). In the X-ray region, an entirely different convention is used. In this region "soft X-rays" as those closest to the ultraviolet region, and "hard X-rays" as those closest to gamma rays. Thus, an X-ray astronomer might say one spectrum is "harder" than another, meaning it has more short-wavelength (high energy) emission than a comparison spectrum. 12 Light is a disturbance of electric and magnetic fields that travels as packets called photons as a wave function. Imagine throwing a pebble into a still pond and watching the circular ripples moving outward. Like those ripples, each light wave has a series of high points known as crests, where the electric field is highest, and a series of low points known as troughs, where the electric field is lowest. The wavelength is the distance between two wave crests, which is the same as the distance between two troughs. The number of wave crests that pass through a given point in one second is called the frequency, measured in units of cycles per second called Hertz. The speed of the wave equals the frequency times the wavelength. The wavelength and frequency of EMR are closely related - the higher the frequency, the shorter the wavelength. Because all light waves move through a vacuum at the same speed, the number of wave crests passing by a given point in one second depends on the wavelength. That number, also known as the frequency, will be larger for a short- wavelength wave than for a long-wavelength wave. The equation that relates wavelength and frequency is: λ f = c where λ is the wavelength, f is the frequency and c is the speed of light. The greater the energy, the larger the frequency and the shorter (smaller) the wavelength. Given the relationship between wavelength and frequency described above, it follows that short wavelengths are more energetic than long wavelengths. The equation that relates frequency and energy is: E = h f where E is energy, f is frequency, and h is Planck's constant (6.626 x 10 -34 Joule-sec.) Black Body Radiation & the Radiation Laws All objects emit electromagnetic radiation, and the amount of radiation emitted at each wavelength depends only on the temperature of the object. Hot objects emit more of their light at short wavelengths, and cold objects emit more of their light at long wavelengths. The temperature of an object is related to the wavelength at which the object gives out, or radiates, the most light. This is the basis of blackbody radiation and the radiation laws. The amount of light produced at each wavelength depends on the temperature of the object producing the light. Stars as hot as the Sun - about 6,000 Kelvin (K) - radiate most of their light in the yellow region of the spectrum. Stars cooler than the Sun - below 5,000 Kelvin (K) - radiate most of their light in the red and infrared regions of the spectrum. Solid objects heated to 3,000K appear red but are radiating more infrared light than visible red light. 13 The radiation laws describe both the amount and the wavelengths of radiation emitted by an object, which depend only upon its temperature. All objects absorb some type of radiation. That radiation must then be emitted, or the object’s temperature would continuously increase. Not all objects absorb or emit energy in the same way: some are more reflective or have a greater capacity for absorption. Some also transmit various wavelengths with their corresponding amounts of energy. A theoretical model, call a black body, is defined as the perfect absorber and radiator. Black bodies do not reflect any radiation, but rather absorb all radiation that falls on them and then radiate it all away. Stellar atmospheres are good approximations of black bodies. They absorb all radiation rising from the core, and then emit the radiation into the surrounding space. Stars, like hypothetical black bodies, follow the three radiation laws: Planck’s law, Wien’s law, and Stefan-Boltzmann’s law. Black body radiation is thermal radiation emitted from a black body at a particular temperature. When an object is heated until it glows, it emits all wavelengths, or colors, of the visible spectrum. However, there is always one dominant, or peak, wavelength emitted that depends upon the temperature of the object. An object heated to 3,000K emits radiation whose peak wavelength falls in the infrared or near-infrared part of the spectrum. A 6,000K object has a maximum wavelength output in the yellow; 12,000K is greenish, and 24,000K is in the ultraviolet or near-ultraviolet region of the spectrum. At lower or higher temperatures, the maximum wavelength output falls outside the visible spectrum. Therefore, the temperature of an object determines the dominant wavelength being radiated, which corresponds to a particular color. The continuous radiation from a star does not follow theoretical black body radiation exactly; however, it is similar enough to apply the black body radiation laws. Planck’s law describes the shape of the radiation curve of a “perfect radiator,” which is represented graphically in the black body radiation graph on the previous page. By inspecting the graph, the major points of Planck’s law become apparent: ● Any black body emits energy at every wavelength but not in the same proportions. ● A hotter body produces more energy at every wavelength than a cooler body. ● The hotter the body, the shorter the frequency of the dominant wavelength emitted; color depends on temperature. Wien’s law is simply a mathematical statement of this point. Since a 3,000K object produces a maximum wavelength peak of about 9,500Ǻ (angstroms), and a 6000K object peaks at about 5,000Ǻ, Wien determined that λ max = 2.9 x 10 7 /T where T is the temperature in degrees Kelvin, λ is the wavelength of maximum output in angstroms, and 2.9 x 10 7 is Wien’s displacement law constant in angstroms. NOTE: A constant is a number which represents the proportionality between two different units. In the above relationship it allows temperature in Kelvin to be turned into the equivalent wavelength in angstroms. ● Stefan-Boltzmann’s law also applies to the same black body radiation graph. The total energy emitted by a star at a specific temperature, such as 24,000K, is equal to the area under the radiation curve for that temperature. In mathematical terms, the following relationship gives the energy emitted per unit area of body surface: E = σT eff 4 where T eff is the temperature in Kelvin, E is the energy per unit surface area in erg/cm2, and σ is the Stefan-Boltzmann constant, 5.70 x 10 -5 erg/cm 2 K 4 s. 14 Stellar Classification & Spectra Stars are classified by temperature or spectral type from hottest to coolest as follows: O B A F G K M R N S. (Sometimes R and N stars are grouped together into spectral type C.) These categories are further subdivided into subclasses from hottest (0) to coolest (9). The hottest B stars are B0 and the coolest are B9, followed by spectral type A0. Each major spectral classification is characterized by its own unique spectra. Stars of spectral type G, like our Sun, have an effective (surface) temperature of 5,000 – 6,000K, with a maximum peak output that falls in the yellowish-green part of the spectrum, and have the strongest double calcium lines of any spectral type. Spectral lines can show different characteristics within the same spectral type, and so a second type of classification system for stars was devised using luminosity. The differences in spectral lines among stars having the same spectral type are a function of the radius of the star, which results in different luminosities. Luminosity (L) is related to the absolute magnitude of a star, and is equal to the total outflow of power. Two stars with similar effective temperatures but greatly different luminosities must differ in size: they belong to different luminosity classes within that spectral type, as determined from their spectra. The Sun is assigned the value of one solar luminosity. Stellar luminosities range from one million times more luminous than the Sun, to one ten-thousandth of the luminosity of the Sun. Stars emit radiation, but produce absorption lines because the outermost layers absorb radiation from the core. Because a stellar atmosphere is a black body, it absorbs the radiation and then emits it into the surrounding interstellar medium. This radiation is emitted over a range of wavelengths, so we see dark lines, called absorption lines, where the radiation is “missing”. All stars have a similar basic chemical composition; differences between spectral types are due only to the different effective temperatures. Hydrogen produces dominant spectral lines in stars with an effective temperature near 10,000K. At this temperature, electrons of the hydrogen atoms are becoming excited and then undergoing de-excitation and transiting down to the second energy level, or Balmer line, giving off photons in the visible part of the spectrum. At hotter temperatures, most of the hydrogen is ionized – the electrons have been stripped away. There are fewer intact hydrogen atoms to produce the characteristic spectral lines. The few hydrogen atoms that have managed to retain their single electron are mostly in such highly excited states that their spectral lines are invisible, since they fall back down to the Lyman line (ground state) and emit photons in the ultraviolet part of the spectrum. Only the few neutral atoms of hydrogen that manage to retain their electrons and are not in a highly excited state can absorb and re-emit visible radiation. Since there are fewer electrons that can fall back down to the Balmer line, there are fewer photons emitted in the visible part of the spectrum and the absorption lines are weaker than in cooler stars. The representative spectra for each stellar classification on the following page are based on the following: ●All stars have very similar elemental abundances. ●Stars are good approximations of blackbody radiation - the gaseous atmospheric layers absorb the radiation emitted by the fusion process in the core. ●The resulting absorption spectra are not based upon elemental composition, but ONLY on the temperature and luminosity of the star. ●Stars with the same temperature and luminosity produce characteristic spectral lines. 15 Representative Stellar Classification Spectra: O Stars: 30,000K - 60,000K Prominent ionized hydrogen and helium lines and weak neutral hydrogen lines. Class O stars emit most of their radiation in ultra-violet. B Stars: 10,000K - 30,000K Stronger neutral hydrogen lines, lines of neutral helium instead of ionized helium are present. A Stars: 7,500K - 10,000K Strongest hydrogen lines, lines of singly ionized elements like magnesium and calcium begin to appear. F Stars: 6,000K - 7,500K Hydrogen lines are weaker, and singly ionized lines of calcium are stronger. Singly ionized calcium has a pair of lines that are particularly conspicuous - the H and K lines. G Stars: 5,000K - 6,000K Hydrogen lines are visible, however the CA H and K lines are the strongest lines in the spectrum - they are stronger in G stars than any other spectrum type. K Stars: 3,500K - 5,000K Many neutral metal lines appear. M Stars: Less than 3,500K Many molecular lines appear, including titanium oxide. NOTE: The hotter the star the fewer spectral lines; the cooler the star the more spectral lines. O stars have strong ionized helium lines, B stars strong neutral helium lines, A stars have strong hydrogen lines, F and G stars have ionized metallic lines, K stars have neutral metallic lines, and M stars have molecular lines. 16 Introduction to Stellar Classification Activity Introduction: Classifying stars based on brightness is somewhat problematic. A star’s apparent brightness can be affected by its distance from the observer, its size, or by the presence of interstellar dust. Instead, astronomers classify stars based on the major components of their spectra. Much like bar-codes on grocery store items, stellar spectra are each slightly different but have many characteristics in common. The study of spectra provides scientists with important information about stars that is otherwise inaccessible. This information includes composition and temperature. Part I: Classifying Stellar Spectra Included in this activity is a table of simulated stellar spectra (page 17). Your first task is to sort the spectra by creating a classification scheme. As with real stellar spectra, you will never find two exactly the same. The thickness of each line represents how much light is received at a particular wavelength, so both the thickness and the position of the lines are very important. Astronomers usually focus on the broadest lines first. Record your results in the table below. Note: The table contains five rows but you do not need to use them all. Or you may decide there are more than five categories. Also, there is no requirement that your classification scheme results in the same number of stars in each category. Hint: Imagine that the sixteen bar codes represent food items from four departments— meat, dairy, produce, and groceries. You might expect that all the bar codes from the same department look similar, but not identical. Your task would be to sort them into groups representing the four departments. Spectra ID Numbers Defining Characteristics (provide enough detail so that anyone could use your scheme) Category I Category II Category III Category IV Category V 17 Part II: Matching Stellar Spectra The International Astronomical Union has decided that a set of standard spectra to represent the different classes of stars is necessary. Your task is to match the 16 unknown stellar spectra with the 4 standard spectra on page 18. You should identify four unknown spectra similar to standard A, and the same for B, C, and D. Known Spectra A B C D Unknown Spectra Numbers Part III: Determining Relative Stellar Temperatures Blackbody radiation curves were acquired for all simulated stars, including the standards, and the results are listed on the Data Sheet at the end of the activity. Remembering that the peak wavelength is a measure of the star’s temperature, sort all twenty stars, including stars A, B, C, and D, into four new categories and record the star ID’s in the table below. REMEMBER: The smaller the wavelength, the hotter the star. Hot Stars Medium-Hot Stars Medium-Cool Stars Cool Stars Carefully compare and contrast the stellar temperature classification (table above) with the stellar spectra classification scheme used in Part II. How are the two classification schemes related? Part IV: Determining the Temperature of a Star At the bottom of the Data Sheet on page 18, you will find a table that relates the peak wavelength of the blackbody spectrum to the surface temperature of the star. Suppose a new star is discovered and its spectrum is shown below. Determine its temperature and justify your answer. 18 SIMULATED STELLAR SPECTRA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 19 Stellar Spectra Classification Data Sheet Standard Spectra Classifications A B C D Blackbody Radiation Peak Values Star ID Peak Value (angstroms) Star ID Peak Value (angstroms) 1 3625 11 7005 2 2810 12 3610 3 3612 13 2805 4 7040 14 5515 5 5470 15 7010 6 2812 16 5555 7 2790 A 3600 8 3595 B 2800 9 5510 C 5500 10 6940 D 7000 Corresponding temperatures for four classes of stars studied. Standard Peak blackbody wavelength (angstroms) Temperature (degrees) A 3600 8000 B 2800 10,000 C 5500 5000 D 7000 4000 [This activity is adapted and included with permission from the original, written by Tim Slater, University of Arizona, Tucson] 20 Answers to Introduction to Stellar Classification Activity: Part I: There are no right or wrong answers. Any classification system and justification is as good as any other. Part II: Standard A: 1, 3, 8, 12; Standard B: 2, 6, 7, 13: Standard C: 5, 9, 14, 16; Standard D: 4, 10, 11, 15 Part III: Hot Stars (hottest to coolest): 7, B, 13, 2, 6 Medium-Hot Stars: 8, A, 12, 3, 1 Medium-Cool Stars: 5, C, 9, 14, 16 Cool Stars: 10, D, 11, 15, 4 There is no difference between the classification by spectral lines and the Classification by temperature since spectral lines are determined by the temperature of a star. Part IV: The new spectra is similar to the B star, probably belongs between B and 13, the next coolest star. The peak blackbody wavelength would be around 2800, and the temperature approximately 10,000K. Sample Spectra Question: Arrange the following spectra from coolest to hottest: 1 2 3 4 5 6 Answer: 4 (M star); 2 (K star); 6 (G star); 1 (A star); 5 (B star); 3 (O star) The sequence can be determined by the number of spectral lines. The stellar bar code spectra above are actually simplified from the actual spectra, which look like the graph to the left (an F spectral type star). A few of the widest absorption lines on this graph would be represented as dark lines like the spectra above. To practice classifying spectra using actual spectra like this graph, access the following website: http://skyserver.sdss.org/dr1/en/proj/basic/spectraltypes/studentclasses.asp This Sloan Digital Sky Survey (SDSS) SkyServer website presents a classification activity that uses actual spectra from the SDSS archive; or practice with A Stellar Classification Activity on the following page. 21 A Stellar Classification Activity: NOTE: BEFORE beginning this activity, print the Spectral Plot Overlays for A Stellar Classification Activity page onto an overhead transparency. The overlays will be used with the spectral plots on the worksheet pages to identity the Balmer and other emission lines to classify stars 1 though 7 and A though D. Also print the three worksheet pages on plain paper. Procedure - Part A 1. Classify the spectra of the seven stars provided with this activity according to the strength of their Balmer lines, which are emission lines produced by electrons in the second energy level of hydrogen atoms. NOTE: For the seven stars, both the spectral plot (graph) and the spectral image are provided. The images provide a visual inspection of the widths of the Balmer lines. However, in order to analyze the lines, it is necessary to use the spectral plots in order to more accurately determine the wavelength associated with each line. Both are provided so that you can see how the more familiar spectral images are just a different representation of the spectral plots you will use in this activity. Balmer Line Wavelength (Å) H-α 6560 H-β 4860 H- γ 4340 H- δ 4100 Deep, broad absorption lines at the wavelengths listed in the table above are strong Balmer lines. Using the spectral plots on the Spectral Plots Worksheet, cut out the spectral plots for each of the seven stars and arrange them in order according to the strength of their Balmer lines from strongest to weakest. Write the strength of the Balmer lines of each star in the box beside the spectral plot and record the numbers of the stars in data table 1. 2. Write the spectral classes A, B, F, G, K, M, O (in that order) underneath each star number in table 1- note that these letters are in alphabetical order and based upon the strength of hydrogen lines as first proposed by Williamina Fleming at the Harvard College Observatory in the early 1900’s. 3. Hot dense objects such as stars produce a continuous spectrum also called a thermal spectrum. The spectra of stars 1-7 show this thermal spectrum with absorption lines of elements superimposed. As the temperature of the star increases, the peak of its continuous spectrum will shift to shorter (bluer) wavelengths. Arrange the stars from hottest to coolest and record their numbers in data table 2. 4. Write the spectral classes O, B, A, F, G, K, M (in that order) underneath each star number in table 2- this is the system used today that was developed by Annie Jump Cannon at the Harvard College Observatory in the early 1900’s. This system is based on temperature rather than Balmer lines. 22 Data – Part A: Table 1: Classification according to strength of Balmer Lines strongest weakest Table 2: Classification according to temperature hottest coolest Analysis – Part A 5. Which spectral class of star is the hottest? The coolest? 6. Which spectral classes have the weakest Balmer lines? Are these the very hot stars, the cool stars or both? 7. In a cool star, most of the electrons are in the ground state (few electrons in the second energy level). In a very hot star, the hydrogen atoms are either completely ionized or the electrons are only in very high energy levels. How does this explain the results you observed above? 8. Which of the stars are assigned the same spectral classes in both data tables? Which of the stars have different spectral classes? These differences in classification will be resolved in Part B. Procedure - Part B 9. Since both cool and very hot stars have weak Balmer lines, other spectral lines must be examined to distinguish between the two. Record the numbers of the stars that fit the following in your data table: • In the spectra of O-class stars, lines for ionized helium are present (look for a line at 4540Å). • The hotter the star, the weaker the ionized calcium lines at 3930Å and 3970Å will be in comparison to the hydrogen line at 4340Å. F and G class stars tend to have a strong ionized calcium line compared to the hydrogen line. • K and M stars have many more visible lines (corresponding to Fe, other neutral metals and molecules) than the spectra of O, B, A, F and G stars. Data – Part B possible O stars: possible F & G stars possible K & M stars 23 Analysis – Part B 10. Using the results from Part B, step 1, reclassify each of the stars, resolving any differences from Part A. Record the results in the table below. # 1 2 3 4 5 6 7 spectral class 11. When finished with #10, look at the answer key provided. Which stars, if any, do not agree with the key? 12. What sources of error might there be that could lead to the misclassification of a star? Conclusions and Further Investigation: 13. Use the formula below to find the surface temperature of the star with the strongest Balmer lines. max = (2.9x10 7 K . Å)/T Does this fall within the range given for that spectral class in the table, Summary of the Classification of Stars, on the answer key provided? What might be some sources of error? 14. How accurate is the classification of stars using only the Balmer lines? For which classes of stars are Balmer lines more useful? For which are they less useful? Explain. 15. Which features were most useful in identifying each spectral class? a. O b. B c. A d. F e. G f. K g. M 16. Classify Stars A-D. For each, explain which spectral features helped with the classification: a. Star A – b. Star B – c. Star C – d. Star D– 24 Star 1 Star 2 25 Star 3 Star 4 26 Star 5 Star 6 27 Star 7 28 Star A Star B 29 Star C Star D 30 ANSWER KEY – refer to this key after Part B, step 2 Key: Star 1 – G Star 2 – A Star 3 – F Star 4 – K Star 5 – B Star 6 – O Star 7 – M Summary of the Classification of Stars Spectral Class Temperature ( o K) Strength of Balmer Lines Other Emission Lines O 30,000 - 60,000 weak or not visible Ionized He (4540Å) B 10,000 - 30,000 moderate A 7,500 - 10,000 strong F 6,000 - 7,500 weak Ionized Ca (3930Å, 3970Å) strong compared to neutral H (4340Å) G 5,000 - 6,000 weak Ionized Ca (3930Å, 3970Å) strong compared to neutral H (4340Å) K 3,500 - 5,000 weak or not visible Many lines, neutral Ca 4230 Å M < 3,500 not visible Many lines 31 References: Based upon this activity: The Spectral Classification of Stars http://www.astro.washington.edu/labs/clearinghouse/labs/Spectclass/spectralclasswe b.html The Sloan Digital Sky Survey/Sky Server website has several excellent advanced astronomical activities listed on this site – including one on Spectral Types http://cas.sdss.org/dr7/en/proj/advanced/ Annie Jump Cannon http://www.sdsc.edu/ScienceWomen/cannon.html Annie Jump Cannon – Wikipedia http://en.wikipedia.org/wiki/Annie_Jump_Cannon Stars - Ruth West http://www.viewingspace.com/ucla_mfa/ucla_pages/stars.htm Electromagnetic Radiation - Production of Light http://astronomynotes.com/light/s4.htm#A2.1 Actual spectra used in this exercise: Star 1 – G2 Star 2 – A5 Star 3 – F5 Star 4 – K4 Star 5 – B3 Star 6 – O5 Star 7 – M2 Star A – O9 Star B – A2 Star C – G8 Star D – M5 32 WORKSHEETS: Star 1 Star 2 Star 3 Star 4 33 Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Star 5 Star 6 Star 7 34 Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Star A Star B Star C Star D 35 Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Balmer lines strength: __________________ Classification based on Balmer lines:________ Temperature:________ Strength of He, Ca, H lines:_______________ Stellar Classification:___ Spectral Plot Overlays for A Stellar Classification Activity: Print this page onto an overhead transparency and overlay them with the spectral plots provided for stars 1 through 7 and A through D to help identify the Balmer Lines for Part A and the other emission lines for Part B Part A: Hydrogen Balmer Lines Part B: Ionized He, Ionized Ca, and Hydrogen Lines 36 Additional materials and resources: ●http://csep10.phys.utk.edu/guidry/java/planck/planck.html This site presents an applet that lets the user plot up to 10 Planck radiation curves for arbitrary temperatures in the range 3,000K - 30,000 K. http://csep10.phys.utk.edu/guidry/java/wien/wien.html This page is the same applet above which displays Planck blackbody radiation curves for the same temperature range, and adds the option of illustrating both Wien's law and Stefan-Boltzmann's law for each temperature. Both of the above pages have a link to The BlackBody Game which allows the user to guess the temperature of a black body distribution curve of unknown temperature. ●CLEA: http://www3.gettysburg.edu/~marschal/clea/CLEAhome.html The CLEA Stellar Classification software is an excellent free simulation for Win PCs. You can download the software, a User's Guide, pre and post tests and a comprehensive Student Manual free from the CLEA site. The simulation allows you to control a telescope and spectrograph to take spectra of a large number of stars. You can then attempt to identify them by comparing with spectral standard reference stars. It includes stars of different luminosity classes. Spectra can be examined as photographic or intensity plots. This is worth spending time with. The student manual is comprehensive and a handy resource. You can use this for classroom activities or even as a practical assessment task with some prior exposure. ● SkyServer SDSS: http://skyserver.sdss.org/dr2/en/proj/advanced/spectraltypes/ has an excellent activity/project leading you through the classification of stellar spectra, Spectral Types using actual Sloan Digital Sky Survey data. ● Mini-Spectroscopy: http://mo-www.harvard.edu/Java/MiniSpectroscopy.html is a "simplified" version of the Harvard-Smithsonian Center for Astrophysics full- featured spectroscopy software called Virtual Spectroscope. The Java applet allows you produce a spectrum from a fluorescent lamp, the Sun, a red LED, Hydrogen and three galaxies. They appear as photographic and intensity plots against a reference spectrum. NOTE: THIS IS FOR MORE ADVANCED STUDENTS. 37 Stellar Evolution – Cycles of Formation and Destruction Interstellar Medium and Nebulae: NGC 3370 is a spiral galaxy similar in size and structure to our own Milky Way Galaxy. In visible wavelengths, the image is dominated by the stars and clouds of gas and dust that reside in and define the spiral arm structure. Not obvious in the image are the dust grains, and atomic and molecular gas that comprise the tenuous interstellar medium (ISM) interspersed between the stars. The extremely low average density of the interstellar medium - about one atom per cubic Spiral Galaxy NGC 3370 (Hubble) centimeter - is nearly a perfect vacuum; however, due to the enormous amount of space between the stars, the ISM constitutes ~20-30% of the mass of a galaxy. The interstellar medium is primarily hydrogen and helium left over from the Big Bang, enriched with heavier elements from the nuclear fusion of elements in the cores of previous generations of stars. The interstellar medium is immersed in radiation, magnetic fields and cosmic ray particles, and has an average temperature of 1,000,000 K. The interstellar dust particles are extremely small – usually less than about one thousandths (1/1000 th ) of a millimeter across – and composed mostly H, C, O, Si, Mg and Fe in the form of silicates, graphite, ices, metals and organic compounds. The size of the dust grains is the same size as the wavelength of the blue portion of the visible spectrum; therefore, the dust grains scatter blue light. Since the light that reaches Earth from distant objects is depleted in blue wavelengths by the dust, the resultant transmitted light appears redder than it actually is. This is called interstellar reddening. The dust particles also absorb incident light, heat up, and emit in the infrared - resulting in the dimming of starlight. This is called interstellar extinction, and dims the light from deep sky objects. Nebulae are denser agglomerations of interstellar gas and dust; the main types of nebulae are diffuse, reflection, and absorption. An emission nebula produces an emission spectrum because of energy that has been absorbed from one or more hot luminous stars that excite the hydrogen gas. The ultraviolet (UV) radiation from the massive hot stars ionizes the hydrogen - it strips electrons from the hydrogen atoms - by the process of photoionization. The free electrons combine with protons, forming hydrogen atoms, and emit a characteristic series of emission lines as they cascade down through the energy levels of the atoms. The visible radiation in these lines imparts to these regions their beautiful reddish-colored glows. These regions of ionized hydrogen gas (called HII regions) have typical temperatures of ~10,000 - 20,000 K, and a density M42 (Stephan Seip) of ~10 atoms/cm 3 . In the image to the right is the emission nebula M42, located in the constellation of Orion. The hot luminous stars to the left of the nebula are ionizing the interstellar hydrogen, and protons and electrons are recombining and emitting red light. 38 A nebula that is mainly composed of cool interstellar dust that reflects and scatters light from nearby stars is called a reflection nebula. They are usually blue because the scattering is more efficient for blue light by the dust particles. The Witch Head Nebula to the left is a reflection nebula, and is also glowing due to the ultraviolet radiation from the nearby hot, blue massive star Rigel in the constellation of Orion. Absorption nebulae are physically very similar to reflection nebulae; they look different only because of the geometry of the cloud of dust, the light source and Earth. Absorption, or dark Witch Head Nebula (Gary Stevens) nebulae, are simply blocking the light from the source behind them. The Horsehead Nebula (Barnard 33) is visible only because it is silhouetted against the emission nebula behind it. Emission, reflection, and absorption nebulae are often seen within the same field of view. The image of NGC 6559 Horsehead Nebula (USNO) below, a bright red emission nebula, also contains a reflection nebulosity surrounding the two hot young stars located in the left central portion of the image. The image also contains dark clouds and filaments, highlighted against the bright emission nebula. Emission and reflection nebulae are associated with star formation regions since they are caused by ultraviolet emissions from hot, young stars; however, stars do not form in these types of nebulae. Emission and reflection nebulae are too warm and diffuse for NGC 6559 (Adam Block, KPNO) stars to form. Giant Molecular Clouds and Protostars: Huge complexes of interstellar gas and dust left over from the formation of the galaxy, called molecular clouds, are composed mostly of molecular hydrogen. These clouds are the coolest (10 to 20 K) and densest (10 6 to 10 10 particles/cm 3 ) portions of the interstellar medium. Since these clouds are cooler than most places, they are perfect locations for star formation. The molecular clouds are puffy and lumpy, with diameters ranging from less than 1 light-year to about 300 Light Years and contain enough gas to form from about 10 to 10 million stars like our Sun. Molecular clouds that exceed the mass of 100,000 suns are called Giant Molecular Clouds (GMC's). A typical full-grown spiral galaxy contains about 1,000 to 2,000 Giant Molecular Clouds and many smaller ones. Such clouds were first discovered in our Milky Way Galaxy with radio telescopes about 25 years ago. Since the molecules in these clouds do not emit optical light, but do release light at radio wavelengths, radio telescopes are necessary to trace the molecular gases and study their physical properties. The image above shows the distribution of GMC's within the Orion and neighboring constellations; produced by radio mapping of carbon monoxide (CO) gas. A map of stars, bright nebulae, and cold clouds within 5000 LY of the Orion spiral arm of the Milky Way Galaxy can be seen at http://www.atlasoftheuniverse.com/5000lys.html 39 Star-forming molecular clouds are mostly found along spiral arms, as seen in the CO molecular map showing the distribution of these clouds in the Milky Way Galaxy image on the left. Individual giant molecular clouds are internally violent and turbulent. The self-gravitational energy of the clumps is counter-balanced by pressure from both the supersonic velocity of the gases and magnetic field lines. Pertubations from the spiral density wave within the spiral arm structure, collisions between clouds, supernovae shockwaves, and nearby massive star formation are some of the possible triggers that eventually cause an imbalance within the GMC's and the clumps begin to collapse. Individual stars within clumps form within their own smaller gaseous structures, called cores. As a gas clump collapses it heats up due to friction as the gas particles bump into each other. The energy the gas particles had from falling under the force of gravity (gravitational potential) gets converted to heat (thermal) energy. The gas clump becomes warm enough to produce infrared and microwave radiation. During the initial collapse, the clump is transparent to radiation and the collapse proceeds fairly quickly. As the clump becomes Proplyds in Orion (Hubble) more dense, it becomes opaque. Infrared radiation is trapped, and the temperature and pressure in the center begin to increase. As the clump starts evolving into a protostar, at first it only has about 1% of its final mass; however the envelope of the star continues to grow as infalling material is accreted. After a few million years, thermonuclear fusion begins in its core, and a strong stellar wind is produced which stops the infall of new mass. Other material in the disk may coalesce to form other stars and/or planets. Protostars reach temperatures of 2000K to 3000K - hot enough to glow red - but the cocoon of gas and dust surrounding them blocks visible light from escaping. The proplyds in Orion are protostars embedded within protoplanetary disks. The close-up of two of these young disks in Orion reveals the torturous conditions they must face while Protoplanetary Disks (Hubble) trying to grow into full-fledged planetary systems. Ultraviolet radiation from one of Orion's nearby hot stars is rapidly destroying the disks surrounding the protostars. Only ~10% if all protostars survive the harsh conditions within stellar nurseries to become stars. Introduction to the H-R Diagram: The evolutionary sequences for stars are describing their position on a diagram called the Hertzsprung-Russell (H-R) diagram. Most stages of stellar evolution, beginning with protostars, have a specific position on the H-R diagram. The different branches of the H- R diagram described below will be referred to throughout the descriptions of the evolutionary sequences for different mass stars that follow. 40 Everyone is familiar with the periodic table of the elements. The periodic table is an arrangement of all the known elements in order of increasing atomic number. The reason why the elements are arranged as they are in the periodic table is to fit them all, with their widely diverse physical and chemical properties, into a logical pattern. The vertical lines of elements, called groups, and the horizontal lines of elements, called periods, are chemically similar, and share a common set of characteristics. The elements are also arranged into blocks that share commonalities. The arrangement of the elements in the periodic table also shows the periodicity and trends of some properties, such as electron configuration, metalicity, atomic radii, and melting points. By looking at the location of any individual element in the table, you automatically know several characteristics and properties of that element, as well as what types of chemical bonds it forms, and the chemical reactions it will undergo. The Hertzsprung-Russell diagram, or H-R diagram, is the periodic table of the stars. It was discovered that when the luminosity (absolute magnitude, or brightness) of stars is plotted against their temperature (stellar classification) the stars are not randomly distributed on the graph but are mostly restricted to a few well- defined regions. The stars within the same regions share a common set of characteristics, just like the groups, periods, and blocks of elements in the periodic table. As the physical characteristics of a star changes over its lifetime, it’s position on the H-R diagram changes also – so the H-R diagram can also be thought of as a visual plot of stellar evolution. It is a graphical tool that astronomers use to classify stars. From the location of a star on the graph, the luminosity, spectral type, color, temperature, mass, chemical composition, age, and evolutionary history is known. The Main Sequence: ~90% of all stars occupy the diagonal band running from the upper left corner (hot, luminous stars) to the lower right corner (cool, dim stars) of the H-R diagram. Stars become main sequence stars when the process of thermonuclear fusion - hydrogen to helium - stabilizes. These stars are in hydrostatic equilibrium - the outward radiation pressure from the fusion process is balanced by the inward gravitational force. When the transition from a protostar to the main sequence star occurs, the star is called a Zero Age Main Sequence star (ZAMS). The determining factor of where a star is located on the main sequence is mass. The Sun is a G spectral class star with an effective surface temperature of ~5800K. Since the luminosity and mass of all other stars are measured relative to the Sun, it has one solar luminosity and one solar mass. The O and B stars are the hottest and most massive, and the K and M stars are the coolest and least massive stars. The O and B stars are sometimes referred to as early sequence stars, and the K and M stars as late sequence stars. These terms refer to stars more massive (early sequence) than the Sun or less massive (late sequence) than the Sun. All one solar mass stars, for instance, occupy the same position on the main sequence as the Sun, and they stay in that location, with that specific relationship of temperature and absolute magnitude, until the star runs out of hydrogen and the fusion of hydrogen nuclei to helium nuclei stops. The mass-luminosity relationship for main sequence stars is defined as: L/L(Sun) ~ [M/M(Sun)] 4 . All main sequence stars with a mass less than ~8 solar masses are 41 sometimes referred to as dwarf stars, with the coolest, least massive stars in the lower right corner called red dwarfs. The more massive the star, the faster the rate of fusion, and the less time is remains on the main sequence. The amount of time that a star spends on the main sequence is also a function of its mass and luminosity and is defined as: T(years) = 10 10 M/L. The Giant Branch: Red giants are luminous, cool giant stars in spectral classes F, G, K, and M located in the middle right portion of the H-R diagram, above the main sequence. As the central core of a main sequence star with a mass from ~0.8 to 8 solar masses runs out of hydrogen, radiation pressure no longer balances gravity and the star begins to collapse. There is still hydrogen in the outer layers surrounding the helium core of the star; however the temperature is not high enough for this hydrogen to fuse. As the star begins to contract, the core gets hot enough to start a thin shell of hydrogen fusion around the helium core. The increase in radiation pressure causes the star's outer atmospheric layers to expand. As the surface of the star increases, so does its apparent brightness. As the surface (photosphere) increases, it becomes cooler, and the color of the star becomes redder. Eventually the hydrogen in the shell becomes depleted and the star begins to contract once again, and this time the temperature becomes hot enough to start helium fusion. The outer layers expand even further, becoming cooler and redder. Giant stars fuse elements up to carbon. Most of these stars go through a Mira variable instability strip with a periodic light curve of ~80 - 1000 days. Stars that have evolved to the giant branch are commonly referred to as red giants. Eventually these red giants will shrug off a planetary nebula and leave a white dwarf core remnant. There is no relationship among mass and luminosity on the giant branch. The Supergiant Branch: Stars greater than ~8 solar masses evolve onto the supergiant branch, located in the extreme upper right corner of the H-R diagram. These red supergiants are extremely luminous and cool, due to their expanded size. Their spectral types range from B - the massive stars just leaving the main sequence - through M, as they finish their transition to the supergiant branch. NOTE: The O and B stars on the main sequence are sometimes referred to as blue supergiants, not to be confused with the highly evolved and aging red supergiants located on the supergiant branch. Because of the mass of these stars, the fusion of heavier and heavier elements continues through neon, magnesium, silicon, sulfur, iron and nickel. Each time a new element is created the star becomes larger and redder. (Some stars with a mass of ~8 solar masses move through the Cepheid variable instability strip and become pulsating Cepheids with a period of 1 - 70 days). Eventually most of these stars reach the supergiant branch and undergo a Type II supernovae explosion and core collapse, leaving behind a pulsar, neutron star, magnetar or black hole. Some hyper-massive stars collapse into back holes without a supernova event, and some of the less massive giant stars manage to avoid a supernova event and become white dwarfs. [NOTE: there are exceptions to some of these evolutionary sequences, and the associated masses are "ballpark" numbers only - there is much to learn about the evolutionary history of stars.] The White Dwarf Branch: The white dwarf branch is located in the lower left corner of the H-R diagram. This branch consists of the end products of stellar evolution for mid- sized stars with an initial mass of ~0.8 to 8 solar masses. All white dwarfs are extremely hot; however they have a very low absolute magnitude because they are very small. They have a size that does not exceed 1.4 solar masses - the Chandrashekar limit. Spectral types for white dwarfs range from O to G as they slowly radiate away their energy. 42 Young Stellar Objects: Any star that has evolved past the protostar stage (i.e. is shining by way of internal nuclear reactions) but has yet to arrive on the main sequence is called a Young Stellar Object (YSO). YSO's come in a variety of forms depending on their age, mass, and environment, and include Herbig-Haro objects, T Tauri stars, and, in general, immature stars prone to irregular brightening, embedded in nebulosity, and associated with bipolar outflows. The montage of HH Objects (Hubble) Hubble HH objects provides a dramatically clear look at collapsing circumstellar disks of dust and gas that build stars and provide the ingredients for planetary systems. Blowtorch- like jets of hot gas are funneled from deep within these embryonic systems, and machine-gun like bursts of material are fired from the young stellar objects at speeds of nearly a half-million kilometers per hour. The Herbig-Haro object HH111 shows the fast-moving jets of material from a newborn star colliding with the interstellar medium. As the bipolar flow from a young star plows into the surrounding gas, it generates strong shock waves that heat and ionize the gas. In the cooling gas behind the shock front, electrons and ions recombine to give an emission line spectrum characteristic of Herbig-Haro objects. All known Herbig-Haro objects have been found within the boundaries of dark clouds, and are strong sources of infrared radiation. The Trifid Nebula is one of the most HH 111 (Hubble) prominent nebulae in the night sky. Radiation from the powerful central star is eating away at the surrounding dense interstellar material. The field of view of this Hubble image includes a region of star formation that will be destroyed by the advancing ionization front in the next ~20,000 years. A prominent jet from a Trifid Nebula (Hubble) young stellar object and a long finger with a a possible young stellar object at its tip are apparent in the image. The stellar jet is emerging from the wall of a cloud in the Trifid Nebula. The jet is remarkable because, unlike most stellar jets, it can be seen along its entire length. This is because the jet is being lit up by radiation from the massive, luminous star that powers the Trifid. The tip of a finger-like Evaporating Gaseous Globule, or "EGG", is pointing back at the Trifid’s central star. A tiny Trifid Stellar jet Trifid EGG with jet A tiny jet emerging from the EGG and a patch of reflected Light suggests that a young stellar object is buried in the tip of the jet. This young stellar object was uncovered a few tens of thousands of years ago as radiation from the Trifid's central star disrupted the dense cloud from which the star formed. A T Tauri star is a very young, lightweight star, less than 10 million years old and under 3 solar masses, that it still undergoing gravitational contraction; it represents an intermediate stage between a protostar and a mid-mass main sequence star like the Sun. T 43 Tauri stars are found only in nebulae or very young clusters, have low-temperature (G to M type) spectra with strong emission lines and broad absorption lines. They are more luminous than main sequence stars of similar spectral types, and they have a high lithium abundance, which is a pointer to their extreme youth, as lithium is rapidly destroyed in stellar interiors. T Tauri stars often have large accretion disks left over from stellar formation. Their erratic brightness changes may be due to instabilities in the disk, violent activity in the stellar atmosphere, or nearby clouds of gas and dust that sometimes obscure the starlight. Two broad T Tauri types are recognized based on spectroscopic characteristics that arise from their disk properties: classic T Tauri and weak-lined T Tauri stars. Classical T Tauri stars have extensive disks that result in strong emission XZ Tauri (Hubble) lines. Weak-lined T Tauri stars are surrounded by a disk that is very weak or no longer in existence. The weak T Tauri stars are of particular interest since they provide astronomers with a look at early stages of stellar evolution unencumbered by nebulous material. Some of the absent disk matter may have gone into making planetesimals, from which planets might eventually form. According to one estimate, about 60% of T Tauri stars younger than 3 million years may possess dust disks, compared with only 10% of stars that are 10 million years old. T Tauri stars represent an evolutionary stage between protostar and main sequence and are located just above the main sequence on the H-R diagram. Brown Dwarfs & Low Mass Stars: If a protostar forms with a mass less than 0.08 solar masses, its internal temperature never becomes high enough for thermonuclear fusion to begin. This failed star is called a brown dwarf, halfway between a planet (like Jupiter) and a star. A star shines because of the thermonuclear Gliese 229B (Palomar) reactions in its core, which release enormous amounts of energy by fusing hydrogen into helium. For the fusion reactions to occur, though, the temperature in the star's core must reach at least three million K. And because core temperature rises with gravitational pressure, the star must have a minimum mass: about 75 times the mass of the planet Jupiter, or about 8 percent of the mass of our sun. A Brown Dwarfs in Orion (Hubble) brown dwarf, like Gliese 229B pictured above, just misses that mark; it is heavier than a gas giant planet but not quite massive enough to be a star. Brown dwarfs still emit energy, mostly in the infrared, due to the potential energy of collapse converted into kinetic energy. There is enough energy from the collapse to cause the brown dwarf to shine for more than ~15 million years. Brown dwarfs eventual radiate all their heat into space and fade away. The composite Hubble image shows the Trapezium stars (optical) within the Orion Nebula combined with an infrared image that shows a swarm of brown dwarfs. 44 All through the long life of a low mass star, the relentless compression of gravity is balanced by the outward pressure from the nuclear fusion reactions in the core. Eventually, the hydrogen nuclei in the core is all converted to helium nuclei and the nuclear reactions stop. No stellar evolution takes place in stars with less than 0.8 solar masses. The time it takes for low mass stars to use up all their hydrogen fuel is longer than the current age of the universe (about 14 Proxima Centauri, Chandra billion years). These extremely low mass stars are called red dwarfs, and they are located on the lower right corner of the main sequence on the H-R Diagram. Proxima Centauri, the nearest star to the Sun, is a red dwarf star. Mid-Sized Stars: Thermonuclear fusion in stars with masses between ~0.8 and 8 solar masses, similar to our Sun, produces the outward radiation pressure to counterbalance gravitational forces for approximately ten billion years. When all the hydrogen nuclei have been converted to helium nuclei and fusion stops, gravity takes over and the core begins to collapse. The layers outside the core collapse too - the layers closer to the center collapse more quickly than the ones near the stellar surface. As the layers collapse, the gas compresses and heats up. The temperature becomes high enough for helium nuclei to fuse into carbon and oxygen nuclei, with hydrogen fusing in a thin shell Sun (SOHO) surrounding the core. The outer layers expand to an enormous size and the star is now called a red giant. The star brightens by a factor of ~1,000 to 10,000, and the surface temperature of the extended envelope drops to about 3,000K - 4,000K, giving the star its reddish appearance. A strong wind begins to blow from the star's surface, carrying away most of the hydrogen envelope surrounding the star's central core. During the Mira (Hubble) final shedding of its envelope, when the mass loss is greatest, the star pulsates - the surface layers expand and then contract in repeating cycles - with periods from several months to more than a year. During this pulsating stage the star is called a Mira Mira Light Curve variable star. The pulsations of Mira variable stars result in a change in the magnitude, or brightness, of the star. A plot of the change in brightness over time is call a light curve. During this stage, as mid-sized stars evolve to the giant branch, they move through an area referred to as the Mira instability strip - on the H-R diagram shown on the left this area is further divided into long- period and semiregular variables. Eventually, the material ejected by the star forms an envelope of gas called a planetary nebula which expands into the surrounding interstellar medium at ~17-35 km/hr. The core of the star left in the center of the planetary nebula is called a white dwarf. The planetary nebula is very tenuous, and becomes so thin that after ~50,000 years it is no longer visible - therefore all planetary nebulas that we see are very young, less Helix Nebula (Hubble) 45 than ~50,000 years old. The white dwarf is extremely dense. It is held in equilibrium with gravity by electron degeneracy pressure. The repulsive forces of the electron clouds of the individual atoms are strong enough to stop any further gravitational contraction. The mass limit for a white dwarf to remain in equilibrium between gravity and electron degeneracy pressure is 1.4 solar masses - the Chandrasekhar limit. Eventually the white dwarf will radiate all of its remaining energy away and become a black dwarf - a cold, dark mass. The universe is not old enough for any white dwarf to have become a black dwarf, so black dwarfs are not considered as part of the evolutionary stage of a star. This H-R diagram the shows the evolutionary track of the Sun, which is halfway through its lifetime of ~9 billion years on the main sequence. It is a spectral type G star, has an effective surface temperature of ~5800K, and one solar luminosity. When the Sun runs out of hydrogen fuel in its core and fusion stops, it will begin its journey to the red giant branch. The Sun will contract, heat up until a shell of hydrogen is fusing around the helium core, and become cooler, ~3000K, reddish in color, and more luminous – in excess of 500 solar luminosities. After ~one billion years, the hydrogen shell fusion stops and the Sun contracts again, becoming less luminous, hotter, and less red in color. During this phase it is sometimes referred to as a yellow giant. The contraction will cause the core to heat up until helium fusion begins in the core. The fusion of helium nuclei to carbon nuclei causes the Sun to expand again, becoming more luminous. The core will contract again when it runs out of helium and fusion stops again; this time there is not enough mass for the shrinking core to achieve the temperature necessary for the fusion of carbon to begin. The Sun will throw off its outer atmospheric layers into a planetary nebula and the remaining carbon core – called a white dwarf – will then reside on the white dwarf branch of the H-R diagram. The white dwarf is very dim and very hot – with a temperature of ~20,000K. The white dwarf will radiate away its heat over the next ~12 billion years and become a burnt out carbon cinder called a black dwarf. A white dwarf is not the end produce is the stellar evolution of a mid-sized star if it is in a binary system. Suppose two stars, one with one solar mass and the other with five solar masses are in a binary system. The five solar mass star runs out of hydrogen faster than its less massive companion, becomes a red giant, shrugs off a planetary nebula, and collapses into a white dwarf. Eventually the companion Dana Berry, Artist star runs out of hydrogen and enters the red giant stage. The outer layers of the red giant are loosely held by the star, and the extreme gravitational field of the white dwarf starts pulling the material from the red giant into an accretion disk around the white dwarf. The mass transfer continues, with the material orbiting the white dwarf in the accretion disk. Friction slows the matter’s orbital motion, which causes the matter to spiral through the disk down to the surface of the white dwarf. The falling and spiraling of the matter toward the white dwarf releases large amounts of gravitational energy and heats the accretion disk. 46 The white dwarf is predominately carbon and oxygen, and accretes matter from its companion relatively rapidly. Consequently, the white dwarf grows in mass. When the accretion has raised the white dwarf's mass to the critical mass of 1.4 solar masses, the density and temperature in the center of the white dwarf become so severe that carbon starts burning explosively. Within one second the burning front moves all the way to the surface, making the entire white dwarf one huge nuclear fireball. The white dwarf explodes and is completely destroyed. There is no stellar remnant. All of the core's matter - namely, the products of the nuclear burning (iron, nickel, silicon, magnesium, and other heavy elements) plus unburned carbon and oxygen - Tycho's SNR (Chandra) are ejected into space at speeds upwards of 48,000,000 km/hr. Tycho's supernova remnant is the result of a Type Ia supernova event; the core was completely destroyed by the explosion. Massive Stars: Massive star formation seems to take place in clusters. Studying the distribution of massive stars and how they form is complicated because most of their energy is emitted at far- ultraviolet wavelengths that are not accessible from Earth, and they have short main sequence lifetimes; stars greater than 40 solar masses may not even finish their assembly until after fusing a significant portion of their core hydrogen, so a zero-age main sequence stage may not even exist for the M7 Open Cluster in Scorpius (NOAO) most massive stars. Massive stars are low in number but make a large contribution to the properties of galaxies. They are fundamental to the production of the heavy elements and to the energy balance in the interstellar medium. Massive stars regulate the rate of star formation on large scales through feedback via intense winds, radiation and, finally, through supernova explosions. Most stars are born in the neighborhood of a massive star, so they influence the rate Eagle Nebula (NOAO) of low-mass star formation. The Eagle Nebula is a major star-forming region. Star formation will stop after a relatively small number of stars have been born. That's because the stellar nursery is blown away by some of the newly formed stars. The hottest of these stars heat the surrounding molecular gas, break up its molecules, and drive the gas away. As the gas and dust clears, the previously hidden young stars become visible, and the molecular cloud and its star-forming capability cease to exist. So, ironically, the same climate that is conducive to star formation also may shut off the star formation process. Young stars are very hot and can heat the molecular gas to more than 800 K, which is an unfavorable climate for star birth. When the temperature exceeds about 1900 K, the gas molecules break down into atoms. 47 The Orion Nebula (M42) is ~1500 LY away, and the closest stellar nursery. The Orion Nebula is an emission nebula, excited by four young hot luminous stars in its center, called the Trapezium. The trapezium stars are ~2,000,000 years old. Eventually, the entire Orion complex, which includes the Orion Nebula, the trapezium, and the Horsehead nebula, will slowly disperse over the next Orion Nebula (CFHT) ~100,000 years. Eventually this area will resemble the Pleiades - an open cluster of young, hot Trapezium in Orion (Hubble) stars that formed together, produced intense untraviolet radiation that blew away the gas clouds surrounding them, and began slowly drift apart over time. This image of N44F captures the gas cavity carved by the stellar wind and intense ultraviolet radiation from a hot young star. This young star was once buried deep within a cold dense molecular cloud. The cloud fragmented and condensed, forming a core which became a protostar. Eventually the protostar became hot enough for thermonuclear fusion to begin, and the hydrogen nuclei in the core started fusing into helium nuclei. After the core N44F (Hubble) hydrogen has been depleted in these massive stars (greater than ~8 solar masses) helium begins fusing into carbon and oxygen nuclei. The carbon- oxygen core contracts and heats until it is hot enough for carbon and oxygen to start the fusion process. Their fusion yields neon, magnesium, silicon, and sulfur nuclei. Eventually, silicon and sulfur fuse in the star's core to form iron, nickel, and other nuclei of similar atomic weight. The star's structure now resembles an onion. The central core of the onion consists of iron nuclei. Surrounding it is a shell in which silicon and sulfur are fusing, adding more iron nuclei to the iron core. In additional levels further out, lighter elements fuse - oxygen, carbon, helium, and hydrogen. The iron core is very compact and Hodge 301(Hubble) cannot ignite to induce further nuclear fusion. Nuclear fusion, just like chemical burning, is possible only if the reactions release energy. The fusion of iron with other nuclei to make still heavier nuclei requires an input of energy - it is an endothermic reaction. The energy required to manufacture elements heavier than iron becomes available only during the catastrophic collapse of the star's core and the violent explosion of the star's outer envelope that is about to occur. The cluster of hot stars in the lower right corner of Hodge 301, located within the Tarantula Nebula, is rapidly approaching collapse. This massive star-forming region is in the Large Magellanic Cloud, 48 a galaxy ~180,000 LY away. As the hydrogen fuel begins to run out, massive stars leave the main sequence of the H-R diagram and start evolving towards the supergiant branch. The transition to the supergiant branch is not smooth, and the stars expand and contract as the fusion process changes from one type of nuclei to the next. Many of these stars pulsate because they are not in hydrostatic equilibrium: the force of gravity acting on the outer mass of the star is not quite balanced by the interior radiation pressure pushing outwards. If a star expands as a result of increased gas pressure, the material density and pressure decrease until the point that hydrostatic equilibrium is reached and then overshot, owing to the momentum of the expansion. At this point the star is transparent and photons can escape. Then gravity dominates, and the star begins to contract. The momentum of the infalling material carries the contraction beyond the equilibrium point. At this point the star becomes opaque and photons are trapped and the star is dimmer. The pressure again becomes too high, and the cycle starts over again. They system acts as an oscillator. This type of star is called a variable star, because the star changes its brightness, or magnitude, as it pulsates. One type of massive pulsating variable star is called a Cepheid. Most massive stars pass through the Cepheid instability strip of the H-R diagram as they progress towards the red supergiant branch. Cepheids have a repeating cycle of change that is periodic - as regular as the beating of a heart. Observations of the changes in apparent magnitude of variable stars - including Cepheids - are plotted as the apparent magnitude versus time, usually in Julian Date (JD). The resulting graph is called a light curve. The light curve for the Cepheid variable star X Cyg (located in the constellation Cygnus) is shown below. Each data point represents one observation. Once many observations have been plotted, important information can be obtained from the resulting pattern of changing magnitudes. The period for X Cyg is the amount of time it takes for the star to go through one complete cycle from maximum magnitude (brightness), through minimum magnitude (dimmest), and back to maximum magnitude (brightness.) http://www.aavso.org/vstar/types.shtml The mass of the star's iron core approaches 1.4 solar masses - the Chandrasehkar Limit - due to the continued silicon and sulfur fusion in the thin shell adjacent to the iron core, and the continued fusion of iron requires more energy than is available. Once the Chandrasekhar Limit is reached, the electron degeneracy pressure of the atoms within the core is Sher 25 (ESO) no longer able to stop to further collapse of the star; radiation pressure is no longer able to support the core against gravity and the iron core collapses. In less than a second, the core collapses from a diameter of ~8000 kilometers to ~19 kilometers - the collapse happens so fast that the outer layers have no time to react or collapse along with the core. The energy released during core collapse is unimaginable - more energy than is produced by 100 stars like the Sun during their entire lifetimes of more than 10 billion years! Most of the energy released during collapse is carried off into space by SNR 0103-72.6 (Chandra) 49 neutrinos; however a small fraction of the energy triggers the accompanying supernova explosion. It is possible that Sher 25 will be the next observable supernova event. The supernova Remnant SNR 0103-72.6 occurred ~10,000 LY away in the Small Magellanic Cloud - a neighboring galaxy. The X-ray image shows great detail within this remnant, even though it is ~190,000 LY away. It is easier to study remnants in other galaxies, because within the Milky Way these objects are obscured by the gas and dust within the spiral arms. The core collapses so fast that it momentarily goes past its equilibrium point and instantaneously rebounds. The innermost layers of the star are still in-falling and meet the rebounding core, creating a super strong shock wave that runs outward through the layers towards to the star's surface. The shock wave heats the outer layers, inducing explosive nuclear burning, and ejects the outermost layers in excess of speeds of ~16 million kilometers per hour. The energy released by the shockwave manufactures elements heavier than iron. When the shock wave reaches the star's surface, it heats the surface layers and brightens them – SN1987A (AAO) within a day or two the exploding star becomes brighter than a billion Suns. The SN1987A supernova event in the Large Magellanic Cloud galaxy was the first witnessed supernova event since Johannes Kepler recorded his in 1604. The Cas A (Hubble) expanding gaseous shell plows into the surrounding interstellar medium, and pushes, compresses, and intermingles with it. The material, rich in heavy elements, now seeds the interstellar space surrounding the star, and may trigger the formation of a Veil Nebula (NOAO) new generation of stars. The images of the Veil Nebula and Cas A show supernovae remnants plowing through space, carrying the newly created elements into the interstellar medium. The core collapse of a massive star is a Type II supernova event. The stellar end product left behind depends upon the initial mass of the star, and is either a neutron star, pulsar, magnetar, or black hole. Neutron stars have passed the 1.4 solar mass Chandrasekhar limit, and are not held in equilibrium by electron degeneracy pressure. The repulsive force between electrons is not strong enough to balance gravity in a star that begins with more than ~8 solar masses and has a core remnant between 1.4 and 2.5 solar masses. The collapsing core is so massive that the electrons are forced into the atomic nuclei where they Puppis A Remnant (ROSAT) combine with protons and become neutrons. Neutron stars are held in equilibrium with neutron degeneracy pressure (strong nuclear force) which provides the pressure to stop gravity from contracting the core any further. The Type II supernova remnant Puppis A contains a a neutron star. RXJ 1856.5-3754 is the closest neutron star. 49 RX J1856.5-3754 (ESO) Pulsars are spinning neutron stars that have jets of particles moving almost at the speed of light streaming out from the magnetic poles. These jets produce very powerful beams of high energy particles that emit x-rays. For a similar reason that "true north" and "magnetic north" are different on Earth, the magnetic and rotational axes of a pulsar are also misaligned. Therefore, the beam of particles and x-rays from the jets sweep around as the pulsar rotates, just as the spotlight in a lighthouse does. Like a ship in the ocean that G292.0+1.8 (Chandra) sees only regular flashes of light, we see pulsars turn on and off as the beam sweeps over the Earth. The oxygen-rich supernova G292.0+1.8 contains a pulsar. Neutron stars have very intense magnetic fields, about 1,000,000,000,000 times stronger than Earth's own field. The combination of this strong magnetic field and the rapid rotation of the neutron star produces extremely powerful electric fields, with electric potential in excess of 1,000,000,000,000 volts. Electrons are accelerated to high velocities by these strong electric fields. These high-energy electrons produce radiation in two general ways: as a coherent plasma the electrons work together to produce radio emissions, and individually the electrons interact with photons or the magnetic filed to produce high-energy emission such as optical, X-ray and gamma-ray. The pulses of radiation match the rate of the rotation of the neutron star. Magnetars are neutron stars that have super strong magnetic fields, about 100 trillion times as strong as the Earth's magnetic field. These fields are so intense that the solid neutron star crust buckles and shifts under its influence. The resulting star quakes could repeatedly generate brief flashes of hard X-rays and soft gamma-rays - giving rise to the rare but Magnetar Illustration, Robert Mallozzi mysterious "soft gamma repeaters" - because magnetars seem to be rotating too slowly to produce the observed energy output. The Hubble image of N49, a Type II supernova remnant in the Large Magellanic Cloud, N49 (Hubble) contains a magnetar. One million seconds of x-ray image data were used to construct this view of supernova remnant Cassiopeia A, the expanding debris cloud from a stellar explosion. Cas A's outer green ring, ~10 light-years in diameter, marks the location of the expanding shock from the original supernova explosion. In the upper left portion of the remnant, a structure extends beyond it, evidence that the initial explosion may have also produced energetic jets. Still glowing in x-rays, the tiny Cassiopeia A (Chandra) point source near the center of Cas A is a neutron star, the collapsed remains of the stellar core. In the blue-colored Cas A image specially processed to highlight silicon Cassiopeia A (Chandra) 51 ions, a counter-jet can be seen on the lower right The X-ray spectra show that the jet and counter-jet are rich in silicon atoms and relatively poor in iron atoms. This indicates that the jets formed soon after the initial explosion of the star; otherwise, the jets should have contained large quantities of iron from the star's central regions. The bright blue fingers located near the shock wave on the lower left are composed almost purely of iron gas. This iron was produced in the central, hottest regions of the star and somehow ejected in a direction almost perpendicular to the jets. The bright source at the center of the image is presumed to be a neutron star created during the supernova. Unlike the rapidly rotating neutron stars in other supernova remnants that are surrounded by dynamic magnetized clouds of electrons called pulsar wind nebulas, this neutron star is quiet, faint, and so far shows no evidence for pulsed radiation. One explanation could be that the explosion that created Cas A produced high-speed jets similar to but less energetic than the hypernova jets thought to produce gamma-ray bursts. During the explosion, the neutron star may have developed an extremely strong magnetic field that helped to accelerate the jets. This super-strong magnetic field later stifled any pulsar wind activity, so the neutron star today resembles other strong-field neutron stars in lacking a pulsar wind nebula; Cas A may contain a magnetar. If the core remnant of a collapsed massive star exceeds 3 solar masses, neutron degeneracy pressure cannot stop the complete and total collapse of the star. The neutrons get pushed into each other until the star becomes a region, or boundary, in space around the black hole, called the event horizon, beyond which Black Hole (April Hobart, Chandra) we cannot see. The extreme gravitational field within the event horizon emits no radiation; however, it can be indirectly detected by its effects on the spacetime around it - including accretion Binary System (NASA artist) disks and companion stars. Artist illustrations are usually used to portray these conditions, such as the black hole and binary system shown. Gamma-ray bursts (GRBs) are among the most energetic and most luminous explosions in the Universe. They occur roughly once a day, last from a few thousandths of a second to a few hundred seconds, and come from all different directions of the sky. Their gamma radiation is more energetic than visible light and can be measured by satellites orbiting the Earth in space. The energy set free by the bursts in just one Hypernova in M100 (Hubble) second is comparable to the energy production of the Sun during its whole life. There is evidence that GRBs are produced during catastrophic explosions which end the lives of extremely massive stars. Two possible candidates for this type of massive explosive event have been discovered in the spiral galaxy M100. The gigantic energy which powers the gamma- ray burst is thought to be provided by rapidly spinning black holes which form when the central core of a very massive star becomes unstable 52 GRB 020813 (Chandra) and collapses under its own gravity. The infalling stellar material becomes part of the newly formed black hole, which releases enormous amounts of energy in two jets. The jets expand relativistically, at almost the speed of light, along the rotation axis. Before they break out from the stellar surface, they have to drill their way through thick layers of stellar material, thus getting collimated into very narrow beams with an opening angle of only a few degrees. Recent observations, like GRB 020813, are confirming that the origin of long gamma-ray bursts comes from exploding massive stars. Stellar evolution is a fascinating and fundamental topic. We are just beginning to construct the knowledge necessary to understand the processes of star formation and destruction. Ground-based and orbiting spacecraft are imaging stars in all stages of evolution from radio through gamma rays. Images, like the radio image of the Cygnus region shown here, give us fascinating views of stellar evolution - from protostars just emerging from their stellar cocoons to thermonuclear fusion in massive hot, blue Cygnus Region (CGPS) stars, to supernovae remnants that result from the catastrophic collapses of stellar cores. Somehow, within this maelstrom of turbulence, intense radiation and ferocious stellar winds, stars and planetary systems form. Technological advances are allowing us to explore the universe in unprecedented detail, and with these dramatic improvements in resolution come the prospect of significant advances in understanding a wide range of cosmic phenomena, including the never- ending cycle of stellar formation and destruction. 53 The Chandra X-Ray Observatory Stellar Evolution Activities and Resources The Chandra X-ray Observatory is the most sophisticated X-ray observatory launched by NASA. Chandra is designed to collect X-rays from high-energy objects in the universe, including supernova remnants, colliding galaxies, black holes, neutron stars and X-ray binary stars. The unique sensitivity and precision of the mirror assembly, transmission gratings, high resolution camera and spectrometer have made possible significant advances in Chandra X-Ray Observatory our understanding of stellar processes, high energy matter and anti-matter particles, the formation and evolution of galaxies, black holes, and stellar evolution. The spectacular results from the first nine years of the Chandra observations are having a profound impact on our understanding of such exotic phenomena as super-massive black holes, rivers of gravity that define the cosmic landscape, a swarm of black hole activity at the center of the Milky Way Galaxy, and a supernova event so powerful that it is a completely different type of super-massive stellar explosion. The Chandra Education and Public Outreach Office has developed a set of materials for educators that incorporate technology and authentic data analysis and research in the classroom. All materials are available online; and the image sets and posters are free upon request. STELLAR EVOLUTION An impressive body of evidence suggests that approximately 14 billions years ago the space, time, matter and energy that make up what we call the universe came into existence. During the first 10 billion years, galaxies and stars were formed. Many generations of massive stars underwent catastrophic core collapse and left behind supernova remnants, neutron stars, pulsars and black holes. Before the final collapse, these massive stars fused hydrogen to helium to carbon, Stellar Evolution Poster oxygen, silicon, sulfur and iron. Elements heavier than iron were produced in the outer envelopes of the stars during the supernova explosions and the resulting shock waves from the core collapse. The shockwaves traveled through the remnants, carrying the heavier elements from the interior of the star into the surrounding interstellar medium, enriching the medium with the newly created elements. The interstellar medium - the gas and dust between the stars - provided the raw materials for the formation of a new generation of stars. 54 Stellar formation begins when fragments of giant molecular clouds of gas and dust - each with tens to hundreds of solar masses of material each - start collapsing. Possible trigger mechanisms could be a shock wave from the explosion of a nearby massive star or from the passage of the cloud through regions of more intense gravity as found in the spiral arms of galaxies. These shock waves compress the gas clouds enough for them to gravitationally collapse. Eventually the clumps of gas compress enough to become protostars. As a gas clump collapses it heats up due to friction as the gas particles bump into each other. The gravitational potential energy the gas particles had from falling under the force of gravity gets converted to thermal energy. The gas clump becomes warm enough to produce infrared and microwave radiation. During the initial collapse, the clump is transparent to radiation and the collapse proceeds fairly quickly. As the clump becomes more dense it becomes opaque. Infrared radiation is trapped, and the temperature and pressure in the center begin to increase. After a few million years, thermonuclear fusion begins in its core, and a strong stellar wind is produced which stops the infall of more mass. The protostar is now considered to be a young star. Thermonuclear fusion in stars with masses between 0.8 and 8 solar masses produces the outward pressure to counterbalance gravitational forces for approximately ten billion years. When the core hydrogen has been converted to helium and fusion stops, gravity takes over and the core starts to collapse. The layers outside the core collapse also - the layers closer to the center collapse more quickly than the ones near the stellar surface. As the layers collapse, the gas compresses and heats up. The core temperature becomes high enough for helium to fuse into carbon and oxygen, with hydrogen to helium fusion Cat’s Eye Nebula Continuing in a thin shell surrounding the core. The outer layers expand to an enormous size and the star is now called a red giant. The star brightens by a factor of 1,000 to 10,000, and the surface temperature of the extended envelope drops to about 3,000K - 4,000K, giving the star its reddish appearance. A strong wind begins to blow from the star's surface, carrying away most of the material surrounding the star's central core. The material ejected by the star forms a planetary nebula which expands into the surrounding interstellar medium. The core of the star left in the center of the planetary nebula is called a white dwarf. The white dwarf is extremely dense. It is held in equilibrium with gravity by electron degeneracy pressure - the repulsive forces of the electron clouds of the individual atoms. The mass limit for a white dwarf to remain in equilibrium between gravity and electron degeneracy pressure is 1.4 solar masses - the Chandrasekhar limit. Over hundreds of billions of years the white dwarf will radiate all of its remaining heat away and become a black dwarf. A white dwarf is not the end product in the collapse of a mid-sized star if it is in a binary system. Suppose two stars, one with one solar mass and the other with five solar masses are in a binary system. The five solar mass star runs out of hydrogen faster than its less massive companion, becomes a red giant, shrugs off a planetary nebula, and collapses into a white dwarf. Eventually the companion star runs out of hydrogen and enters the red 55 giant stage. The outer layers of the red giant are loosely held by the star, and the extreme gravitational field of the white dwarf results in mass transfer from the red giant into an accretion disk around the white dwarf. Friction slows the matter's orbital motion, which causes the matter to spiral through the accretion disk down to the surface of the white dwarf. The falling and spiraling of the matter toward the white dwarf releases large amounts of gravitational energy and heats the accretion disk. The white dwarf accretes matter from its companion relatively rapidly and grows in mass. When the accretion has raised the white dwarf's mass to the critical mass of 1.4 solar masses, the density and temperature in the center of the white dwarf become so severe that carbon starts fusing explosively. The white dwarf undergoes a thermonuclear explosion and is completely destroyed; only the remnant remains. All of the core's matter – the products of nuclear fusion (iron, nickel, silicon, magnesium, and other heavy elements) plus unfused carbon and oxygen - are ejected into the interstellar medium. The Tycho Supernova Remnant – Type I thermonuclear explosion of a white dwarf is a Type Ia supernova event. Stars with masses greater than eight solar masses continue nuclear fusion beyond core helium, and after all of the core helium is gone carbon and oxygen begin to fuse. Their fusion yields neon, magnesium, silicon, and sulfur. Eventually, silicon and sulfur fuse in the star's core to form iron, nickel, and other elements of similar atomic weight. The central core now consists of iron, surrounded by a shell in which silicon and sulfur fuse, adding more iron to the core. In additional layers further out, lighter elements fuse - oxygen, carbon, helium, and hydrogen. The iron core is very compact and cannot induce further nuclear fusion. Nuclear fusion is possible only if the reactions release energy. The fusion of iron with other nuclei to make still heavier nuclei is an endothermic nuclear reaction. The energy required to produce elements heavier than iron becomes available only during the imminent catastrophic collapse of the star's core and the violent explosion of the star's outer envelope. The mass of the star's iron core approaches 1.4 solar masses due to the continued silicon and sulfur fusion in the thin shell adjacent to the iron core, and the continued fusion of iron requires more energy than is available. Radiation pressure is no longer able to support the core against gravity and the iron core collapses. In less than a second, the core collapses from a diameter of 8000 kilometers to 19 kilometers - the collapse happens so rapidly that the outer layers have no time to react or collapse along with the core. The energy released during core collapse is unimaginable - more energy than is produced by 100 stars like the Sun during their entire lifetimes of more than 10 billion years. Most of the energy released during collapse is carried off into space by neutrinos; a small fraction of the energy triggers the accompanying supernova explosion. The core collapses so fast that it momentarily goes past its equilibrium point and instantaneously rebounds. The innermost layers of the star are still in-falling and meet the rebounding core, creating a super strong shock wave that runs outward through the layers towards the star’s surface. The shock wave heats the outer layers, inducing explosive nuclear fusions, and ejects the outermost layers. The energy released by the shockwave produces elements heavier than 56 iron. When the shock wave reaches the star's surface, it heats the surface layers and brightens them - within a day or two the exploding star becomes brighter than a billion suns. The expanding gaseous shell, referred to as a supernova remnant, plows into the surrounding interstellar medium, and pushes, compresses, and intermingles with it. This is a Type II supernova event - the core collapse of a massive star. The end product within the remnant depends upon the initial mass of the star; neutron star, pulsar, magnetar, or black hole. Cas A Supernova Remnant – Type II NOTE: A more extensive discussion of Type II and Type Ia supernovas is included in the Investigating Supernova Remnants ds9 activity on pages 164 – 169. ACTIVITIES AND RESOURCES A major focus of the Chandra mission is the study of the structure and evolution of the universe - including understanding when and where elements are created, exploring the cycles of matter and energy in the evolving universe, and examining the ultimate limits of extreme gravity and energy. The following activities and supporting materials are based on Chandra data and have been developed to give educators the content and resources to investigate stellar evolution. These materials support the National Science Standards and Benchmarks. http://chandra.harvard.edu/edu/formal/stellar_ev/cosmic/alignment.html Our Cosmic Connection is a sequencing activity using the set of 24 images provided with this journal. All information and materials necessary for educators to use this activity in the classroom are on the Chandra Education Website. Additional sets of images can also be requested. The Stellar Evolution module is on the Chandra website and consists of the following components: The Story of Stellar Evolution: A complete introduction that describes the stages of stellar evolution of all stars. http://chandra.harvard.edu/edu/formal/stellar_ev/story/ Stellar Evolution: A Journey with Chandra: A poster which displays the cycles of the evolutionary stages of stars of different masses. http://chandra.harvard.edu/edu/prod_descriptions.html Poster Request Form: http://chandra.harvard.edu/edu/request.html The Interactive Guide to Stellar Evolution: An interactive flash version of the Stellar Evolution: A Journey with Chandra poster. http://chandra.harvard.edu/edu/formal/stellar_ev/ Blast from the Past: Historical Supernovas: A poster displaying 9 historical supernova events. A copy of this poster is included with this journal. http://chandra.harvard.edu/edu/prod_descriptions.html Poster Request Form: http://chandra.harvard.edu/edu/request.html 57 Podcasts: Supernovas and Supernova Remnants: A list of podcasts that highlight Chandra observations of supernovas. http://chandra.harvard.edu/resources/podcasts/by_category.html?catid=4 Cassiopeia A (Cas A)—The Death of a Star: A timeline that describes the Cas A supernova event. http://chandra.harvard.edu/edu/formal/casa_timeline/ Our Cosmic Connection Activity: A sequencing activity which uses a set of 24 colored images to assist students in acquiring a basic understanding and appreciation for stellar evolution from formation to destruction - and their connection to planet Earth. http://chandra.harvard.edu/edu/formal/stellar_ev/cosmic/ (HTML, PDF and PowerPoint (PPT) versions) Card Sets Request Form: http://chandra.harvard.edu/edu/request_special.html Cosmic Webquest Activity: An internet version of the Our Cosmic Connection Activity. For each of the 24 images, students are sent to similar objects on the internet to gather information about each of the objects in the image set. (HTML, PDF, PPT and flash versions) http://chandra.harvard.edu/edu/formal/stellar_ev/cosmic/ Stellar Cycles Performance Task: A pre or post assessment activity complete with a scoring rubric to determine student understanding of stellar evolution. The activity is similar to the Our Cosmic Connection activity, but uses a different image set. (HTML, PDF and PowerPoint (PPT) versions) Card Sets Request Form: http://chandra.harvard.edu/edu/request_special.html Teacher Guide: Suggestions for Our Cosmic Connection and Stellar Cycles activities and card sets with descriptions and a web site link for each image, visual answer keys with several possible sequences for the different types of evolution. http://chandra.harvard.edu/edu/formal/stellar_cycle/guide.html#cosmic Investigating Supernova Remnants: An activity that uses Chandra data and ds9 image analysis software to investigate supernova remnants to determine if they are Type II core collapse or Type Ia thermonuclear events. http://chandra.harvard.edu/edu/formal/snr/ Download instructions for ds9: http://chandra-ed.harvard.edu/install.html Tutorial to use ds9 software: http://chandra-ed.harvard.edu/learning_ds9index.html X-Ray Spectroscopy and Supernova Remnants ds9 Version: http://chandra.harvard.edu/edu/formal/snr/ds9.html X-Ray Spectroscopy and Supernova Remnants Pencil and Paper Version: http://chandra.harvard.edu/edu/formal/snr/paper.html Cas A: The Supernova as Cosmic Recycling Center: A set of 6 activities that utilize ds9 and Chandra data to explore the science of Cas A. http://chandra-ed.harvard.edu/casa/index.html 58 How and What to Study for Stellar Evolution: Summary: The following information summarizes the basic content of stellar evolution that is necessary to answer the sample questions on the following page: ●All stars progress through the following stages: stellar nursery, proto-star, T-Tauri star, living stars - thermonuclear fusion of hydrogen to helium taking place in the core. ●The mass of the star determines how long it will take to run out of hydrogen fuel - the more massive the star the faster it fuses hydrogen and the sooner it runs out of fuel: Stellar Classification O ~ 3 million years, Stellar Classification B ~ 80 million years, Stellar Classification A ~ 1.5 billion years, Stellar Classification F ~ 5 billion years, Stellar Classification G ~ 10 billion years, Stellar Classification K ~ 35 billion years, Stellar Classification M ~ 250 billion years ●While a star is fusing hydrogen into helium equilibrium is maintained by radiation pressure from fusion directed outwards from the core and gravity directed inwards. ●When a star runs out of hydrogen there is no longer radiation pressure to counter the force of gravity and the star begins to collapse. The resulting evolutionary stages the star experiences depends upon the initial mass of the star. ●Final evolutionary stages for a mid-sized star (0.8 - 8 solar masses): red giant, planetary nebula, white dwarf ●Final evolutionary stages for a mid-sized star in a binary star system: red giant, planetary nebula, white dwarf, type Ia supernova event, no core remnant ●Final evolutionary stages for a massive star (more than 8 solar masses): red giant, red supergiant, type II supernova event, and either neutron star (including pulsar or magnetar), or black hole ●Differences between Type Ia and Type II supernovae events: Type Ia: Thermonuclear explosion of a white dwarf, no stellar remnant left, only the supernova remnant left behind, brighter in magnitude. Type II: Core collapse of a massive star, leaves a neutron star, pulsar, magnetar, or a black hole stellar remnant - as well as the supernova remnant. ●Processes holding stars and stellar remnants in equilibrium: Living star: Radiation pressure from thermonuclear fusion and gravity White Dwarf (limit 1.4 solar masses): Electron degeneracy pressure and gravity Neutron Star (1.4 - 2.5 solar masses): Neutron degeneracy pressure and gravity Black Hole (more than 2.5 solar masses): No equilibrium, a singularity 59 Practice Questions with Answers: Stellar Cycle Activity 1. Arrange the images with the following numbers in a sequence from birth to final end product for a mid-sized star: 1,2,5,6,8,10,12,16,18 2. Arrange the images with the following numbers in a sequence from birth to final end product(s) for a massive star: 3,4,6,7,8,9,11,17,18 3. Arrange the images with the following numbers in a sequence from birth to final end produce for a mid-sized star in a binary system: 1,2,5,6,8,10,12,13,14,15,16,18 NOTE: Most of these images are from the Cosmic Connections and Stellar Cycles card sets posted on the Chandra X-Ray Observatory educational pages described on preceding pages 55-56. 60 Descriptions for images: 1.Mid-sized star - the Sun - optical image 2. White dwarf - Dana Berry artist illustration 3. Black hole - April Hobart artist illustration 4. Type II supernova - Cas A - Chandra x-ray image 5. Red giant - the Sun - Jeff Bryant artist illustration 6. Stellar nursery - M16, the Eagle Nebula - AAO optical image 7. Massive star(s) - the Pleiades - David Malin astrophotography - AAO 8. Stellar nursery close-up - M16, the Eagle nursery - Hubble optical image 9. Massive star pre-Type II supernova event - Eta Carinae - Hubble optical image 10. Proto-planetary system - Dana Berry - artist illustration 61 11. Pulsar - the Crab Pulsar - Chandra X-ray image 12. Planetary nebula and white dwarf remnant - Dana Berry - artist illustration 13. Binary system with white dwarf and red giant - Dana Berry - artist illustration 14. Type Ia supernova remnant - Tycho's remnant - Chandra X-ray image 15. Supernova explosion event - Dana Berry - artist illustration 16. Planetary nebula - M57, the Ring Nebula - Hubble optical image 17. Type II supernova - SN1987A - David Malin astrophotography - AAO 18. Red giant becoming unstable - V838 Mons - Hubble optical image ANSWER KEY: 1. 6, 8, 10, 1, 5, 18, 16, 12, 2 2. 6, 8, 7, 18, 9, 17, 4, 3 and/or 11 3. 6, 8, 10, 1, 5, 18, 16, 12, 2, 13, 15, 14 Visual Answer Key: 1. 2. 3. 4. Another Example: Both mid-sized and massive star from the same stellar nursery 62 The materials on the CD-ROM include the following: ●Stellar Cycle & Cosmic Connection card sets: These image sets are in a folder on this CD on PowerPoint slides and are also available upon request from the Chandra website. ●Stellar Evolution and the ds9 Image Analysis Software: In the DS9 Image Analysis Software Tutorial section are activities designed to investigate supernova remnants. ●URL Links listed below. Additional internet resources for images and information related to stellar evolution: ● Chandra X-Ray Center: http://chandra.harvard.edu/edu/formal/stellar_ev/ NOTE: A complete list and description of these materials is compiled on pages 55- 56 – including activities, movies, interactive tutorials, podcasts, and resources that are available upon request. ● Georgia State University HyperPhysics Website: http://hyperphysics.phy-astr.gsu.edu/hbase/astro/astcon.html#astcon An interactive site which gives very detailed information about different stages of stellar evolution, as well as other astrophysics concepts. ● Hubble Newsdesk Archive: http://hubblesite.org/newscenter/newsdesk/archive/releases/category/star/ Images and press releases for different types of stars, including different stage of stellar evolution. ●A board game field-tested by NASA scientists about stellar evolution:[ NOTE: this is a commercial product] http://stellarjourney.net/ Linder Winter, Developer NOTE: This site is currently under construction and will be available ~April 2010 ● DS9 stellar evolution investigations in this manual on pages 156 – 192. 63 Variable Stars & Light Curves Stars appear to shine with a constant light; however, thousands of stars vary in brightness. The brightness that a star appears to have (apparent magnitude) from our perspective here on Earth depends upon its distance from Earth and its actual intrinsic brightness (absolute magnitude.) The behavior of stars that vary in magnitude (brightness) - known as variable stars - can be studied by measuring their changes in brightness over time and plotting the changes on a graph called a light curve. Measuring and recording the changes in apparent magnitude and drawing the resulting light curves will allows astronomers to begin to unravel the stories of the often turbulent and always exciting lives of variable stars. Cepheid Variable Stars: Variable stars are stars that vary in brightness, or magnitude. There are many different types of variable stars. One group of variable stars is the pulsating variables. These stars expand and contract in a repeating cycle of size changes. The change in size can be observed as a change in apparent brightness (apparent magnitude.) Cepheid variables are one type of pulsating variable stars. Cepheids have a repeating cycle of change that is periodic - as regular as the beating of a heart. Observations of the changes in apparent magnitude of variable stars - including Cepheids - are plotted as the apparent magnitude versus time, usually in Julian Date (JD). The resulting graph is called a light curve. The light curve for the Cepheid variable star X Cyg (located in the constellation Cygnus) is shown below. Each data point represents one observation. Once many observations have been plotted, important information can be obtained from the resulting pattern of changing magnitudes. The period for X Cyg is the amount of time it takes for the star to go through one complete cycle from maximum magnitude (brightness), through minimum magnitude (dimmest), and back to maximum magnitude (brightness.) Light curve for the Cepheid variable star X Cyg. Analysis of the light curve for X Cyg shows that the magnitude ranges from an average maximum magnitude of 6.0 to an average minimum magnitude of 7.0 with a period of approximately 16 days. X Cyg exhibits periodic behavior - it is a Cepheid variable star with a predictable cycle of changing magnitudes, a stellar heart that beats once every 16 days. Cepheid variable stars have a period of 1-70 days with an amplitude of variation of 0.1 to 2.0 magnitudes. These massive stars (8 solar masses) have a high luminosity and are of F spectral class at maximum, and G to K at minimum. The later the spectral class of a Cepheid, the longer is its period. Cepheids obey a strict period-luminosity relationship – this relationship is discussed in the Cosmological Distances section. 64 Origin of Units of Magnitude and Julian Day used to Graph Light Curves Magnitudes: The magnitude estimates are plotted on the vertical or y-axis. The method we use today to compare the apparent brightness (magnitude) of stars began with Hipparchus, a Greek astronomer who lived in the second century BC. Hipparchus called the brightest star in each constellation "first magnitude." Ptolemy, in 140 A.D., refined Hipparchus' system and used a 1 to 6 scale to compare star brightness, with 1 being the brightest and 6 the faintest. This is similar to the system used in ranking tennis players, etc. First rank is better than second, etc. Unfortunately, Ptolemy did not use the brightest star, Sirius, to set the scale, so it has a negative magnitude. (Imagine being ranked -1.5 in the tennis rankings!) Astronomers in the mid-1800's quantified these numbers and modified the old Greek system. Measurements demonstrated that 1st magnitude stars were 100 times brighter than 6th magnitude stars. It has also been calculated that the human eye perceives a one-magnitude change as being 2 ½ times brighter, so a change in 5 magnitudes would seem to be 2.5 5 (or approximately 100) times brighter. Therefore a difference of 5 magnitudes has been defined as being equal to a factor of exactly 100 in apparent brightness. Magnitudes for Selected Objects 65 Julian Day System: The Julian Day is plotted along the horizontal or x-axis. Astronomers simplify their timekeeping by merely counting the days, and not months and years. Each date has a Julian Day number (JD), beginning at noon, which is the number of elapsed days since January 1st, 4713 B.C. For instance, January 1st, 1993, was JD 2448989; January 2nd, 1993, was JD 2448990; and January 1st, 2000, was JD 2451545. Why the year 4713 B.C.? The Julian Day system of numbering the days is a continuous count of days elapsed since the beginning of the Julian Period. This period was devised during the 16 th century and first used for counting purposes by Joseph Justus Scaliger, a French classical scholar. Scaliger calculated the Julian Period by multiplying three important chronological cycles: the 28-year solar cycle, the 19-year lunar cycle, and the 15-year cycle of tax assessment called the Roman Indiction. To establish a beginning point for his Julian Day system, Scaliger calculated the closest date before 1 B.C. which marked the first day for the beginning of all three cycles. This day is January 1, 4713 B.C., which is Julian Day number 1. RR Lyrae Variable Stars: RR Lyrae variable stars are another class of pulsating variables. These are older, pulsating red giants, with a 0.5 solar mass and a pulsation period of 0.2 to 1.0 day. RR Lyrae stars have an absolute magnitude of 0.75 – only 40 to 50 times our Sun. They are common in globular clusters – dense groups of old stars in the halo of the galaxy – and since they all have the same absolute magnitude they are used to measure distances to other galaxies. This will be discussed in the Cosmological Distances section. The graph shows that if you plot luminosity (absolute visual magnitude) of Cepheids and RR Lyrae variables versus their period, the luminosity of RR Lyrae stars does not change with period, and the Cepheids follow the Period- Luminosity relationship – the longer the period, the brighter the star. Mira Variable Stars: One of the largest groups of pulsating variables is the long-period variables (LPV's). One class of LPV's is the Mira-type variable. The visual light curves of Mira-type variables show well-defined periods ranging from 80 to nearly 1000 days, with amplitudes of 2.5 magnitudes or more. Mira variables are red giant stars, often of enormous size, that have entered the final evolutionary stages of their existence and will eventually become white dwarfs. Many of them are slowly ejecting a steady stream of matter into the surrounding interstellar space; their mass loss can have very dramatic consequences for their future evolution. The light curve shown is Mira (also called omicron Cet) – the prototype of all Mira-type variable stars. Cepheids, RR Lyraes, and Mira variable stars are all pulsating variable stars. A star pulsates because it is not in hydrostatic equilibrium: the force of gravity acting on the outer mass of the star is not quite balanced by the interior radiation pressure pushing outwards. If a star expands as a result of increased gas pressure, the material density and pressure decrease until the point that hydrostatic equilibrium is reached and then overshot, owing to the momentum of the expansion. At this point the star is transparent 66 and photons can escape. Then gravity dominates, and the star begins to contract. The momentum of the infalling material carries the contraction beyond the equilibrium point. At this point the star becomes opaque and photons are trapped and the star is dimmer. The pressure again becomes too high, and the cycle starts over again. They system acts as an oscillator. However, with loose atmospheric layers of gases, the oscillations get out of phase with one another and set the stage for chaotic motions. Energy is dissipated during such pulsations (analogous to losses caused by friction forces), and eventually this loss of energy should result in a damping or lessening of the pulsations. The prevalence and regularity of pulsating stars imply that the dissipated energy is replenished in some way. The dynamics of pulsating variable stars is not well understood. Cataclysmic Variable Stars: There are several different types of cataclysmic, or eruptive, variables. One type occurs in a binary system, with two stars orbiting very close to each other – one of them a normal Sun-like star or giant star, and the other a white dwarf. White dwarfs are very compressed, with a strong gravitational field. Some of the outermost material from the larger star is pulled away by the white dwarf’s gravity, but this material does not fall directly onto the white dwarf. Instead, it builds up in a disk called an accretion disk, which orbits the white dwarf. The combination of normal or giant star, white dwarf, and accretion disk can lead to some very spectacular celestial fireworks. That is why, instead of varying smoothly like most pulsating variables, eruptive variables exhibit outbursts or activity, usually brightening by a large amount. The changes in their light curves are usually very unpredictable, and tend to be sudden and dramatic; that is why these stars are also called cataclysmic variables. Novae explosions (eruptions) occur in close binary systems consisting of a white dwarf orbiting a larger and cooler star. A layer of hydrogen-rich material is slowly accreted from the cooler star onto the compact white dwarf. The accreted material provides the fuel for the nova explosion – a thermonuclear fusion reaction similar to the detonation of a hydrogen bomb. The system increases in brightness by 7 to 16 magnitudes in a matter of one to several hundred days, then the light slowly fades back to its original brightness over several years or decades. Other close binary systems are made up of a Sun-like star, a white dwarf, and an accretion disk surrounding the white dwarf. As matter accumulates in the accretion disk, the disk becomes unstable. Eventually, matter from the unstable disk will fall onto the white dwarf, leading to an outburst. If the material dump onto the surface of the white dwarf is extreme, a thermonuclear explosion occurs which literally destroys the white dwarf – this results in the most spectacular of all variable star activity – the Type Ia supernova event. A Type II supernova is the result of the core collapse of a massive star. The star can brighten by 20 magnitudes or more; a large supernova may briefly outshine the entire rest of the galaxy. The light curve above is SN 1987A, a Type II supernova; the composite light curve shows that the Type Ia thermonuclear explosion releases more energy and produces a higher magnitude event than the Type II core collapse explosion. 67 Eclipsing Binary Stars: Eclipsing binaries are binary star systems whose members eclipse each other, blocking one another’s light, thereby causing the system to look fainter to observers on Earth. The light curve of an eclipsing binary depends on the sizes and brightnesses of the stars, their separation from each other, and the geometry of our view from Earth. When the orbital inclination of the eclipsing binary is edge on to Earth, the stars will seem to pass in front of one another as they orbit, when the light from the brighter star is eclipsed we see a deep decline in the amount of light received from the star – this is called the primary minimum. When the light from the dimmer star is blocked by the brighter star the light received declines again, but not so deep – this is called the secondary minimum. When both stars are side by side we are able to observe the light from both stars. The light curve for Algol (Beta Persei) is shown to the left. This is the prototype of all eclipsing binaries and is located in the constellation of Perseus. The sharp “V’s” in the curve are the primary minima, and the much smaller secondary minima are half-way between the two primary minima. NOTE: The light curve for Algol is plotted as magnitude versus phase instead of magnitude versus Julian Day. This type of variable star plot is called a phase diagram. A phase diagram is a folded light curve, with the cycles superimposed on each other and plotted twice. When the same cycle repeats over and over as regularly as clockwork it is exhibiting periodic behavior. If we want to know what is happening at any moment, it does not matter which cycle we are observing, because every cycle is exactly the same. What does matter is which part of the cycle we are observing. So if a star – or any other phenomena – is perfectly periodic, then its variation depends only on where it is in its cycle, a quantity called the phase. A good example is an accurate clock. If it is a 24-hour clock (with an AM/PM indicator), it repeats exactly the same behavior, over and over, with a period of 1 day. Each day the clock goes through one cycle, and each cycle is just like every other cycle. If we want to know what the clock reads, we do not need to know which day it is (which cycle it is in), we just need to know the time of day (how far we are into the cycle). On the phase diagram of Algol above, 0.0 is the beginning of the cycle, 0.5 is half way through the cycle, and 1.0 is a complete cycle. If only that one cycle is folded over itself, it would be difficult to see the entire behavior of the binary system at secondary minimum. In order to be able to see the entire variation of a star or binary system, the beginning point cannot be either at a minimum or a maximum. For this reason, the cycles are always plotted twice on a phase diagram. The phase diagram above consists of several cycles folded over on themselves into one cycle and then plotted twice (-1.0 to 0 and 0 to +1.0). This is especially beneficial for a variable star or binary system that has so few observations to plot that it is difficult to see the shape of the light curve. Investigation of a Light Curve Versus a Phase Diagram: Study the continuous light curve for V CAS on the opposite page. Make an overhead transparency of the light curve. Cut out the sections and tape them together to see the periodic behavior of V CAS from JD 2440000 to JD 2450000. If you use just two sections, do you still have a representation of the star’s behavior? With just one section? Can you cut the sections in 68 different places and still have the same behavior pattern? Stack several sections over each other. Determine how small a segment is needed to give the same information as all four segments. What if you only had one cycle of the light curve? What is you start your cycle at maximum? Minimum? Describe your results. [The investigation should show that the periodic behavior represented by the light curve for V CAS can be shown in less space and in greater detail if several segments are stacked on top of each other (folded over each other) in a phase diagram, and that a only one cycle would not adequately show the the entire behavior at both minima and maxima so a segment of two cycles folded over on themselves would allow the most detailed analysis of the behavior of the star. 69 How and What to Study: I. Intrinsic Variable Stars: Stars whose variability is intrinsic - due to physical changes within the star or star system. A. Pulsating: Pulsating variables change brightness because they change their size and/or shape; the whole star is actually "vibrating." Most of them simply expand and contract repeatedly, swelling and shrinking in a continuing cycle of size changes. Like most vibrating systems, pulsating variables repeat their changes; they tend to be periodic. Cepheids, RR Lyrae, and LPV's are pulsating variables. Cepheid Variables: Large yellow stars with 8 solar masses and periods of 1-70 days. They range from spectral class G and K at minimum to F spectral class at maximum. The periods of Cepheids follow a strict period-luminosity relationship which will be discussed in the section on Cosmological Distances. Long-Period Variables (LPV's): One class of LPV's are the Mira Variables. Miras are red giant stars with periods ranging from 80-1000 days, and amplitudes of more than 2.5 magnitudes. RR Lyrae: Older red giants with 0.5 solar masses and a pulsation period of 0.2 to 1.0 day, and an absolute magnitude of 0.75. Located in globular clusters. B. Eruptive (Cataclysmic): These variable stars show sudden and dramatic increases in magnitude due to either the core collapse of a massive star (Type II supernovae), or instabilities in mass transfer from the surface of one star to another either directly or via an accretion disk. This can result in either small increases in magnitude (novae), or the destruction of a white dwarf (Type Ia supernovae). II. Extrinsic Variable Stars: Due to circumstances not involving internal properties and processes within the star or star system. Eclipsing Binaries: Due to an eclipse of one star by another star, due to our line of view here on Earth, in a gravitationally bound two-star system. If the two stars are nearby and not too far apart, the eclipse of one star by the other can be seen optically. If the system is far away and/or the stars are lose together, the eclipse can only be determined by analysis of their spectra. III. Graphs: Light Curves: Observations of variable stars are plotted on a graph called a light curve as the apparent brightness (magnitude) versus time, usually in Julian Date/Day (JD). Analysis of the graph gives information about the periodic behavior, the orbital period of eclipsing binaries, and the regularity (or lack) of stellar eruptions. Phase Diagrams: A phase diagram is a light curve that has been folded over and over on itself. Stars that exhibit periodic behavior have light curves that repeat the same cycle over and over - so only one segment of the periodicity (plotted twice) is necessary to study the behavior of the star. It is important to be able to recognize light curves for: eclipsing binaries, supernovae events (Type Ia is brighter than Type II), Cepheids, RR Lyrae, and Mira variables. A set of flash cards, including images of representative objects is available on the CD-ROM. Completing the following activities will assist in learning how to construct a light curve, and determine the period, maximum magnitude and minimum magnitude. NOTE: The following activity is available in PDF on the CD-ROM, and as HTML, PDF and an online Flash version at http://chandra.harvard.edu/edu/formal/variable_stars/ 70 Activity: Stellar Heartbeats Look at the simulated reproduction of a star field on the following three pages. It contains a variable star that is located in the middle of a set of crosshairs, and surrounding the variable star are several comparison stars of known magnitudes. These stars, which do not vary in brightness, are used to compare the changing brightness, or magnitude, of the variable star. Knowing the values of the magnitudes of the comparison stars, you can estimate the magnitude of the variable star as it changes over time. On a star chart, different magnitudes are portrayed as different sizes - the brighter the magnitude the larger the size of the star, and the dimmer the magnitude the smaller the size of the star. Magnitudes have one decimal, such as 6.3 - however in star fields, the decimals are not indicated. A magnitude of 6.3 is written as 63 so that the fields are not as cluttered and the decimal points are not mistaken for stars. When you record your magnitude estimation you need to include the decimal. Print out the table provided below. Estimate the magnitude of the variable star on the first picture of the star field using the magnitudes of the stars around it. Proceed through each of the pictures and place your estimated magnitudes and the corresponding Julian Day (JD) numbers in the table provided below. 71 72 73 74 Recording Stellar Heartbeats To determine if the variable star that you have "observed" has a regular cycle, you will need to plot your observations on a graph and analyze the resulting light curve. A graph of magnitude versus Julian Day (JD) has been provided for you below. Transfer your magnitude estimations from the table onto the graph. 1. What is the period of this variable star? 2. What is the maximum magnitude (maxima)? 3. What is the minimum magnitude (minima)? 4. What type of variable star is it? Answers (will vary): 1. __~300 days__; 2. __~5.7__; 3. __~11.0__; 4. __Mira variable __ This seems to be fairly periodic, has the period range of an LPV, and more than 2.5 magnitude amplitude (~5.3) 75 Activity: Recognizing Periodic Curves A periodic curve is one which repeats identically within a fixed time interval. Study the following curves and determine which ones seem to exhibit periodic behavior. Determine the maxima, the minima, and the periods. From the description of the types of variable stars included within this manual, what type(s) of variable star(s) do you think each of the light curves represent that you have selected as periodic? NOTE: If you are interested in finding out what types of variable stars have produced the non-periodic light curves, access the Types of Variable Stars page at the American Association of Variable Star Observers (AAVSO) at: http://www.aavso.org/vstar/types.shtml - this page gives a brief description and sample light curve for other types of variable stars. This activity is part of the Variable Star Astronomy curriculum on the website. http://www.aavso.org/ 76 77 Answer Key: The answers for all light curves are listed - including maxima, minima, period, and type. The periodic light curves are ( c ), ( d ), and ( j ). This activity includes other types of variables as they may be on future national and state events. NOTE: slightly different answers are acceptable. Periodic light curves are in bold type. (a) R CrB (f) Z Uma Maximum magnitude: 6.0 Maximum magnitude: 6.8 Minimum magnitude: 13.8 Minimum magnitude: 8.7 Period: No specific period Period: Star has more than one period Type: R Coronae Borealis (RCB) Type: Semiregular (SR) (b) RS Oph (g) Z Cam Maximum magnitude: 5.3 Maximum magnitude: 10.5 Minimum magnitude: 12.3 Minimum magnitude: 13.2 Period: No specific period Period: 22 days Type: Recurrent Nova (NR) Type: U Geminorum (UG) (c) Chi Cyg (h) SS Cyg Maximum magnitude: 5.2 Maximum magnitude: 8.2 Minimum magnitude: 13.8 Minimum magnitude: 12.2 Period: 408 days Period: 49.5 days Type: Mira (M) Type: U Geminorum (UG) (d) S UMa (i) CH Cyg Maximum magnitude: 7.8 Maximum magnitude: 5.8 Minimum magnitude: 11.7 Minimum magnitude: 9.2 Period: 225.9 days Period: Star has more than one period Type: Mira (M) Type: Z Andromedae (Z And) (e) W Cyg (j) X Cyg maximum magnitude: 5.6 Maximum magnitude: 6.0 Minimum magnitude: 6.8 Minimum magnitude: 7.0 Period: Star has more than one period Period: 16.4 days Type: Semiregular (SR) Type: Cepheid (C) The http://chandra.harvard.edu/edu/formal/variable_stars/ URL provides a second activity on estimating the magnitudes of a variable star - titled A Variable Star in Cygnus. This activity is also in HTML, PDF, and an online Flash version. The activity is also on the http://www.aavso.org/ website – it is part of the Variable Star Astronomy curriculum. This variable star activity uses a series of 7 slides taken of the variable star W Cyg over a period of approximately 150 days. The set covers nearly the entire range from maximum magnitude (brightest) to minimum magnitude (dimmest.) You will note as you move through the slides that W Cyg does not appear in exactly the same spot in each of the slides. This is because it is difficult for a photographer to set up in the exact same spot when photographing the sky several days apart. The slides also appear in different hues and sometimes with fewer stars in the field. This is the result of different atmospheric conditions on the dates that Cygnus and W Cyg were photographed. This activity is more difficult as it uses a real variable star. A set of the images is included on the CD-ROM in a PowerPoint format; however, requires a good quality printer. The best way to do this activity is on the website. 78 Activity: Who's Light Curve is that Anyway? Study the images and light curves below, and answer the questions. NOTE: The images are easier to identiy in color - this activity is on the CD-ROM in color. Most of the images have all been used in the explanations in this section and in the Stellar Evolution section, so they should be fairly easy to recognize. 1 2 3 4 5 6 7 8 9 10 11 12 1. Look at the series of six images of a star (in the center of each image) in image 9. Which of the light curves represents the behavior of this star? __(1)__ 2. What type of star is shown in image 9? __(2)__ 3. Which image(s) have the potential to produce the light curve shown in image 5? __(3)__ 4. What type of light curve is shown in image 5? __(4)__ 5. Image 12 contains a star that will produce what type of light curve during one of the future stages of its evolution? __(5)__ 6. Which two images show the next two stages in the evolution of image 12?__(6)__ 7. Which of the image(s) above is/are a precursor to a Type Ia supernova event? __(7)__ 8. Image 7 represents what type of event? __(8)__ 9. What image(s) show the event represented in image 7? __(9)__ 10. Which light curve represents a late stage of stellar evolution? __(10)__ ANSWERS: 1. __image 11; 2. __Cepheid variable; 3. __8,10; 4. __Eclipsing Binary; 5. __4; 6. __2,6; 7. __8; 8. __Type II Supernova; 9. __1,3; 10. __4 79 The materials on the CD-ROM include the following: . ● Light Curves: A folder of light curves that can be used to make flash cards for additional practice. Additional internet resources for images and information related to variable stars: ● Chandra X-Ray Center: http://chandra.harvard.edu/edu/formal/variable_stars/ This URL has both the Stellar Heartbeat Activity presented in this section, and a second activity – A Variable Star in Cygnus. Both activities are in HTML, PDF, and Flash versions ● AAVSO: http://www.aavso.org/education/vsa/Chapter6.pdf This is a good introductory activity for learning how to estimate the magnitudes of stars. (same as two activities above on Chandra website with background information) ● AAVSO: http://www.aavso.org/data/software/hoafun.shtml An interactive and easy-to-use tutorial for making variable star estimates and understanding the light curves of different types of variable stars. It contains a game to estimate the magnitudes of a variable star as you build your own light curve as well as several tutorials that illustrate the different light curves of popular variable stars. ● Julian Day Calendar: http://aa.usno.navy.mil/data/docs/JulianDate.php This site has a program will convert the dates and times of any calendar day into the Julian Date, and the Julian Date to the corresponding calendar date. ● SEDS website: http://www.seds.org/~spider/spider/Vars/vars.html History of variable stars and their discoverers. ● Cepheid in M100: http://www.seds.org/messier/more/m100_hst2.html Information about the Hubble image of the Cepheid variable in M100 ● Variable Star Astronomy [NOTE] Variable Star Astronomy is the web version of the Hands-On-Astrophysics (HOA) curriculum. All materials which were included in the HOA curriculum are still available on the aavso.org website at http://www.aavso.org/education/vsa/ including the student and teacher chapters, star charts and slide sets. The VSTAR software – originally written in DOS, has now been converted and is also available on the AAVSO website at http://www.aavso.org/content/vstar ● DS9 variable star activity in this manual on pages 193 – 204. The Variable Star Astronomy curriculum is a complete introduction to understanding, observing and analyzing variable stars. It contains the following units and chapters: Using the Manual, teacher.pdf Introduction and Table of Contents, .pdf UNIT 1: Planets and Stars Chapter 1: The Solar System and Beyond, .pdf | teacher.pdf Chapter 2: The Nature of Stars, .pdf | teacher.pdf 80 Go to http://www.aavso.org/ education/vsa to access the Variable Star Astronomy Curriculum UNIT 2: Introducing the Sky Chapter 3: Familiarizing Yourself With the Night sky, .pdf | teacher.pdf Chapter 4: Our Bearings in the Sky, .pdf | teacher.pdf UNIT 3: Observing Variable Stars Chapter 5: Introducing the Hands-On Astrophysics Constellations, .pdf | teacher.pdf Chapter 6: Measuring Variable Stars Visually, .pdf | teacher.pdf Chapter 7: Observing Variable Stars in the Real Sky, .pdf | teacher.pdf UNIT 4: The Message of Light Chapter 8: The Nature of Light, .pdf | teacher.pdf Chapter 9: The Life of a Star, .pdf | teacher.pdf UNIT 5: Analysis of Variable Stars Chapter 10: Statistical Concepts, .pdf | teacher.pdf Chapter 11: Variable Stars, Light Curves, and Variability, .pdf | teacher.pdf Chapter 12: Variable Stars and Phase Diagrams, .pdf | teacher.pdf Chapter 13: Variable Stars and O-C Diagrams, .pdf | teacher.pdf GLOSSARY, .pdf [NOTE] The URL for Chapter 1 is http://www.aavso.org/education/vsa/Chapter1.pdf Each chapter uses the same URL - just exchange the 1 for other chapter numbers. 81 The AAVSO Citizen Sky Project Citizen Sky is citizen science project providing a chance for involvement with real and ongoing scientific research. Professional and amateur scientists are trying to understand a star that has been a mystery for many years. This star is epsilon Aurigae (eps Aur), a very interesting and very bright star located in the constellation Auriga, Orion’s charioteer. The star is bright enough to be seen with the unaided eye even in the most light-polluted cotoes. And it is visible for three seasons – autumn, winter, and spring. Epsilon Aurigae is a variable star—this means it changes in brightness over time. Collecting data on these changes can help understand the star. There are many types of variables - epsilon Aurigae is an eclipsing variable. The AAVSO – an organization, which maintains the largest variable star data base in the world, has an extensive description of eps Aur at http://www.aavso.org/vstar/vsots/eps_aur.shtml. The change in brightness that this star undergoes is called an eclipse (a process of fading and coming back to its usual brightness.) This process takes over 600 days. One of the things that makes epsilon Aurigae so interesting is that it only has an eclipse once every 27.1 years.Eps Aur will not come out of eclipse until 2011. Some things about the way that this star fades and then regains it brightness are still not fully understood by astronomers after over 175 years of study. The current eclipse of eps Aur began in August 2009. The AAVSO is asking anyone interested to help collect data to help acquire a better understand this mysterious star. Because the star is very bright, it can be observed by anyone regardless of background, training, or equipment: with just good pair of eyes and a finder chart, which AAVSO will provide, you can monitor this eclipse. Information about the AAVSO organization can be at: http://www.aavso.org/ The Citizen Sky Project welcomes everyone to be a citizen scientist. AAVSO will provide guidance through the process of how to observe epsilon Aurigae, how to send your observations, and how to access your results, analyze them, and even publish them in a scientific journal. No previous experience is required. The AAVSO hopes that this project will involve thousands of people all over the world in real, active scientific research. The http://www.citizensky.org/ site serves as “home base” for participants. The website launched in June, 2009, and includes blogs, discussion forums, training materials, and submission and analysis of observational data. Workshops: A 3-day workshop, focused on observing and education/public outreach was held at the Adler Planetarium in Chicago on August 4-7, 2009. There will be a second workshop focusing on data analysis and scientific paper writing at the California Academy of Sciences in San Francisco September 3-5, 2010. Prior to the San Francisco workshop an application form will be posted in the Workshops section of the citizen Sky website. Videos all of the workshop presentations will be posted on the site as well, so even if you can’t attend you can benefit from these talks. 82 Observation and Analysis: Epsilon Aurigae is an ideal target for those interested in learning how to observe variable stars. By following the Ten Star Tutorial available on the AAVSO website, you can learn how to make and report an observation using visual observations. Information on making the observations of epsilon Aurigae with a digital camera will is available also. The AAVSO has developed data analysis software, which will come with tutorials, to help train participants in how to analyze data in astronomy. The software, referred to as VSTAR, was originally developed to support analysis activities in the Hands-On Astrophysics curriculum package. That curriculum has been converted to a web-based package and is now called Variable Star Astronomy. Further information about Variable Star Astronomy is listed with the resources at the end of this section. A special edition of the peer-reviewed Journal of the AAVSO will be dedicated to papers written by Citizen Sky project participants. This project will last beyond the end of the eclipse in 2011 as participants continue to analyze their observational results and publish them in the AAVSO Journal. The fact that epsilon Aurigae can be seen even from large cities provides a rare opportunity to engage the general public in citizen science. Participants are needed to help write newsletter and newspaper articles, prepare talks and slide shows, develop artwork, give talks, and participate in other forms of community outreach. Teams of interested participants with complementary skill sets are being assembled right now, and will continue to be assembled throughout the project. Epsilon Aurigae: The “Star” Of the Citizen Sky Project is epsilon Aurigae, a mysterious, bright, eclipsing binary variable star. The name of the star is pronounced as follows: ep’ si lon Au ry’ gee. Epsilon Aurigae (eps Aur) is a bright star located in the constellation Auriga, the charioteer. It is an eclipsing binary variable star. Variable stars change in brightness over time. Collecting data on these changes assists in understanding the physical processes that are causing the epsilon Aurigae to vary in brightness. Eclipsing binary variable stars are systems consisting of two stars orbiting around their common center of mass in a plane along our line of sight. So imagine 2 stars circling around each other on an invisible Frisbee. Now imagine holding the invisible Frisbee up and looking at the 2 stars on it from the edge of the Frisbee. From time to time one star will get in the way and block your view of the other star – this is an eclipse. When one star eclipses the other it blocks the light shining from that eclipsed star, so the total light shining from the two stars is less during the 83 eclipse. Now imagine that the invisible Frisbee is all the way across the park, still side- on. You may not be able to tell that there are 2 separate stars circling around on it, but you can still see that during the eclipse the overall brightness, or magnitude fades. A light curve is a graph of brightness versus time for a variable star. So as time moves along the graph from left to right the data points will move up and down based on whether the star is getting brighter or fainter. The shape of the light curve for an eclipsing binary star system depends on a few things: 1) the difference in brightness between the two circling stars, 2) the difference in size between the two stars, and 3) their orbital inclination as seen from Earth. (This last one is basically a measurement of how tipped the imaginary Frisbee is. Is it exactly edge on or is it angled a little?) The light curve above shows how epsilon Aurigae faded and changed in magnitude during its last eclipse. The analysis of light curves provides the following information: • p = Period (How long it takes for the two stars to make one full orbit.) • i = Orbital Inclination (How tipped the imaginary Frisbee is - see question above.) • M1, M2 = Masses of the Stars (How much matter makes up each of the 2 stars.) • L1, L2 = Luminosities of the Stars (How bright each of the 2 stars is.) • R1, R2 = Radii of the Stars (The distance from the center of the star to the edge - a measure of the size of each star.) The period of epsilon Aurigae is 27.1 years and the eclipse lasts from 640 to 730 days. Johann Fritsch was the first to note the variability of epsilon Aurigae in early 1821, when the star was likely in the midst of a deep eclipse. The German astronomers Argelander and Heis both began “regular” observing once every few years around 1842 – 1843, and the data from both men showed that the star became significantly fainter around 1847. Observers later in the 19 th Century recorded another dimming event in 1874 – 1875, and another from 1901 – 1902. The Mystery of Epsilon Aur: Although they did not know it at the time, what these 19th century astronomers had observed was an extremely long-period eclipsing binary, and one that was interacting as well. In 1928, Harlow Shapley correctly concluded that the two stars were about equal in mass. Based on this information they should be about equal in brightness as well. But the spectrum of the system showed no light from the companion at all. The visibly bright first star Epsilon Aurigae, (the primary) was being eclipsed by a massive, invisible second star (the secondary.) What could the mysterious invisible secondary be? A 1937 paper by three of the greats of observational astronomy, Gerard Kuiper, Otto Struve, and Bengt Strömgren, suggested the system was an eclipsing binary composed of an F2 star and an extremely cool and tenuous star that they described as "semitransparent". 84 According to this model, the F star was being eclipsed by this ‘transparent shell star’, and its light was scattered by the extremely thin atmosphere of the eclipsing star. A 1965 paper by Su-Shu Huang introduced the suggestion of an edge-on thick disk as the eclipsing body. In 1971, Robert Wilson introduced a tilted, thin disk with a central opening, suggesting that this model could most easily describe all of the observed effects of the eclipses, particularly the mid-eclipse re-brightening. There is a slight brightening during mid-eclipse, suggesting the disk has a hole in it which the F star shines through. The central brightening was stronger in 1954-56 than in earlier eclipses. It is possible that the hole is growing. The time of minimum light lengthened by about 64 days while the overall duration of the eclipse had decreased by 44 days! During the 1982-84 eclipse the central brightening was the brightest ever. The duration of minimum was the longest, and the fading and brightening happened fastest. The F star’s companion is changing on timescales of decades. From 1901 to 1983 the time of minimum has increased from 313 to 445 days. The overall eclipse duration has declined from 727 to 640 days. Precise measurements out of eclipse revealed a quasi-periodic low amplitude variation of 96 days from 1984-87. During the 2003-2004 observing season this variation had sped up to 71 days. In 2007-2008 the period became 65 days. What is the nature of the object or objects at the center of the disk? It could be two B type stars in a tight orbit. This would account for the mass with less luminosity than one larger star. A pair of stars would act as a gravitational eggbeater, keeping the center of the disk clear. One or more proto-hot Jupiters would affect the distribution of matter in the disk. A hot Jupiter spiraling inward to meet its destruction might account for the low amplitude variations and their decreasing periodicity. The primary is 300 times the diameter of the Sun! The secondary orbits almost at the distance of Neptune from the Sun. Both components are 14-15 solar masses. This is indeed a very strange eclipsing binary system; with 27.1 years between eclipses, scientists are hoping that enough observations will be contributed to the AAVSO data base for Epsilon Aurigae will enable them to greatly increase their understanding of this exotic system. The Citizen Sky Project was developed to enable citizens, students, and amateur observers to contribute to the scientific understanding of the Epsilon Aurigae eclipsing binary system. All information necessary to observe, contribute observational data, and analyze the results for this mysterious star are at the Citizen Sky website http://www.citizensky.org/. 85 The materials on the CD-ROM include the following: Internet resources for the AAVSO Citizen Sky Project: ● The American Association of Variable Star Observers (AAVSO) website: http://www.aavso.org/ ● The AAVSO Citizen Sky Project website: http://www.citizensky.org/ ●: An overview of Citizen Sky Project was presented in an episode of the 365 Days of Astronomy Daily Podcast of the International Year of Astronomy.. ● AAVSO Variable Star Astronomy A complete curriculum package that explains how to observe variable stars, collect data, construct light curves and phase diagram, and analyze the results to study the behavior of variable stars. A complete Table of Contents is listed at the end of the preceding section on pages 78-79. The curriculum is posted at: http://www.aavso.org/education/vsa/. 86 Introduction to the H-R Diagram NOTE: The introduction to the H-R diagram is a repetition from the Stellar Evolution section, then goes into great detail. Everyone is familiar with the periodic table of the elements. The periodic table is an arrangement of all the known elements in order of increasing atomic number. The reason why the elements are arranged as they are in the periodic table is to fit them all, with their widely diverse physical and chemical properties, into a logical pattern. The vertical lines of elements, called groups, and the horizontal lines of elements, called periods, are chemically similar, and share a common set of characteristics. The elements are also arranged into blocks that share commonalities. The arrangement of the elements in the periodic table also shows the periodicity and trends of some properties, such as electron configuration, metalicity, atomic radii, and melting points. By looking at the location of any individual element in the table, you automatically know several characteristics and properties of that element, as well as what types of chemical bonds it forms, and the chemical reactions it will undergo. The Hertzsprung-Russell diagram, or H-R diagram, is the periodic table of the stars. It was discovered that when the luminosity (absolute magnitude) of stars is plotted against their temperature (stellar classification) the stars are not randomly distributed on the graph but are mostly restricted to a few well-defined regions. The stars within the same regions share a common set of characteristics, just like the groups, periods, and blocks of elements in the periodic table. As the physical characteristics of a star changes over its lifetime, it’s position on the H-R diagram changes also – so the H-R diagram can also be thought of as a visual plot of stellar evolution. It is a graphical tool that astronomers use to classify stars. From the location of a star on the graph, the luminosity, spectral type, color, temperature, mass, chemical composition, age, and evolutionary history is known. The Main Sequence: ~90% of all stars occupy the diagonal band running from the upper left corner (hot, luminous stars) to the lower right corner (cool, dim stars) of the H-R diagram. Stars become main sequence stars when the process of thermonuclear fusion - hydrogen to helium - stabilizes. These stars are in hydrostatic equilibrium - the outward radiation pressure from the fusion process is balanced by the inward gravitational force. When the transition from T-Tauri star to main sequence star occurs, the stars are called Zero Age Main Sequence stars (ZAMS). The determining factor of where a star is located on the main sequence is mass. The Sun is a G spectral class star with an effective surface temperature of ~5800K. Since the luminosity and mass of all other stars are measured relative to the Sun, it has one solar luminosity and one solar mass. The O and B stars are the hottest and most massive, and the K and M stars are the coolest and least massive stars. The O and B stars are sometimes referred to as early sequence stars, and 87 the K and M stars as late sequence stars. These terms refer to stars more massive (early sequence) than the Sun or less massive (late sequence) than the Sun. All one solar mass stars, for instance, occupy the same position on the main sequence as the Sun, and they stay in that location, with that specific relationship of temperature and absolute magnitude, until the star runs out of hydrogen and the fusion of hydrogen to helium stops. The mass-luminosity relationship for main sequence stars is defined as: L/L(Sun) ~ [M/M(Sun)] 4 . All main sequence stars with a mass less than ~8 solar masses are sometimes referred to as dwarf stars, with the coolest, least massive stars in the lower right corner called red dwarfs. The more massive the star, the faster the rate of fusion, and the less time is remains on the main sequence. The amount of time that a star spends on the main sequence is also a function of its mass and luminosity and is defined as: T(years) = 10 10 M/L. The Giant Branch: Red giants are luminous, cool giant stars in spectral classes F, G, K, and M located in the upper right-hand corner of the H-R diagram. As the central core of a main sequence star with a mass from ~0.8 to 8 solar masses runs out of hydrogen, radiation pressure no longer balances gravity and the star begins to collapse. There is still hydrogen in the outer layers surrounding the helium core of the star; however the temperature is not high enough for this hydrogen to fuse. As the star begins to contract, the core gets hot enough to start a thin shell of hydrogen fusion around the helium core. The increase in radiation pressure causes the star's outer atmospheric layers to expand. As the surface of the star increases, so does its apparent brightness. As the surface (photosphere) increases, it becomes cooler, and the color of the star becomes redder. Eventually the hydrogen in the shell becomes depleted and the star begins to contract once again, and this time the temperature becomes hot enough to start helium fusion. The outer layers expand even further, becoming cooler and redder. Giant stars fuse elements up to carbon. Most of these stars go through a Mira variable instability strip with a periodic light curve of ~80 - 1000 days. Stars that have evolved to the giant branch are commonly referred to as red giants. Eventually these red giants will shrug off a planetary nebula and leave a white dwarf core remnant. There is no relationship among mass and luminosity on the giant branch. The Supergiant Branch: Stars greater than ~8 solar masses evolve onto the supergiant branch, located in the extreme upper right corner of the H-R diagram. These red supergiants are extremely luminous and cool, due to their expanded size. Their spectral types range from B - the massive stars just leaving the main sequence - through M, as they finish their transition to the supergiant branch. NOTE: The O and B stars on the main sequence are sometimes referred to as blue supergiants, not to be confused with the highly evolved and aging red supergiants located on the supergiant branch. Because of the mass of these stars, the fusion of heavier and heavier elements continues through neon, magnesium, silicon, sulfur, iron and nickel. Each time a new element is created the star becomes larger and redder. (Some stars with a mass of ~8 solar masses move through the Cepheid variable instability strip and become pulsating Cepheids with a period of 1 - 70 days). Eventually most of these stars reach the supergiant branch and undergo a Type II supernovae explosion and core collapse, leaving behind a pulsar, neutron star, magnetar or black hole. Some hyper-massive stars collapse into back holes without a 88 supernova event, and some of the less massive giant stars manage to avoid a supernova event and become white dwarfs. [NOTE: there are exceptions to some of these evolutionary sequences, and the associated masses are "ballpark" numbers only - there is much to learn about the evolutionary history of stars.] The White Dwarf Branch: The white dwarf branch is located in the lower left corner of the H-R diagram. This branch consists of the end products of stellar evolution for mid- sized stars with an initial mass of ~0.8 to 8 solar masses. All white dwarfs are extremely hot; however they have a very low absolute magnitude because they are very small. They have a size that does not exceed 1.4 solar masses - the Chandrashekar limit. Spectral types for white dwarfs range from O to G. Stellar Evolution on the H-R Diagram: This image shows the evolution of a massive star from birth to supernova explosion on the left, and a mid-sized star from birth to planetary nebula and white dwarf on the right. This is an artistic rendition of stellar evolution; however, in order to begin to understand the processes of how stars evolve it is necessary to see how the physical properties of stars change. Plotting stellar evolution on an H-R diagram shows how temperature, luminosity, mass, and spectral type change. The image below shows the future evolution of a mid-sized star - the Sun. On the H-R diagram the Sun is halfway through its lifetime of 9 billion years on the main sequence. It is a spectral type G star, has an effective surface temperature of ~5800K, and one solar luminosity. When the Sun runs out of hydrogen fuel in its core and fusion stops, it will begin its journey to the red giant branch. The Sun will contract, heat up until a shell of hydrogen is fusing around the helium core, and become cooler, ~3000K, reddish in color, and more luminous – in excess of 500 solar luminosities. After ~one billion years, the hydrogen shell fusion stops and the Sun contracts again, becoming less luminous, hotter, and less red in color. During this phase it is sometimes referred to as a yellow giant. The contraction will cause the core to heat up until helium fusion begins in the core. The fusion of helium to carbon causes the Sun to expand again, becoming more luminous. The core will contract again when it runs out of helium and fusion stops again; this time there is not enough mass for the shrinking core to achieve the temperature necessary for the fusion of carbon to begin. The Sun throws off the outer atmospheric layers into a planetary nebula and the remaining carbon core – called a white dwarf – now resides on the white dwarf branch of the H-R diagram. The white dwarf is very dim and very hot – with a temperature of ~20,000K. The white dwarf will radiate away its heat over the next ~12 billion years and become a burnt out carbon cinder called a black dwarf. 89 The H-R diagram on the left shows the evolution of the Sun prior to the main sequence. During the T-Tauri stage, hydrogen fusion has begun; however it has not stabilized. T-Tauri stars have an enormous amount of surface flares and eruptions, and greatly vary in brightness. This stage is highly luminous - as much as 10,000 solar luminosities - with effective surface temperatures of ~3000 to 5000K. When the fusion process stabilizes the Sun drops onto the main sequence and becomes a zero age main sequence star. There is sometimes a little movement along the main sequence as the fusion process settles down to a steady rate of fusion. Once the fusion process stabilizes, the star remains at that location until all the hydrogen fuel is depleted and the transition to the giant branch begins, as described in the previous paragraph. The H-R diagram to the right shows the location of some familiar stars. Aldebaran, the orangish star in the constellation of Taurus the bull, has evolved to the red giant stage. Betelgeuse in Orion and Arcturus in Bootes are red supergiant stars, nearing the end of their stellar lives, and will eventually go through a type II supernova event - leaving behind a neutron star or pulsar. They do not have enough mass to become a black hole. Rigil in Betelgeuse and Deneb in Cygnus are both massive B stars that have started running out of hydrogen fuel. They have recently (astronomically speaking!) left the main sequence and started evolving towards the supergiant branch. Sirius A and Sirius B, in Canis Major, occupy different locations on the H-R diagram, even though they are orbiting each other in a binary system. Sirius A is a main sequence star of ~2 solar masses, and Sirius B is a white dwarf - the remnant of a mid-sized star that began its life on the main sequence. There are many types of H-R diagrams; however, they all plot temperature and/or spectral type (classification) and luminosity and/or absolute visual magnitude. They all show the relationship between temperature and luminosity, and the stars on the main sequence have specific relationships between mass, luminosity, and the amount of time spent on the main sequence. Planetary nebula and supernovae remnants can also be plotted on an H-R diagram. The diagram to the right shows the relationship of temperature and luminosity for stars before they shrug off their planetary nebulae and drop into the white dwarf region. Objects such as pulsars, neutron stars and black holes are too extreme to be located within the graph. Although the general evolutionary stages for different mass stars is supported by both theory and observations, there remains much to be discovered about the processes of stellar evolution. 90 This H-R diagram shows the areas, referred to as instability strips, where the Cepheid and RR Lyrae variable stars are located. These are the periodic variable stars that were discussed in the Variable Stars & Light Curves section, and are also included in the Cosmological Distances section. The T-Tauri stars are also classified as variable stars, though their variability is due to the eratic nature of the thermonuclear fusion process before it becomes stable. NOTE: Always look at the axes of an H-R diagram, as the range of values is not always consistent from graph to graph. The H-R diagram below is a more visual representation, combining the coordinate grid with images of actual objects in different stages of stellar evolution. Below is a brief description of the objects located on the H-R diagram: 1. On the upper left of the main sequence is the Pleiades, an open cluster of hot, luminous spectral class B stars. 2. In the middle of the main sequence is the Sun, a spectral type G star. 3. Just below the main sequence in the lower right corner is Gliese 229, a brown dwarf or failed star. It does not have enough mass for fusion to occur. 4. Just above the Sun on the main sequence is a T-Tauri star. When thermonuclear fusion becomes stable, it will drop onto the main sequence as a stable star. 5. On the giant branch is an artist illustration of a red giant. 6. On the supergiant branch is Betelgeuse, a massive red supergiant nearing the end of its lifetime. 7. To the right of and slightly below the Pleiades is a Cepheid variable star from the M100 galaxy. 8. On the white dwarf branch is Sirius B, the end product of a mid-sized star that is in a binary system with a main sequence spectral type A star. 9. Above Sirius B is the Cat's Eye - a planetary nebula shrugged off by a mid-sized star as it drops onto the white dwarf branch of the H-R diagram. 91 Spectra and the H-R Diagram: The H- R diagram is a plot of temperature, or spectral classification (O,B,A,F,G,K,M, etc.). Each spectral class has a signature spectrum as the classification system is determined by temperature, so representative images of spectra can be plotted on the H-R diagram. Study the spectra on the diagram. In the section on Spectroscopy & Spectra the absorption lines of the different spectral types were discussed; the hotter the star the fewer lines, and the cooler the star the more absorption lines.The absorption lines for compounds, such as titanium oxide, can only exist in the coolest stars. Each spectra, from the upper left corner to the lower right corner of the main sequence belongs to each of the spectral types from O through M. Though difficult to see in this image, the spectrum shown on the supergiant branch has an iron/nickel peak. Since iron is the last element manufactured in massive stars that are undergoing catastrophic core collapse, any spectra that contains a strong iron/nickel absorption line or peak and no heavier elements has to be associated with a Type II supernova event. Type II events can not be plotted on the H- R diagram. NOTE: Some variable stars also occupy specific regions on the H-R diagram - such as the Cepheids, RR Lyraes, and Miras. These regions are called instability strips. Mira variables are periodic pulsating red giants with a period of ~80 to 1000 days. It is a stage that many mid-sized main sequence stars go through as they evolve to the red giant branch. The diagram on the left with the strip labeled long period variables is where the Miras are located. On the diagram below is the H-R diagram with images representing actual stages of evolution. Below the image of the red giant is the corresponding light curve for a Mira variable star. The only position on the diagram that these long period periodic light curves can exist is on the giant branch. The same is true for the Type II supernova light curve at the top of the diagram on the right. A Type Ia light curve (no actual light curve has been recorded for a Type Ia event) can only happen on the white dwarf branch as this type of event is the nuclear destruction of a white dwarf core in orbit around a red giant companion. Cepheid variable stars are ~8 solar mass stars evolving to the giant or supergiant branch and only occur within the Cepheid instability strip to the right of the main sequence. Note that the instability strip for Miras and Cepheids are elongated. This is because they expand and brighten, then contract and dim. Cepheids can change in temperature by two spectral classes during one cycle from maximum to minimum. RR Lyrae variables occupy a small horizontal strip. These older red giants located in globular clusters do not change in luminosity as they pulsate. 92 Globular Clusters and the H-R Diagram: Globular clusters are systems of between ~0.1-1 million stars, gravitationally-bound into a single structure about 100 light-years across. The picture on the left is 47 Tucanae (47 Tuc) , the second brightest globular cluster in the Milky Way Galaxy. Globular clusters are a stable gravitationally- bound system with a typical separation of stars around 1 light year. Globular clusters are distributed in a spherical halo around the galactic center, mostly above and below the plane of the Galaxy. This is because these clusters of stars formed early on in the history of the Galaxy, before the majority of the proto- galactic material had settled into a disk. The apparent absence of globular clusters in the plane of the disk of our Galaxy arises from a combination of two effects. First, the huge amount of dust within the disk of the galaxy makes globular clusters hard to find in directions close to the disk. Secondly, any globular clusters on orbits close to the plane of the disk may be destroyed through interactions with the disk of the Galaxy. Approximately 160 globular clusters have been discovered in our Galaxy, and large numbers are seen around nearby galaxies. Globular clusters are important for three reasons: ● The homogeneity of the stars in these clusters indicates that they have similar chemical compositions and ages. This makes them the simplest systems to use to test theoretical models of star formation and evolution. ● Globular clusters are some of the oldest stellar systems known and estimates of their ages can be used to determine the age of the universe as a whole. ● The distribution of their ages, and the correlations between cluster ages and metal abundance makes these systems an invaluable probe into the formation of galaxies. Since the stars of any one globular cluster share a common history (age, chemical abundance, etc), differ one from the other only in their original mass, and are basically the same distance from Earth, they are ideal candidates for the study of stellar evolution. The fact that all the stars in the cluster are at the same distance is convenient. If two stars in a cluster have different apparent magnitudes, it must be because they have different absolute magnitudes. It is not necessary to determine the individual distance to each of the many stars within the same globular cluster. The H-R diagram shown here is a plot of the stars in 47 Tuc. All of the massive stars (shortest lifetimes on the main sequence) have evolved to into red giants. The point at which they are currently leaving the main sequence is called the turnoff point. Using the mass and luminosity of the stars at the turnoff point with the equation T(years) = 10 10 M/L gives the age of the cluster. 47 Tuc is ~12 - 14 billion years old - one of the oldest known objects in the Milky Way Galaxy. Several stars have evolved to the white dwarf branch. Even though the turnoff point is well defined, there are stars on the main sequence above the turnoff point. These interesting objects, called blue stragglers, are blue and bright; however since all stars in a globular cluster form at the same time, how is it possible for young, hot stars to be there? It is thought that the blue stragglers were formed by the slow coalescing of two stars in a binary system. This Hubble image to the right shows blue stragglers in the center of 47 Tuc. 93 Luminosity Classification: A second classification system is used to further define the spectral types of stars. This classification system involves surface gravity - which is proportional to the stellar mass divided by the radius squared. This is useful because spectra can measure the gas pressure in the part of the atmosphere where the spectral lines are formed, and this pressure depends closely on surface gravity. Because surface gravity is related to stellar radius, it is also related to stellar luminosity. Every unit of stellar surface area emits an amount of radiation that mostly depends on the temperature, and for a given temperature the total luminosity thus depends on surface area which is proportional to radius squared hence inversely proportional to surface gravity. As a result, there are dwarf stars of relatively high surface gravity, small radius, and low luminosity, and giant stars of low surface gravity, large radius, and high luminosity - and their spectra look different. Six different luminosity classes are distinguished: • Ia most luminous supergiants • Ib less luminous supergiants • II luminous giants • III normal giants • IV subgiants • V main sequence stars • VI subdwarfs (rarely used - older main sequence stars with low metalicity) • VII white dwarfs (rarely used) The Sun is a G stellar classification, subclass 2, luminosity class V star - so the complete classification for the Sun is G2V. Pi Cephei in the constellation Cepheus is also a G2 star, however it is a G2III star - a star that has evolved from the main sequence to the giant branch of the H-R diagram. B-V Color Index: Many H-R diagrams label the horizontal axis with the B-V color index. By the late 19th century astronomers were using photography to record the sky and measure stellar brightness, and a problem appeared. Some stars having the same brightness to the eye showed different brightnesses on film, and vice versa. Compared to the eye, photographic emulsions were more sensitive to blue light and less sensitive to red light. Accordingly, two separate scales were devised. Apparent visual magnitude (mvis) described how a star looked to the eye; photographic magnitude (mpg) referred to star images on blue- sensitive black-and-white film. These are now abbreviated as m v and m p , respectively. The difference between photographic and visual magnitudes was named the "color index." Color index is now defined as the B magnitude minus the V magnitude. A pure white star has a B-V of about 0.2, our yellow Sun is 0.63, orange-red Betelgeuse is 1.85, and the bluest star believed possible is -0.4; the color index value is increasingly positive for yellow, orange, and red stars, and negative for blue stars. 94 How and What to Study: The following is a summary of the most important information to know about H-R diagrams. • Horizontal axis - spectral type, color index, or effective surface temperature ● Vertical axis - absolute magnitude or luminosity • Data for individual stars plotted, but they are not randomly scattered • Data points define definite regions, suggesting common characteristics for stars composing each region • Each region represents a stage in the evolution of stars • Consequently, there are common physical processes that apply to all stars in a region ● Main sequence - most conspicuous region is sequence of stars running from extremely bright, hot stars in upper left-hand corner to faint, cool stars in lower right-hand corner ○ Region is called main sequence because it contains ~90% of all stars ○ Sun is G2 main-sequence star ○ Lies in middle of diagram among what are referred to as yellow dwarfs - stars further down from Sun all called dwarfs (late sequence), stars above the Sun called giants (early sequence) ○ Temperatures for main-sequence stars varies from approximately 3000 o K for M stars to approximately 50,000 o K for O stars ○ Main-sequence stars are all members of one luminosity class, luminosity class V - the Sun is a G2V spectral/luminosity type star ○ Luminosity class V stars vary from extremely luminous O stars to very faint M dwarfs ○ Luminosity is assigned relative to the Sun - the Sun is one luminosity and the range of luminosities spans 10 orders of magnitude from .0001 to 10 6 solar luminosities. ○ Because of their number and common internal structure, main-sequence stars are considered to constitute a single class of stars ○ Number of M-type stars far exceeds number of K-type stars ○ Number of K-type stars in turn exceeds number of G-type stars and so on up the main sequence - cool, faint M-type stars most common type of star in our galaxy - known as red dwarfs ●Mass-Luminosity Relation for Main-Sequence Stars: ○ Masses of main-sequence stars increases from spectral class M up main sequence to spectral class O ○ Mass-luminosity relation - plot of mass against luminosity ○ Luminosity of main-sequence stars proportional to approximately fourth power of their mass - the mathematical form of this relationship is stated as: L α M 4 ●Other Properties of Main-Sequence Stars: ○ Radii of stars on main sequence increases from small radii M dwarfs in the lower right corner to large radii O giant stars in the upper left corner ○ Luminosity, temperature, radius, and mass for main sequence stars increases from M to O stars ○ Fundamental property upon which luminosity, temperature, and radius depend is the mass of gas composing main-sequence stars 95 ●Red Giants: ○ Red giants - second most prominent region in H-R diagram, composed of bright, cool stars ○ Red giants are luminous stars in spectral classes F, G, K, and M lying above main sequence in a region that angles up to bright, cool stars in upper right-hand corner ○ Despite being members of same luminosity class, red giants vary by at least a factor of 100 in luminosity ○100 times more luminous than Sun on average ○ Surface temperature varies from ~3000 o K to 7000 o K ○ No relationship exists between mass and position on red giant branch ○ No mass-luminosity relation has been found for red-giant stars ○ Radii of giant stars does increase progressing upward toward upper right-hand corner of H-R diagram ●Blue and Red Supergiants: ○ Supergiants are stars of luminosity classes I and II ○ Blue supergiants are early-type stars of classes O and B that have just evolved from the main sequence towards the supergiant branch ○ Red supergiants are late-type stars in classes G, K, and M that are located on the supergiant branch in the extreme upper right corner of the H-R diagram ○ Blue and red supergiants can be hundreds of thousands of times more luminous than Sun ○ Blue and red supergiant stars do not have a definite relationship between mass and position in the H-R diagram ○ Radii do increase toward upper right-hand corner ○ Although supergiants can be seen at tremendous distances because of their great luminosity, they appear to be a very rare type of star ○ There are far more red-giant stars in our Galaxy than blue and red supergiants ● White Dwarfs: ○ White dwarfs ~span spectral classes B, A, and F, and are composed of faint, hot stars in the lower left corner of the H-R diagram ○ Note: when star referred to as being "on" or "off main sequence," reference is to position in H-R diagram and not to its actual position in space ○ White dwarfs appear to be the second most populous region in H-R diagram ○ Supergiants are rare but can be seen at great distance across Galaxy; white dwarfs are more numerous but due to their small size and low luminosity are less visible at great distances ●Instability Strips on the H-R Diagram: ○ There are regions where some types of variable stars are found on the H-R diagram ○ The vertically elongated Mira instability strip contains long period pulsating red giant Mira variable stars ○ The vertically elongated Cepheid instability strip contains pulsating yellow and white giant pulsating stars that are periodic ○ The horizontally elongated RR Lyrae instability strip contains older pulsating red giants that reside in globular clusters ○ These regions contain stars that begin to vary either periodically or irregularly as they evolve from the main sequence to the giant and supergiant regions 96 ● Globular Cluster H-R Diagrams: ○ All stars in the cluster are basically the same age, so only differ in mass ○ Differences in brightness and appearance are true differences among the stars ○ All had the same basic initial chemical composition ○ All stars in the cluster have the same age ○ The turnoff point on a star cluster H-R diagram gives the age of the cluster ○ Globular clusters formed at the same time as the galaxy they inhabit ○ The age of globular clusters gives an upper limit to the age of galaxies ● Open Clusters of young gravitationally bound stars can also be plotted on the H-R diagram to study the characteristics of these stellar populations also. Characteristics of Main Sequence Stars Percentage of Stars in Regions of H-R Diagram Temperature Regions on H-R Diagrams 97 Plotting Stars on the HR Diagram Activity: For this activity, you will plot stars on a simple H-R Diagram, based on absolute magnitude and spectral type. The following pages include: Table I: Some of the Brightest Stars Visible from Earth, Table II: Some of the Nearest Stars to Earth, and the The H-R Diagram Template. Plot the brightest stars from Table I and the nearest stars from Table II with the asterisk and circle symbols indicated at the top of the H-R Diagram Template. Once you have plotted all of the stars, note any patterns that might appear, and answer the following questions. Reminder: The greater the negative number the brighter the star, the greater the positive number, the dimmer the star. Note that there is some overlap between the two tables. For instance, the star Sirius A - being the brightest star visible from Earth and the 9th closest star to the Sun - is on both Table I and Table II. You can plot the two symbols in the same location. You will not use the distances in light years - that information is provided for your edification only. NOTE: You will be plotting variable stars on this same H-R diagram in the next activity. 1. Label the following branches of the H-R diagram: Main Sequence, Giants, Supergiants, White Dwarf. Calculate the percentage of stars that occupy each branch, and briefly describe, from the information on the two axes, the types of stars that occupy each branch. 2. What patterns distinguish the brightest stars from the nearby stars? 3. Which stars are similar in magnitude and spectral class to the Sun? 4. Which list (brightest or nearest) gives the more typical example of the star population of the Milky Way Galaxy? Explain your reasoning. 5. Write a brief statement describing the relationship between absolute magnitude and stellar classification (temperature) of main sequence stars. 6. Does the above relationship hold for stars on the other branches of the H-R diagram? 7. Can you describe any relationships between absolute magnitude and stellar classification for any of the non-main sequence branches? Explain why you can or cannot. 8. Would you expect the same percentage of stars to occupy each branch of the diagram if all stars within the Milky Way Galaxy were plotted? Explain why or why not. 9. Why are there places on the diagram where no stars exist? 10. The next activity involves plotting variable stars on the same H-R diagram that you have constructed. Where do you think stars that vary in magnitude will end up on the diagram? Will they occupy one or more of the existing branches? Some of the empty places? Both? Write down your prediction, along with your reasoning. How would you plot a star that changes in brightness? What exactly is changing in these stars besides brightness? 98 Table I: Some of the Brightest Stars Visible from Earth Names: The common names of the stars are followed by the more scientifically correct nomenclature. The star with the brightest apparent magnitude in each constellation is named "alpha," followed by the possessive form of the Latin name for the constellation; the second brightest, "beta," the third brightest, "gamma," and so on down through the Greek alphabet. For example, the most common name for the brightest star in the constellation Auriga is "Capella." The scientific name of this star is "alpha Aurigae" or just "α Aurigae," or even "α Aur." NOTE: The A and B denote binary star systems; if they are in close contact they are considered to have the same absolute magnitude - if their separate absolute magnitudes have been measured, they are plotted separately. Star Spectral Class Absolute Magnitude 1. The Sun G2 4.8 2. Sirius (α CMa A) A0 1.8 3. Canopus (α Car) A9 -5.5 4. Vega (α Lyr) A0 0.6 5. Arcturus (α Boo) K2 -0.1 6. α Cen A G2 4.5 7. Rigel (β Ori) B8 -6.7 8. Capella (α Aur A,B) G6 -0.3 9. Achernar (α Eri) B3 -2.8 10. Procyon (α CMi A) F5 2.7 11. Agena (β Cen A,B) B1 -5.5 12. Acrux (α Cru A) B0 -3.3 13. Altair (α Aql) A7 2.3 14. Spica (α Vir) B1 -3.6 15. Aldebaran (α Tau A) K5 -0.5 16. Becrux (β Cru) B0 -4.0 17. Formalhaut (α Ps A) A3 1.8 18. α Cen B K1 5.6 19. Pollux (β Gem) K0 1.2 20. Regulus (α Leo A) B7 -0.6 21. Adhara (ε CMa A) B2 -4.2 22. Shaula (λ Sco) B1 -5.1 23. Bellatrix (γ Ori) B2 -2.8 24. Castor (α Gem A,B) A2 0.6 25. Alnath (β Tau) B7 -1.4 26. Betelgeuse (α Ori) M2 -7.1 27. Antares (α Sco) M1 -5.2 99 Table II: Some of the Nearest Stars to Earth Star Spectral Class Absolute Magnitude 1. The Sun G2 4.8 2. α Cen C M5 15.2 3. α Cen A G2 4.5 4. α Cen B K1 5.6 5. Barnard's star M5 13.2 6. 70 Oph A K0 5.6 7. Sirius A (α CMa A) A0 1.8 8. V1216 Sgr M4 13.0 9. ε Eri K2 6.3 10. HIP 114046 M0 9.8 11. FI Vir M4 13.4 12. V1803 Cyg K5 7.7 13. Procyon (α CMi A) F5 2.7 14. 61 Cyg B K7 8.4 15. HIP 91772 M3 12.3 16. GX And M1 10.4 17. HIP 91768 M3 11.2 18. ε Ind K4 7.0 19. τ Cet G8 5.8 20. YZ Cet M4 14.1 21. Luyten's star M3 11.9 22. Kapteyn's star M1 11.0 23. AX Mic K7 8.8 24. Kruger 60A M3 11.6 25. V577 Mon M4 12.9 26. Sirius (α CMa B) A0 11.2 27. Procyon (α CMi B) F0 13.0 * The absolute magnitudes of all stars except the Sun, Sirius (α CMa B), and Procyon (α CMi B) were calculated from parallax measurements and apparent magnitude (Hp) measurements taken from The European Space Agency, et al., The Hipparcos and Tycho Catalogues (17 Vols.), Noordwijk, The Netherlands: ESA Publications Division, 1997. ISBN 92-9092-399-7 (Vols. 1-17). 100 The H-R Diagram Template 101 Answers to the questions in the Plotting Stars on the H-R Diagram Activity: 1. Graphs and answers will vary. See answer key on next page to see where the regions are located. Percentages are ~85% on Main Sequence, 7% on Giant branch, 3% on Supergiant branch, and 3% on White Dwarf branch. NOTE: the two stars that have evolved off the main sequence (spectral class A,F with absolute magnitudes greater than -5) were included as main sequence stars as they have not gotten to the Supergiant branch yet. The four stars on the giant branch are on their way to going through the planetary nebula stage and will end up on the White Dwarf branch. The two stars on the Supergiant branch will go through Type II supernova events and become neutron stars or pulsars. The two white dwarfs are the end products of mid-sized stars. 2. The patterns that emerge should indicate that the nearby stars are generally dim, whereas most of the bright stars appear bright to us because they are genuinely quite luminous, not because they are close. A large percentage of the nearby stars are cool class M red dwarfs and a few are white dwarfs. Many of the brightest stars are hot class A and B Main Sequence stars and giants, with a few highly luminous class M red giants mixed in. 3. Alpha Centauri is similar both in absolute magnitude and spectral type to the Sun. 4. Neither one. The dim stars that are far away cannot be seen - we can see brighter stars further away than the dimmer stars - so both sets together will give a "typical" view of the stellar population of the entire Milky Way Galaxy. 5. The spectral classification of stars depends upon their temperature - from hottest to coolest the spectral types are O,B,A,F,G,K,M,C,S - the hotter the star the greater the absolute magnitude; the hotter the star the greater the absolute magnitude. 6. For the other regions on the H-R diagram there is no relationship. Spectral type M, for example ranges from ~16 to -8 magnitudes. 7. White Dwarf stars are spectral type A-F and have a low absolute magnitude so they are hot and dim, Giants and Supergiants have a high absolute magnitude and spectral type of K-M so they are bright and cool. 8. There would be some differences as this is a small sample of 54 stars; however, the Galaxy on average should have approximately the same number of stars in the same stages of development that we see in the local stellar neighborhood. 9. A star's position in the diagram is a function of its mass, chemical composition, and current age. There is a physical reason why the points in the diagram are not scattered at random: the natural forces that guide the evolution of stars confine them to portions of the diagram where they can convert matter into radiant energy. 10. Various answers. 102 The H-R Diagram Answer Key for Nearby and Bright Stars 103 Supergiants White Dwarfs Sun Giants Main Sequence Plotting Variable Stars on the H-R Diagram Activity: Plot the variable stars in Table III below on the same diagram you used to plot the bright and nearby stars. This will help you to see the relationship among main sequence stars, giants, supergiants and white dwarfs to variable stars. Variables have two absolute magnitudes, one at maximum and one at minimum. They also have enough variation to change spectral classes. To show the entire cycle of change for variable stars, it is necessary to plot them twice. The Spectral Class column shows the range in spectral class for both maximum (left) and minimum (right); the Absolute Magnitude shows the range from maximum (left) to minimum (right). Plot both sets of values using a triangle for a symbol, and draw a line connecting the two points. Table III: Variable Stars and the H-R Diagram Star Type Distance Spectral Absolute (parsecs) Class Magnitude (M V ) RT Aur Cepheid(C) 480 F4 to G1 -3.4 to -2.6 Delta Cep Cepheid(C) 300 F5 to G1 -3.9 to -3.0 Rho Cas Semi-Regular(SR) 3600 F8 to K0 -8.7 to -6.6 T Cas Mira(M) 1700 M6 to M9 -3.2 to +0.8 TU Cas Cepheid(C) 1100 F3 to F5 -3.3 to -2.0 UU Aur Semi-Regular(SR) 560 C5 to C7 -0.9 to +1.3 Chi Cyg Mira(M) 106 S6 to S10 +0.0 to +8.2 X Cyg Cepheid(C) 680 F7 to G8 -3.3 to -2.3 T Cep Mira(M) 210 M5 to M8 -0.6 to +3.7 Y Oph Cepheid(C) 880 F8 to G3 -3.8 to -3.3 RS Boo RR Lyrae(RR) 1300 A7 to F5 -0.9 to +0.2 VX Her RR Lyrae(RR) 2100 A4 to F4 -1.7 to -0.4 * The absolute magnitudes were calculated from parallax measurements and apparent magnitude (Hp) measurements taken from The European Space Agency, et al., The Hipparcos and Tycho Catalogues (17 Vols.), Noordwijk, The Netherlands: ESA Publications Division, 1997. ISBN 92-9092-399-7 (Vols. 1-17). QUESTION: Are the Cepheid, RR Lyrae and Mira variable stars located on the H-R diagram where you expected them to be (Question 10 in previous activity)? 104 The H-R Diagram Answer Key for Variable Stars 105 Red Giants Giants Main Sequence White Dwarfs Miras Cepheids RR Lyraes Red Supergiants H-R Diagrams Sample Questions: Use the image set below to answer the questions on the following page: 1 2 3 4 5 6 7 8 9 10 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) 106 A B C D E F G Questions for images 1 through 9 on the previous page: 1. The H-R diagrams numbered 1 through 4 are for open and globular clusters. Place the diagrams in order from youngest to oldest. Explain your reasoning. 2. Which of the diagram(s) represent open clusters? Explain your reasoning. 3. Which of the diagram(s) represent globular clusters? Explain your reasoning. 4. Image 5 is Pleiades and image 6 is Hyades. Which H-R diagrams belongs to these two star clusters. Explain your reasoning. 5. Which H-R diagram(s) represent the object in image 7? Explain your reasoning. 6. Image 9 is the H-R diagram for image 8. What type of star cluster is this? Explain your reasoning. Questions for the H-R diagram and objects (a) - (m) shown in image 10: 1.Where is image (a) located in on the H-R diagram? 2a. What type of light curve is image (j)? 2b. Where on the H-R diagram would an object reside that produces this type of light curve? 2c. What is this area of the H-R diagram called? 3. Where on the H-R diagram is object (f) located? 4a. Which object is located at C on the diagram? 4b. Which object shows the behavior of the answer to 4a? 4c. Which object shows the next stage for the object located at C? 4d. Where on the H-R diagram will the final product for the answer to 4b be located? 5a. What is the name of the area of the diagram labeled A? 5b. Which of the objects are associated with this area of the H-R diagram? 5c. Which object shows one possible end result for stars after they leave location A? 6. Which two objects show events that take place before the main sequence? 7a. Where on the H-R diagram are the coolest, dimmest objects located? 7b. Where are the coolest, brightest objects located? 7c. Where are the hottest, dimmest objects located? 7d. Where are the hottest, brightest objects located? 8. Which object is located in location B on the H-R diagram? 107 Answers to H-R Diagrams Sample Questions: Answers for images 1 through 9: 1. From youngest to oldest: 2, 4, 1, 3 2 - stars just beginning to leave the main sequence in the upper left corner. No stars have evolved to the giant branch. 4 - still a lot of main sequence stars, a few giants, and stars have evolved all the way to the white dwarf branch. 1 - the turnoff point is further down the H-R diagram, many stars are in the transition to the giant branch, and many stars are on the giant and supergiant branches. 3 - Again, the turnoff point in further down the diagram, some "blue stragglers" are left behind, there are several white dwarfs. 2. H-R diagrams 2 and 4 are open clusters. Open clusters are gravitationally bound groups of stars that condensed together from the same cloud of gas and dust. The stars in the cluster slowly drift apart over time, so open clusters are relatively young. 3. H-R diagrams 1 and 3 are globular clusters. Globular clusters are dense clouds of older stars that are located outside the plane of the galaxy and contain many highly evolved giant stars. 4. H-R diagram 2 is the Pleiades - a very young group of hot O and B types stars. The cluster is not old enough for any stars to have evolved off the main sequence. Diagram 4 is the Hyades - an older open cluster. The stars have drifted further apart and some of the stars have evolved to the giant and white dwarf stage. 5. Image 7 is a globular cluster - a tightly packed and dense group of stars. Either 1 or 3 are representative diagrams for this object. 6. This is not a globular cluster, however there appear to be two separate concentrations of stars. This is actually "h and Chi Persei" - a rare double open cluster. The diagram has many stars on the main sequence, with some stars that have evolved to the giant branch; the diagram does not have a sharp turnoff point like you would see in the H-R diagram of a globular cluster. Answers for the H-R diagram and objects (a) - (m) shown in image 10: 1. location F 2a. Cepheid, 2b. location G, 2c. Cepheid Instability Strip 3. The red giant would be located at A, and the white dwarf at D 4a. (d) - red giant; 4b. (c) - Mira variable stage star; 4c. (k) - planetary nebula; 4d. D - the white dwarf branch 5a. Supergiant branch; 5b. (b) - supernova explosion (1987A), (g) supernova remnant, Cas A, (l) - supernova explosion light curve (1987A); 5c. (h) pulsar (Crab Pulsar) 6. (e) - stellar nursery and (i) protostar with protoplanetary system 7a. location E; 7b. location A; 7c. location D, 7d. location B 8. (m) - the Pleiades 108 The materials on the CD-ROM include the following: Additional internet resources for images and information related to H-R diagrams: ● http://zebu.uoregon.edu/~soper/Stars/hrdiagram.html VERY BASIC information ● http://www.peripatus.gen.nz/Astronomy/SteCla.html General description of spectral classifications, including subclasses ● http://cassfos02.ucsd.edu/public/tutorial/StevI.html A brief description of stellar evolution on the H-R diagram ● http://www.rssd.esa.int/index.php?project=HIPPARCOS&page=HR_dia H-R diagrams from the Hipparcos missions - most accurate H-R plots to date of nearby stars Excellent on-line activities: ● This Sloan Digital Sky Survey website (SDSS) allows the user to create their own H-R diagram (advanced project): http://cas.sdss.org/dr6/en/proj/advanced/hr/ And to plot a globular cluster H-R diagram (advanced project): http://cas.sdss.org/dr6/en/proj/advanced/hr/globularcluster.asp ● AAVSO Variable Star Astronomy A description of this curriculum is at the end of the section on Variable Stars (pages 78-79). The two H-R diagram plotting activities are from Chapter 9, Core Activities 9.2 and 9.3, on pages 11 – 16. More information about the activities can be accessed in the teacher pdf. Chapter 9 is located at: http://www.aavso.org/education/vsa/Chapter9.pdf 109 Cosmological Distances Measuring distances is one of the most important, and often most difficult, tasks in astronomy. The term "cosmic distance ladder" refers to the methods by which astronomers determine the distances to objects. Each rung of the ladder provides information which is used to determine the distances at the next higher rung. Beyond the Solar System, the succeeding rungs of the cosmic distance ladder are parallax, spectroscopic parallax, variable stars (Cepheids and RR Lyraes), Type Ia supernovae, the Tully-Fisher relationship, and Hubble's law. These methods are currently the most reliable, though many others are used and studied. Trigonometric (Stellar) Parallax (Stars within ~100 Light Years from Earth): Trigonometric parallax is the apparent displacement of a nearby star against the background of more distant stars resulting from the motion of the Earth in its orbit around the Sun. Mathematically speaking, the parallax of a star is the angle at the star that is subtended by the mean distance between the Earth and the Sun. A shift in the angular position of a star will be greatest when observed at intervals of six months; this makes the parallax equal to the value of one half of the semiannual displacement of the star. If a star's parallax can be measured, it then determines the distance to the star. The unit of measurement is the parsec (pc); it is the distance at which a star would have a parallax of one second of arc and is equivalent to 206,265 times the distance from the Earth to the Sun (in Astronomical Units or AU), or 3.26 light years. A star's distance d in parsecs is the reciprocal of its parallax p (or d = 1/p). The nearest star, Proxima Centauri, has a parallax of 0.763" of arc and a distance of about 1.31 parsecs. NOTE: 1 pc = 206,265 AU = 3.26 LY = 3.08 × 10 13 km Spectroscopic Parallax (Stars and Clusters ~100,000 Light Years from Earth): Despite the name, this method has nothing to do with measuring parallaxes. Distances for stars too far away to show a detectable trigonometric parallax are found using spectroscopic parallax.. This method uses the correlation between luminosity (absolute magnitude) and temperature (spectral type) for stars and their luminosity class to calculate their distances. 110 Cosmic Distance Ladder The spectral type and luminosity class of a distant star is determined from its spectrum and it is plotted on the H-R diagram. The luminosity, or absolute magnitude, of the star can then be read directly from the diagram. The apparent magnitude of the star is easy to measure, and both magnitudes - apparent and absolute - can be used to calculate the distance to the star. The distance modulus is a mathematical relationship that relates absolute magnitude, apparent magnitude, and distance. The general relationship is written as: m - M = 5 log 10 [ d / (10 pc) ], where m = apparent magnitude, M = absolute magnitude, and d = distance. NOTE: (m - M) is the distance modulus. EXAMPLE: A star of spectral class A5V (main sequence) has an apparent visual magnitude (m) of 9.2, and from its location on the H-R diagram an absolute magnitude (M) of 1.5. The distance modulus of the star is m - M = 9.2 - 1.5 = 7.7 So the distance (in parsecs) can be found: 7.7 = 5 log 10 (d) - 5 d = 347 pc, or 1130 LY Variable Stars - Cepheids and RR Lyraes (Globular Clusters and Galaxies Within ~10,000,000 Light Years of Earth): High luminosity Cepheid variable stars have a longer period than less luminous Cepheids. A plot of the absolute magnitude versus period is called the period-luminosity relationship (P-L). Cepheid Variable Stars: There are two types of Cepheid variable stars. Type I: classical Cepheids are from young high-metalicity stars and are about 4 times more luminous than Type II Cepheids. To the right is the light curve (the plot of brightness vs. time) of a classical Cepheid from the Hipparcos database of variable stars. These are younger (Population I) stars found in galactic spiral arms and irregular galaxies. Type II: W Virginis Cepheids are from older low-metalicity stars and are about 4 times less luminous than Type I. To the right is the light curve of a W Virginis Cepheid from the Hipparcos database of variable stars. Note the differences in the shape of the light curve. The two types of Cepheids are distinguished from each other by the shape of the light curve profile. These are older stellar (population II) stars located galactic halos, globular clusters, and elliptical galaxies. 111 Type I Type II Because the luminosity of Cepheids can be easily found from the pulsation period, they are very useful in finding distances to the star clusters or galaxies in which they reside. Early measurements of the distances to galaxies did not take into account the two types of Cepheids and underestimated the distances to nearby galaxies. To calculate distances to other galaxies, a Cepheid variable is observed and its period is calculated from its light curve and the type - I or II - from the shape (profile) of its light curve. The period-luminosity relationship is then used to determine the absolute magnitude. The observed apparent magnitude of the Cepheid and its absolute luminosity are then used with the distance modulus to calculate the distance to the Cepheid - and the galaxy in which it is located. Another type of pulsating star similar to the Cepheids is the RR Lyrae variable stars. They are smaller than Cepheids and, therefore, have shorter periods and lower luminosities. They pulsate with a period between ~5 and 15 hours (Cepheid pulsation periods are greater than ~24 hours). Many lower-mass giant stars will go through a RR Lyrae pulsation stage while many higher-mass giant stars will go through a Cepheid stage. Because low-mass stars live longer than high-mass stars, the Cepheid stars as a group are younger than the RR Lyrae stars. RR Lyraes are found in old star clusters called globular clusters and in the stellar halo part of our galaxy. All of the RR Lyrae stars in a cluster have the same average apparent magnitude. In different clusters, the average apparent magnitude is different. This is because all RR Lyrae have about the same average absolute magnitude (+0.75, or ~45 solar luminosities). If the cluster is more distant from us, the RR Lyrae in it will have greater apparent magnitudes (remember fainter objects have greater magnitudes.). RR Lyrae stars can be used as standard candles to measure distances out to ~760,000 parsecs (2.5 million light years). The more luminous Cepheid variables can be used to measure distances out to ~40 million parsecs (130 million light years). Summary: 1. Identify a Cepheid or RR Lyrae and plot its light curve. 2. Calculate the period. 3. Use the period-luminosity relationship to determine the absolute magnitude. (Cepheids) 4. Use the distance modulus to calculate the distance. 112 Type Ia Supernovae and the Tully-Fisher Relation (Galaxies and Galaxy Clusters ~10 Billion Light Years from Earth) Type Ia Supernovae (SN): Type Ia supernovae, like 1994D in galaxy NGC4526 to the left, are the explosions of white dwarf stars in binary systems. Accretion from a companion raises the mass above the maximum mass for stable white dwarfs, the Chandrasekhar limit. The white dwarf then starts to collapse, but the compression ignites explosive carbon burning leading to the total disruption of the star. The light output comes primarily from energy produced by the decay of radioactive nickel and cobalt produced in the explosion. The peak luminosity is correlated with the rate of decay in the light curve: less luminous supernovae decay quickly while more luminous supernovae decay slowly. A few Type Ia supernovae have been in galaxies close enough to us to allow the Hubble Space Telescope to verify the results using Cepheid variables. Because a white dwarf has a mass limit of 1.4 solar masses, they are all assumed to have approximately the same absolute magnitude of M V = -19.9 Type Ia supernovae are so bright that they can be seen from enormous distances and their apparent magnitudes can be observed. The light curve decline is plotted, and from the present apparent magnitude, the apparent magnitude during the supernova event is then calculated. The apparent and absolute magnitudes can be used with the distance modulus relationship to calculate the distance to the Type Ia supernova. Summary: 1. Identify a Type Ia supernova. 2. Observe it for a few weeks to get a light curve. 3. Calculate the maximum apparent brightness. 4. The absolute magnitude is assumed to be -19.9 5. Use the apparent and absolute magnitudes with the distance modulus relationship to calculate the distance. Tully-Fisher Relation: The Tully-Fisher relation is a correlation for spiral galaxies between their luminosity and how fast they are rotating. The idea is that the more massive the galaxy is, the faster it is rotating. If you know the rotational velocity of a spiral galaxy, you can determine its absolute magnitude by using the Tully-Fisher relation. It has been determined that the luminosity, or absolute magnitude, of a spiral galaxy is proportional to its rotational velocity to the 4th power - mathematically this is stated as L = V rot 4 . The absolute magnitude, the apparent magnitude, and the distance modulus are used to calculate its distance. For a cluster of galaxies, the distance to each galaxy can be calculated using the Tully-Fisher relation. The distances can then be averaged to calculate the distance to the entire cluster. The rotation rate of a galaxy can be measured through radio observations of the molecular clouds it contains and the Doppler effect. 113 Radio telescopes are used to measure the 21-cm line of rotating neutral hydrogen gas in the disk of a spiral galaxy. The measurements of the neutral hydrogen (HI) display a "double-horned" profile as seen in the graphic to the right. The Tully-Fisher relation is a plot of the line width (the measure of the rate of rotation) versus the absolute magnitude of the galaxy. From this plot the mathematical relationship of rotation to luminosity was then determined to be L = V rot 4 . Summary: 1. Measure 21-cm HII line width for rotation rate 2. Apply L = V rot 4 3. Use distance modulus Hubble's Law: Hubble's law is the statement that all galaxies in the universe appear to be moving away from the Milky Way Galaxy - and that the velocities with which they are receding is proportional to their distances. The law is stated mathematically as: v r = H 0 d, where v r = recessional velocity (how fast the galaxy is moving away from us), d = distance in megaparsecs (Mpc) the galaxy is away from us, and H 0 = Hubble's constant (the rate at which the velocity changes with distance). The current accepted value for Hubble's constant is 71+/-4. The redshift Doppler equation is: z = λ - λ 0 / λ 0 , where z = redshift and = λ = wavelength. Hubble's constant is "constant" in the sense that it is believed to work for all velocities and distances right now. The value of H 0 (usually called Hubble parameter to distinguish it from its value now, the Hubble constant) decreases over time however. If one assumes that all galaxies retain their speed relative to us and do not accelerate or decelerate, then we have d = vt and it follows that H 0 = 1/t, where t is the time since the Big Bang. This allows us to estimate the age of the universe from H 0 . Based on recent observations, it is now believed that galaxies accelerate away from us, which means that H 0 > 1/t (but still decreases over time) and the current estimates for the age of the universe are too low. For relatively nearby galaxies, the velocity v can be determined from the galaxy's redshift (z) using the formula v ≈ zc where c is the speed of light. All galaxies move relative to each other independent of the expansion of the universe, and these relative velocities - called peculiar velocities - are not accounted for by Hubble's law. For far away galaxies, v cannot easily be determined from the redshift z and can be larger than c. Systems that are gravitationally bound are not subject to Hubble's law and do not expand. 114 How and What to Study: Trigonometric (Stellar) Parallax ● Used to measure the distance to stars within ~100 light years from Earth ● Based on geometry of the Earth, Sun, and apparent movement of the star against more distant background stars. ● d = 1/p Spectroscopic Parallax ● Used to measure the distance to stars and star clusters within ~100,000 light years from Earth ● Based on location on H-R diagram (to determine luminosity) and the distance modulus ● m - M = 5 log 10 [ d / (10 pc) ] Cepheid Variable Stars ● Used to measure the distance to galaxies within ~ten million light years from Earth ● Based on the light curves, the period-luminosity relationship, and the distance modulus ● Light Curve, Period-Luminosity Table & m - M = 5 log 10 [ d / (10 pc) ] RR Lyrae Variable Stars ● Used to measure distances to globular clusters within ~ten million light years from Earth ● Based on light curves, M of +0.75, and the distance modulus ● Light Curve & m - + 0.75 = 5 log 10 [ d / (10 pc) ] Type Ia Supernovae ● Used to measure distances to galaxies and galaxy clusters within ~ ten billion light years from Earth. ● Based on light curve, M of -19.9, and the distance modulus ● Light Curve, M V = -19.9 & m - M = 5 log 10 [ d / (10 pc) ] Tully-Fisher Relation ● Used to measure distances to spiral galaxies ● Based on rotation (to determine luminosity) and the distance modulus ● HII line width, L = V rot 4 & m - M = 5 log 10 [ d / (10 pc) ] Hubble's Law ● Used to measure distances to the most distant galaxies ● Based on Doppler redshift of spectrum equation z = λ - λ 0 / λ 0 ● Linear relationship of recessional velocity to distance with V r = H 0 d NOTE: ● Spectroscopic parallax, Cepheid and RR Lyrae variables, Type Ia supernovae, and The Tully-Fisher relation all use luminosity so these methods of measuring cosmological distances are referred to as Standard Candles. There are other methods that measure distances that have not been discussed in this manual. 115 It is important to know which methods of measuring cosmological distances are used with different objects, especially the designated DSOs in the student manual. Construct a set of flash cards for the designated DSOs and other objects with the method(s) used to measure their distances on the back. It is also necessary to know how to solve problems involving distances so you should also be familiar with the relationships and equations associated with each measurement method. Practice Questions with Answers: Part I. For each of the images below, name the method(s) most commonly used to determine its distance from Earth: (Information for each image is provided) 1 2 3 4 Spiral Galaxy Giant Star in Milky The Pleiades Proxima Centauri Way Galaxy Triple Star System 5 6 7 8 Globular Cluster in Supernova Event Galaxy Cluster Elliptical Galaxy Milky Way Galaxy in Distant Galaxy 9 10 11 12 Quasars Planetary Nebula Star in M100 Galaxy Globular Cluster In Milky Way Galaxy in Large Magellanic Cloud Galaxy *ANSWERS: 1. Tully-Fisher relation 7. Tully-Fisher 2. Spectroscopic Parallax 8. Hubble's Law (if distant)** 3. Spectroscopic Parallax 9. Hubble's Law 4. Trigonometric Parallax (nearest star) 10. Spectroscopic Parallax 5. RR Lyrae 11. Cepheid Variable 6. Type Ia Supernova 12. RR Lyrae (*there could be other possible answers. **these objects mostly use Faber-Jackson relation not discussed) 116 Part II. Solve the following cosmological distances basic sample problem set. QUESTIONS: Trigonometric Parallax: Barnard's star has a parallax of 0.545 arcsec. What is the distance to this star in parsecs and light years? Spectroscopic Parallax: The spectrum of a 14 th magnitude star places its location on the H-R diagram at 0.0 absolute magnitude. What is the distance to the star? Cepheid Variable Stars: What is the absolute magnitude for the variable star, delta Cep? It has an apparent magnitude range of 3.5 to 4.4 and a parallax measurement of 0.00332 arcsec. RR Lyrae Variable Stars: An RR Lyrae variable star in the M51 galaxy has a distance modulus of 29.6. What is its apparent magnitude? How far away is M51? Type Ia Supernovae: A Type Ia supernova is discovered in a distant galaxy. At maximum brilliance, the supernova reaches an apparent magnitude of +10. How far away is the galaxy? Tully-Fisher Relation: The HII 21-cm line width of a spiral galaxy gives a rotation rate that corresponds to a luminosity value of -19. The apparent magnitude is 16.5. How far away is the galaxy? Hubble's Law: The average radial velocity of galaxies in the Hercules cluster is 10,800 km/s. Using H 0 = 70 km/s/Mpc, find the distance to this cluster in Mpc and light years. How would your answer differ if the Hubble constant had a smaller value? More Advanced Problems: 1. The brightness of a certain Cepheid variable star increases and decreases with a period of 10 days. (a) What must this star's luminosity be if its spectrum has strong absorption lines of hydrogen and helium, but no strong absorption lines of heavy elements? (b) Repeat part (a) for the case in which the star's spectrum also has strong absorption lines of heavy elements. (Assume H 0 = 70 km/s/Mpc) 2. When measured in a laboratory on Earth, the so-called K line of single ionized calcium has a wavelength λ 0 = 393.3 nm. When you observe the spectrum of galaxy NGC 4889, you find that the k line has a wavelength of 401.8 nm. How far away is NGC 4889? 117 ANSWERS: Trigonometric Parallax: Type Ia Supernova: d = 1/p m - M = 5 log 10 d / 10 d = 1/0.545 = 1.83 pc m = +10 and M = -19.9 d = 1.83 pc x 3.26 ly/1 pc = 5.98 ly 10 + 19.9 = 5 log d - 5 5 log d = 10 + 19.9 + 5 = 34.9 Spectroscopic Parallax: log d = 34.9/5 = 6.98 m - M = 5 log 10 d / 10 d = 10 6.98 = 9.5 x 10 6 pc = 9.5 Mpc M = m - 5 log (d/10) 0.0 = 14.0 - 5 log (d/10) Tully-Fisher Relation: 5 log (d/10) = 14.0 M = -19.0 , m = 16.5 log (d/10) = 14.0/5 = 2.8 m - M = 5 log 10 d / 10 d/10 = 10 2.8 = 631 pc ; 5 log d = m - M + 5 d = 6310 pc 5 log d = 16.5 + 19 + 5 = 40.5 6310 pc x 3.26 ly/pc = 20,571 ly log d = 40.5/5 = 8.1 d = 10 8.1 = 1.3 x 10 8 pc Cepheid Variable Stars: d = 130 Mpc Absolute magnitude at maximum: apparent magnitude = 3.5 d = 1/p = 1/0.00332 = 301.2048 Hubble's Law: m - M = 5 log 10 d / 10 v = H 0 d ; v = 10,800 km/s ; M = 3.5 - 5 log 10 (301.2048/10) H 0 = 70 km/s/Mpc M = 3.5 - 5 log 10 (30.1205) d = 10,800/70 Mpc = 154 Mpc M = 3.5 - 5 (1.4789) = -3.89 = -3.9 d = = 503 ly minimum: -3.0 Smaller constant, greater distance RR Lyrae Variable Stars: m - M = 29.6 ; RR Lyraes have an M of 0.75 m = 29.6 + 0.75 = 30.35 5 log d = 29.6 + 5 = 34.6 log d = 6.92 d = 10 6.92 = 8.3 Mpc More Advanced Problems: 1. (a) The spectrum establishes that this is a Type II Cepheid. Using the Period- Luminosity (P-L) relation in the diagram for a Type II Cepheid with a period of 10 days gives a luminosity of about 10 3 that of the Sun. (b) In this case it is a Type I Cepheid and the luminosity becomes about 4 x 10 3 that of the Sun. 2. z = 401.8 nm - 393.3 nm/393.3 nm = 0.0216 v = zc = (0.0216) (3 x 10 5 km/s) = 6500 km/s d = zc/H 0 = 6500 km/s/70 km/s/Mpc = 93 Mpc = 300 x 10 6 ly 118 Additional internet resources for images and information related to H-R diagrams: ●http://www.astro.washington.edu/courses/labs/clearinghouse/labs/labs.html This website has an online Hubble's Law Introductory Lab that uses negative images of actual galaxies. Students click on either side to get the angular size of the galaxy, which is then converted into arcseconds, for 12 galaxies. The actual spectra are included. This is an excellent and very realistic Hubble's law activity. This website contains several activities and labs relating to stellar evolution, Hubble’s law, the H-R diagram, and variable stars. Complete instructions, downloadable PDF documents to use with the online activities, and answers are provided. ● http://skyserver.sdss.org/dr2/en/proj/advanced/hubble/ This is an advanced project that allows students to create their own diagram and calculate the Hubble law. It used actual galaxies and spectra, and requires familiarity with Excel spreadsheets. ● http://www3.gettysburg.edu/~marschal/clea/CLEAhome.html The CLEA Hubble Redshift Distance Relation software is an excellent free simulation for Win PCs. At the controls of a simulated telescope, students view distant clusters of galaxies and obtain their spectra with a photon counting spectrometer. A wide variety of instructor-settable options are available. Instructors can construct their own galaxy fields using GENSTAR, a utility supplied by CLEA, and can even install their own image files to represent galaxies. The integration time to reach a given signal- to-noise can be set to conform to the needs of the class and the speed of the computer. Even the value of the Hubble parameter can be specified by the instructor; the default is 75 km/sec/Mpc. Go to the URL above and click on Manuals to locate and download the software. ● http://www.astro.ucla.edu/~wright/distance.htm This site contains basic information about every cosmological method of measuring distances in the universe. [More technical] 119 Mathematical Equations & Relationships: A. Orbital Mechanics and Motion Kepler’s 3rd Law: (MA + MB) = a 3 / p 2 Kepler's law is useful for any orbital motion, such as two stars in a binary system. It is a relationship among mass (M), period (p), and distance of separation in au's (a). 2π r = vP This equation is used to determine the rotational periods of an object. During one rotation a point in the equatorial region will travel a distance equal to 2π r. This distance is equal to the velocity of the point times the time elapsed during one rotation. It is a relationship among radius, velocity, and period. If you know any two of the variables, you can solve for the third variable. v = d/t ; a = v/t ; F c = ma c ; a c = v 2 /r = rω 2 These fundamental physics of motion equations should not be forgotten. Everything is moving in space, and for even stars and galaxies velocity (v) equals the rate at which distance (d) changes over time (t), and acceleration (a) is equal to the rate at which velocity changes over time. Everything also rotates in space, and therefore centripetal forces also apply. Centripetal force (F c ) equals mass (m) times centripetal acceleration (a c ), and centripetal acceleration (a c ) equals velocity squared (v 2 ) divided by the radius (r). Since velocity on a spinning object is an angular displacement, angular acceleration is also equal to radius times angular velocity squared (ω 2 ). B. Stellar Radiation Wein's Law: λ max = 2.9 x 10 7 /T This law relates the maximum peak (angstroms) output of radiation from an emitting object (λ max ) to its temperature (T) in Kelvin (K). Stephan-Boltzmann Law: L = 4πR 2 σT 4 This involves the total luminosity (L) from a stellar surface, which is the produce of its surface area (4πR 2 ) and temperature (T) to the fourth power. Another form of this relationship is E = σT eff 4 where T eff is the effective surface temperature in Kelvin, and E is the energy per unit surface area in erg/cm 2 . σ is the Stefan-Boltzmann constant, 5.70 x 10 -5 erg/cm 2 K 4 s. Other forms of the Stephan-Boltzmann law are as follows: L/L sun = (R/R sun )2 x (T/T sun ) 4 or R/R sun = (T sun /T) 2 x √L/L sun These simpler rearrangements express the stellar properties in terms of solar properties. C. Luminosity The Distance Modulus: M = m - 5log 10 (d)/10 This is a relationship among absolute magnitude (M) - or luminosity, apparent magnitude (m), and distance (d). If you know any two of these three variables, you can use this relationship to find the third variable. Used with Cepheid and RR Lyrae variable stars, and the other standard candles that measure cosmological distances. 120 Inverse Square Law: L = 1/r 2 or L = (r/r sun ) 2 x b/b sun or b/b sun = (r/r sun ) 2 Light, or luminosity, is one of several phenomena that decrease in brightness as the square of the distance. This can be expressed in many ways - two examples are given above. The distance (r), luminosity (L), or brightness (b) can be written relative to the Sun. Tully-Fisher Relation: L = V rot 4 The luminosity of any spiral galaxy is equal to the 4 th power of its rotation, or, the faster a galaxy spins, the more luminous it is. There is a correlation between spin rate and luminosity because the gas and stars are in orbit in the galaxy, so the centripetal and gravitational forces are in balance. Mathematically, v 2 /r - GM galaxy /R 2 = 0. This shows that the greater the rotation, the more mass the galaxy has to have to maintain a balance between the two forces. So the faster a galaxy rotates, the more massive it must be - and the more luminous. D. Expansion of the Universe Hubble's Law: v r = H 0 d Hubble's law states that the recessional velocity (v r )of a distant galaxy is equal to its distance (d) times Hubble's constant. (Assume 70km/s/Mpc for H 0. ) The recessional velocity is determined from the Doppler redshift (z) of the H and K lines in the spectrum of the receding galaxy. Doppler Effect Equation: λ – λ 0 = ν r /c ; z = λ - λ 0 / λ 0 ; v r ≈ zc The first equation is the combination of the next two. First, z = λ - λ 0 / λ 0 is used to measure the redshift (z) by comparing the spectral lines from the galaxy (λ) and the known spectral lines (λ 0 ). The recessional velocity (v r )is then equal to the redshift(z) times the speed of light (c). E. Other Important Calculations: Parallax for nearby stars: d = 1/p Frequency, wavelength, and speed of light: λ f = c Time spent on the main sequence: t(years) = 10 10 m/L Mass-Luminosity relationship on main sequence: L α M 4 or in the more expanded form: L/L(Sun) ~ [M/M(Sun)] 4 D. Basic Math & Conversion Factors Circumference, Area, Surface Area, and Volume of a Sphere Since most stars, star clusters, clusters of galaxies, etc are spherical, there are many instances where the formulas for the above dimensions are useful. 1 parsec (pc) = 206,265 astronomical units (au) = 3.26 light years (ly) = 3.08 x 10 16 m ; 1° = 60 arcmin = 60´ ; 1´ = 60 arcsec = 60˝ 121 Derivations and Sample Problems: Parallax 122 123 Derivations and Sample Problems: Orbital Mechanics 124 125 Derivations and Sample Problems: Radiation Laws 126 127 Derivations and Sample Problems: The Distance Modulus and Luminosity 128 129 Derivations and Sample Problems: Hubble's Law and the Doppler Effect 130 131 Introduction to DS9 Image Analysis Software The home page for the Chandra Education Data Analysis Software and Activities provides a link to a system that allows educators, students, amateur astronomers and the general public to perform X-ray astronomy data analysis using data sets from the Chandra X-ray Observatory, the DS9 image display program, and astrophysical software analysis tools. This allows you to experience much of the same analysis process that an X-ray astronomer would follow in analyzing the data he or she has received from a Chandra Observation. Chandra data analysis requires a level of computing power that is not often found outside of scientific research institutions. Chandra data sets are huge (often taking a Gigabyte of disk space or more) and programs written to analyze these data require very fast CPUs. The programs themselves are almost always written for the UNIX environment: popular commercial systems such as Windows are just not powerful or flexible enough to handle the complex tasks embodied in these programs. Therefore, a system has been developed in which you need only run a single Chandra program on your computer: the DS9 image display. Using DS9 and either the Chandra or Rutgers websites to access the data sets, you will be able to display Chandra data without having to transfer the huge data sets to your computer. You will be able to view the data in different ways, and select regions of the data that interest you. And finally, you will be able to run analysis programs on these data, the same programs used by X-ray astronomers. The actual "number crunching" will be performed on powerful UNIX computers at the Smithsonian Astrophysical Observatory (SAO). Results such as images, graphs and charts will be sent back to you from the Smithsonian Astrophysical Observatory for display in DS9 on your own computer. To use the Chandra Education data analysis software and activities, the first thing that you must do is to install the imaging system ds9 on your computer. The Chandra-ed website http://chandra-ed.harvard.edu/install.html provides a step-by-step guide on how to download the DS9 software onto your computer, and how to access x-ray data for several objects that have been imaged by Chandra. The DS9 software will accept any FITS file image, so eventually you can use DS9 to study images in radio, optical, and other wavelengths. It may be easier for you to use the tutorial provided on the following pages if you are unfamiliar with using software image analysis programs. It is not very much different than the tutorial on the website; however, it does provide screen shots so you can see what the image should look like when using the tools. 132 DS9 Image Analysis Software Installing the DS9 Toolbox on your Desktop: A. Access the URL: http://chandra-ed.harvard.edu/ B. In the New Users box click on Step 1: Install the System C. Scroll down to the following section and click on the operating system you want to download: Directions for installation of ds9: Currently, ds9 can be installed on systems running the operating systems listed below. Please select the links below for (1) Windows OS, (2) Mac OS or (3) Unix OS. If the version of the operating system that you run is not listed in one of those categories (i.e Windows 95, Mac OS9), you most likely will not be able to install ds9. If you have further questions or issues about installation or wish to contact us for help, view the installation notes. NOTE: The download might take a while, especially when using a slow modem, so plan to do the installation well before you want to use the system. 1. For Windows Vista/XP/2000/NT 2. For MacOSX (Tiger/Leopard) 3. For Linux, LinuxPPC, Solaris, SGI, Alpha OSF1, HP-UX D. [NOTE: The follow directions assume that you are installing in a Windows environment.] After clicking on number 1 above, a new page opens: http://chandra-ed.harvard.edu/install_win.html E. In Step 1 click on the word here. The URL http://hea-www.harvard.edu/RD/ds9/ opens up with the title: SAOImage DS9: Astronomical Data Visualization Application. F. Scroll down to DS9 Version 6.0 Binaries Click Windows 7/Vista/XP G. A window opens up asking if you want to open the file or if you want to save it to disk. Check the box for Save to Disk. H. When the next box opens up click on Desktop (it is easier to save the program to the desktop. You can move it somewhere else after the file has been extracted.) Click on save. The zipped file, ds9.windows, is now on your desktop. I. Double click on the ds9.windows file. An unzip window will appear. Click on browse, and then on desktop - so the file will be extracted to the desktop. Click on unzip. J. On your desktop are two new icons, ds9 and cygwin1.dll. Create a folder named DS9 and place both icons in the folder. K. You now have installed a virtual Linux software system onto your desktop. When You use DS9 analysis commands, the analyses are performed on a dedicated Linux server farm at the Harvard-Smithsonian Astrophysical Observatory in Cambridge, Massachusetts. The URL http://chandra-ed.harvard.edu/ contains more detailed installation instructions if you need them. These instructions are a summary of those on the website. 133 Learning to Use the DS9 Imaging Analysis Software: Open the ds9 folder and double click on the DS9 icon. The window shown on the left will appear. Click on the word Analysis in the menu and a drop down menu will appear, like the windows shown on the right. Click on the words Virtual Observatory. A window will open and give you several sites to go to acquire images to drop into DS9. Eventually you can try all of these sites and decide which ones are easier for you to use. They are all useful and contain several objects. We will start by using the Rutgers site, because it is the quickest way to access an image to drop into the DS9 window. Click in the box next to the New Rutgers X-Ray Analysis Server URL. A list of Chandra-Ed images will appear. Click on Obs ID 114, ACID OBSERVATION OF CASA (first 5k seconds only). A window will appear stating that the loading of the Cas A image is complete. Close the window. Now look at the DS9 window, and you will see that the Type II supernova remnant Cas A is now loaded into the software analysis window. A complete description of all the menu tools is at: http://chandra-ed.harvard.edu/learning_ds9.html Scroll down to Looking at an X- ray Image – and there are three pages that explain the quantitative and analysis tools. Below is a very brief look at some of the menu tools. Play around with each of the tools to get a feel for how DS9 works. Co-ordinate Systems: 1. Click on Analysis. 2. Click on Coordinate Grid. 3. Click on Coordinate Grid Parameters and leave open. 4. Click on WCS and in the drop-down menu click on Equatorial J2000. Click on Galactic. 5. Under the Analysis menu click on Coordinate Grid Parameters. 6. Play around with the table. Close Parameters. 7. Click on Analysis. Click on display Co-ordinate Grid again to “unclick” it and remove the grid. 134 Color and Scales: Color: 1. Click on Color. Click on each color in the dropdown menu under Color. Select gray. 2. Grey is neutral – represents intensity (# of photons) without reference to energy (color). Shows # of photons that arrived during the observation. 3. Click on scale. Scale goes from black (0) to white (255). This is a Linear scale and it emphasizes bright features. 4. Ratio of bright to faint is 25:1; the ratio of bright to faint in a square root scale is 5:1 so a square root scale favors seeing faint features. SQRT Scales: 1. Click on Scale and then SQRT (square root). This scale brings out features too faint to be seen in the linear scale. 2. Click on Log. This scale emphasizes the faintest features and the brightest features no longer dominate the image. 3. Click on the other scales to see how the image changes. LOG 4. Click on SQRT. Click on Analysis. On the dropdown menu select Pixel Table. 135 Scales and Zoom: 1. Click on Zoom. On the dropdown menu select Zoom In. Repeat two more times. Individual pixels can be seen. 2. Move the cursor around the image and watch the upper right box. Note how the color changes when intensity changes. Zoom back out to original size and close the pixel table. 3. Toggle between SQRT and Log and look at the “blowout” area in the upper left region of the CASA remnant. Note how Log emphasizes the faintest regions, and SQRT emphasizes faint to medium bright regions. Summary of Scales: 1. The Log scale emphasizes the faintest regions. 2. The SQRT scale emphasizes faint to medium bright regions. 3. The Linear scale emphasizes medium bright to bright regions. 4. The Squared scale emphasizes only the brightest regions. LOG SQRT LINEAR SQUARED 136 Contours 1. Click on Analysis. 2. On the dropdown menu click on Contours. 3. Click on Analysis again. 4. On the dropdown menu click on Contour Parameters. 5. The contour lines enclose pixels of equal intensity. 6. The Contour Parameters menu allows you to change the number of contour levels and the contour smoothness. 7. Toggle between the Linear and Log scales and compare the contours. Contour Levels: 1. Click on Scale – Linear. 2. On the Contour Parameters menu change the number of levels to 30. Click on Generate and then click on Apply. 3. Click on Log, SQRT and Squared scales to compare the contour lines. 4. Change the number of levels and look at the levels in all four scales to see how the contour lines change. 5. The contour lines of equal pixel intensity are similar to lines of equal elevation on a topographic map. Contour Smoothness: 1. On the Contour Parameters menu change the Contour Smoothness to 20. Click on Generate, then click on Apply. 2. Click on Log, SQRT, and Squared scales to compare the contour lines. Note that the greater the level of smoothness, the larger the areas of equal pixel intensity. 3. Set the Contour Level to 5 and the Contour Smoothness to 4. 4. Close the Contour Parameters menu and unclick Contours. 137 Color – Contrast & Bias: 1. Click on Color in the upper menu bar. 2. On the dropdown menu click on Colormap Parameters. 3. Move Contrast to right. Notice the bottom bar compresses. Contrast controls how quickly you move from black to white. 4. Move Bias to right. Bias determines the level at which black changes to white. 5. Another way to do this is to right click and drag. Moving horizontally changes the Bias, and moving vertically changes the Contrast. 6. Leave Contrast at 1.0 and Bias at .50. 7. Close Colormap Parameters. Panning Tool: 1. Click on Linear Scale and Color Grey. 2. Left click, hold and drag from within blue viewing box. End with the image off-center. Alternatively you can click Edit on the horizontal menu, then Pan. NOTE: Pointer changes into a cross. 3. Click anywhere you wish to have the image centered. Click on your center. The image is now centered. 4. Click on Zoom and In. NOTE: the blue box gets smaller and you start seeing pixels. Each pixel is 0.5 arc seconds for Chandra. 5. The more pixels per area on the sky the higher the resolution and the “sharper” the image. 138 Regions: 1. Click on Edit (either menu) and click on pointer. 2. Go anywhere in the image and left click to get a Region. Left click again inside the Region so you can change its size and move it around. Four corners will appear around the Region. NOTE: If you get an unwanted Region, click on Region and then click on Delete All Regions. 3. Grab a corner by left clicking, hold, and drag to the desired size. Left click within the Region, hold and drag to different areas of the image. 4. For fine-tuning the placement, use the arrow keys to move the Region which the cursor is within the region. 5. Click on Regions, then click on Shape. Select Ellipse. Change its shape and move it around. 6. Delete all Regions. Horizontal and Vertical Cut Graphs: 1. Click on View, then Horizontal Graph. 2. Move the cursor up and down in the image. This graph displays the values in the horizontal (x-axis) lines of pixels. 3. Click on View, Unclick Horizontal Graph. Click on View again, and click on Vertical Graph. 4. This graph displays the values in the vertical (y-axis) lines of pixels. 5. Both the Horizontal and Vertical Graphs can be displayed simultaneously. 139 Horizontal and Vertical Cut Graphs Together: The procedures above are for the purpose of showing the different types tools that are available in DS9. If you have used this quick introduction, you should go to the DS9 website at http://chandra-ed.harvard.edu/learning_ds9.html and scroll down to looking at an x-ray image and follow those procedures. They describe the same set of tools; however, they are in a different sequence and have a good description of the purpose of each of the tools. You may want to practice dropping in other images, using both the Rutgers site and the Chandra site. The Chandra-Ed site also allows access to the thousands of Chandra observations. The images you are dropping into the DS9 image analysis software program are FITS files. FITS is an acronym for Flexible Image Transport System. This format is used in many areas of science besides astronomy, such as medical imaging. Any FITS image can be used with DS9 – not just X-ray. It is possible to compare an x-ray image with optical, radio, UV, or IR as long as the images are in the FITS file format. Once you are comfortable with using the tools, it is time to learn some of the analysis tools in DS9. Some of the analysis tools are determining counts in regions, radial profile plots, creating annuli regions and adjusting the annulus parameters, spectral analysis, energy spectrum plots, timing analysis, and plotting a light curve. An introduction to these analysis tools is at: http://chandra-ed.harvard.edu/learning_ds9part3.html 140 First Analysis Task: 1. Click on Analysis. Click on the dotted line at the top of the dropdown menu. Drag the menu to any convenient spot. 2. Click on Region, Shape, and select Annulus. 3. Center the pointer as close to the neutron star using as you can by using the arrow key and magnifier box. 4. Left click to generate. The concentric circle Annulus will appear. Left Click in the center to select. Corners will appear. 5. Left click on one of the corners, hold down and drag until the outer circle fills the entire remnant. 6. Double click inside the region to bring up the properties box. 7. In the Annulus properties box change the number of annuli from 1 to 10, and change the inner radius to 0. 8. Click Generate and then click Apply. 141 9. In the Analysis menu click on Chandra Ed Analysis Tools. 10. Click on Radial Profile Plot (Annulus regions, options: none). 11. A radial profile across the annuli that you generated will appear. 12. This is a graphical plot of the brightness of the X-ray emission (average number of photons per unit area) in concentric annuli around a central point. 13. Play around with changing the number of annuli, the inner radius, dragging the annuli around the image, and re-plotting. See example below. On the Chandra-Ed homepage http://chandra-ed.harvard.edu/index.html click on Step 3 - Images and Analysis Activities. When the next page opens up click on Cas A: The Supernova as Cosmic Recycling Center. This opens a page that has 6 activities that use the Cas A image and the DS9 tools: Activity 1: Pixels, Pixels, Everywhere Activity 2: What is the distance to Cas A and when did it explode? Activity 3: How big is it? Activity 4: Make a light curve Activity 5: Radial Intensity profile Activity 6: Make energy spectra Go through these activities to calculate information about the Cas A supernova event, and plot a light curve, radial intensity profile, and energy spectra for this supernova event. Samples of Activity 6 are on the following page. 142 Cas A Activity 6: Making Energy Spectra – Element Abundances Sample Results: Second Analysis Task: NOTE: This task requires accessing the Rutgers site through the virtual observatory to retrieve the Coma Cluster image. 1. Retrieve and load the Coma Cluster Image, Obs ID 1112 2. Click on Color and then b, then click on Scale and SQRT. 3. Click on Analysis and then Image Servers and SAO-DSS. On the windows that appears, click on Retrieve. WAIT! 4. Click anywhere on the X-ray image on the left to select an area. 5. In the menu at the top click on Frame. On the drop- down menu click on Match Frames, then WCS. 143 6. Click on Edit, then Crosshair. 7. Click on Frame, then Lock Crosshairs and WCS. The crosshairs are now locked in both images and you can match individual features in both the X-ray image on the left and the optical image on the right. 8. Click on Edit, then Pointer. 9. Click on Region, then Shape, then Ellipse. Click anywhere in the X-ray image. 10. Click anywhere inside the Ellipse so that the corners appear. Click on a corner and drag until it fills the cluster region. 11. Click on Analysis, then Chandra Ed Analysis Tools, then Quick Energy Spectrum Plot. NOTE: Any questions on National Science Olympiad Astronomy events will use screen shots and the questions will be general in nature - covering the same information in this tutorial. 144 DS9 Investigations and Activities: A series of image analysis activities and investigations have been developed that focus on one of the ds9 tools. Complete instructions are included within the activity. Reading the tutorial outlined above is not necessary. Ds9 Image Analysis and the Multi-Wavelength Universe: A. 3-Color Composite Images – ds9 Activity Purpose: To produce three-color composite images of supernova remnants from Chandra X-ray Observatory data showing the areas of low, medium and high energies. Introduction and Background – Images and Color: The colors we see are the result of how the human eye and brain perceive different wavelengths of light in the visible part of the electromagnetic spectrum – roughly radiation in the range of 380 nm to 740 nm. The ability of the human eye to distinguish colors is based on the varying sensitivity of different cells in the retina to light of different wavelengths. The retina contains three types of color receptor cells, or cones. Light, no matter how complex its composition of wavelengths, is reduced to three color components by the eye. For each location in the visual field, the three types of cones yield three signals based on the extent to which each is stimulated: red, blue and green. True-color images of a subject are images that appear to the human eye exactly like the original subject would: a blue sky is blue, a red apple is red, and green grass is green. A false-color image is an image that depicts a subject in colors that differ from those a faithful full-color photograph would show. The term false-color is typically used to describe images whose colors represent measured intensities outside the visible portion of the electromagnetic spectrum. Astronomical images are false-colored images. A false- color image is not incorrect – it is an arbitrary selection of colors chosen to represent some characteristic in an image, such as intensity, energy or chemical composition. The colors selected are representative of the physical processes underlying the objects in the images, and display in a single image as much information as possible that's available from the data. The data are transported into image analysis software where adjustments are made to emphasize the individual features or processes that scientists are interested in – or enhanced to make the images more interesting to the public. Although computers and software are used extensively, scientists and programmers go through painstaking calibration and validation processes to ensure that technically correct images are produced. The colors used for the 145 images are selected to emphasize specific information within the data. The color selections used by the Chandra X-ray images are usually associated with intensity or brightness, or energy. For example, in the yellow and orange Chandra X-ray image of the Cas A supernova remnant to the right, the white and yellow colors represent the areas of highest X-ray intensity, the orange to red areas represent the areas of lower intensity, and the black represents little or no emission. Cas A SNR (Chandra) The X-ray image of the pulsar 3C58 on the left shows an image constructed by selecting different X-ray energy bands from the data and representing them with different colors – red, green, and blue. The result is a 3-color composite image. The low, medium, and higher X-ray energy bands of the 3C58 (Chandra) Chandra data are shown as red, green, and blue respectively. In this particular image, red, green and blue represent X-ray energy bands of 0.5 to 1.0 kilovolts, 1.00 to 1.5 kilovolts, and 1.5 to 10 kilovolts, respectively. In this activity, two image analysis software programs, ds9 and ImageJ, are used to construct a three-color composite image of the Cas A supernova remnant. The red, green, and blue regions in the composite will show the intensities of low, medium, and high-energy X-rays – as in the composite image of 3C58 above. The ds9 software utilizes data sets and astrophysical analysis tools from the Chandra X-ray Observatory. The program uses the same process that X-ray astronomers follow in analyzing the data from Chandra observations. The download instructions to install the ds9 toolbox on your desktop are located at http://chandra-ed.harvard.edu/install.html. The introduction at http://chandra-ed.harvard.edu/learning_ds9overview.html describes the overview and purpose of the software and gives a short summary of the Chandra mission. The tutorial for using the ds9 software is located at http://chandra ed.harvard.edu/learning_ds9.html. ImageJ is a software program developed by the National Institute of Health and is available for download from http://rsbweb.nih.gov/ij/download.html. NOTE: It is not necessary to read the tutorial before beginning the 3-Color Composite Images – ds9 Activity . Complete instructions to use the image analysis tools in ds9 are given in the following procedure. Procedure: 1. Download and install ds9 according to the instructions on the Chandra-Ed web site. 2. Open ds9 and maximize the screen. From the pull down menus, choose Analysis>Virtual Observatories and choose Chandra-Ed Archive Server or New Rutgers X-ray Analysis Server from the list that appears. 3. Click Obs ID 114 ACIS OBSERVATION OF CAS A (first 5K seconds only) in the new window that appears. 146 4. Use Analysis>Chandra Ed Analysis Tools>Energy Filter to show only the x- rays in the soft band (lo = 0.6 KeV, hi =1.65 KeV). Leave “Display all images in tile mode?” and “Save image for further analysis” checked. 5. When the new image comes up in a second frame (the frame should be lined in blue, if not, click this frame), go to File>Save Frame as FITS. Name this file casared.fits. Choose Frame>Delete Frame to leave only your original image. 6. Repeat steps #4-5 for the medium (1.65-2.25 KeV) and the hard (2.25-7.50 KeV) bands, saving them as casagreen.fits and casablue.fits, respectively. 7. Download and install ImageJ and run the program. 8. Go to File>Open three times to load casared.fits, casagreen.fits and casablue.fits. 9. Go to Image>Color>RGB Merge. From the pull-down menus in the new window, choose the appropriate files to go with each color as shown below and click OK. 10. You now have a three-color composite of Cas A. You can use the following tools to enhance the image to emphasize different features. • Image>Adjust>Size • Image>Adjust/Brightness/Contrast • Image>Adjust/Brightness/Color Balance • Process>Smooth • Process>Sharpen 147 Extension: Use the same method to produce 3-color composite images for the following two objects. Obs ID 7639 - A Deep Chandra Observation of the Tycho Supernova Remnant Obs ID 115 - ACIS Observation of Tycho and Kepler If the Obs ID for the SNR you wish to investigate is not in list in the internal browser window, scroll to the bottom of the page and click on Unofficial Chandra Public Archive. Enter your Obs ID and click “Search” – then click on the Title of a returned observation to load it into ds9. 148 B. 3-Star Formation and U/HLX’s in the Cartwheel Galaxy – ds9 Activity The Cartwheel Galaxy The Cartwheel Galaxy is part of a group of galaxies ~five hundred million (500x10 6 ) light years away in the direction of the constellation Sculptor. The composite image to the left shows the unique structure of the Cartwheel Galaxy. The image combines data from four different observatories: the Chandra X-ray Observatory (purple); the Galaxy Evolution Explorer satellite (ultraviolet/blue); the Hubble Space Telescope (visible/green); and the Spitzer Space The Cartwheel Galaxy Telescope (infrared/red). The ring-shaped rim of the Multi-Wavelength Composite Cartwheel Galaxy is the result of a rare and spectacular head-on collision between two galaxies. The Cartwheel Galaxy was probably a normal spiral structure galaxy similar to the Milky Way Galaxy before the collision; the spiral structure is beginning to re-emerge, as seen in the faint arms or spokes between the outer ring and the bulls-eye shaped nucleus. The gravitational disruption of a smaller intruder galaxy passing through the Cartwheel Galaxy compressed the interstellar gas and dust – causing a wave of star formation to move out from the impact point like a ripple across the surface of a pond. The image to the right is a composite showing an optical image of the Cartwheel galaxy and several smaller galaxies associated with the Cartwheel group superimposed with high resolution radio observations of neutral hydrogen (traced by the green contours). The neutral hydrogen trail suggests that the intruder galaxy could be the galaxy located at the lower left of the image. The Intruder Galaxy (NRAO, ISU, Hughes STX, STScI, NASA) The Cartwheel Galaxy provides an opportunity to study how extremely massive stars are born in large fragmented gas clouds. The ring structure contains several billion new stars that would not normally have been created in such a short time span. When the most massive of these stars undergo catastrophic collapse as supernova events, neutron stars and black holes are formed. Young supernovas and supernova remnants are ultra and hyperluminous X-ray sources (U/HLXs). Some of the neutron stars and black holes are in contact binary systems with companion stars. Material is pulled from the companion stars and forms accretion discs around the neutron stars and back holes due to their extreme gravitational fields. The in-fall of material from the accretion disc produces highly energetic X-rays, and these systems are also classified as U/HLXs. U/HLX’s Cartwheel Galaxy (Chandra) 149 Image Analysis of the Cartwheel Galaxy The following activity has been designed for students to examine the Cartwheel Galaxy in both optical and X-ray bands and determine the sources that are producing the ultra and hyperluminous X-ray emissions (U/HLX’s). The activity uses ds9 – an image analysis software package. Ds9 allows the user to download a toolbox onto their desktop and remotely access dedicated Linux servers which process the analysis commands. The ds9 image analysis software allows educators, students, amateur astronomers and the general public to perform X-ray astronomy data analysis using data sets from the Chandra X-ray Observatory, the ds9 image display program, and astrophysical software analysis tools. The program uses the same analysis process that an X-ray astronomer would follow in analyzing the data from a Chandra observation. The download instructions to install the ds9 toolbox on your desktop are located at http://chandra- ed.harvard.edu/install.html . The introduction at http://chandra- ed.harvard.edu/learning_ds9overview.html describes the overview and purpose of the software and gives a short summary of the Chandra mission. The tutorial for using the ds9 software is located at http://chandra-ed.harvard.edu/learning_ds9.html. NOTE: It is not necessary to read the tutorial before beginning the Star Formation and U/HLXs in the Cartwheel Galaxy activity. All ds9 educational activities are constructed to use one or two specific software tools, and complete constructions to use the tools are given within the individual activities. Star Formation and U/HLXs in the Cartwheel Galaxy Purpose: To examine and compare the Cartwheel Galaxy in optical and X-ray bands and determine the sources of the ultra- and hyperluminous x-rays (U/HLXs). Procedure: Install the software and load the FITS file (data/image file): 1. Download and install ds9 according to the instructions on the Chandra-Ed web site. 2. Open ds9. From the menus, choose Analysis>Virtual Observatory>Chandra- Ed Archive Server. 3. In the new window that comes up, scroll down to and click ObsID 2019 – THE CARTWHEEL’S RING. 4. When the image is loaded, go back to the SAOImage ds9 window. Maximize your screen. Choose Scale>Square Root and Color>b. Acquiring the optical image: 5. Choose Analysis>Image Servers>SAO-DSS and then click Retrieve in the new window that comes up. What are the coordinates of the Cartwheel Galaxy? right ascension–α ___________________, declination–δ ___________________ 150 6. With the new frame on the right chosen (it should be outlined in blue), choose Zoom>Zoom 4. Center the Cartwheel Galaxy in the frame by moving the blue rectangle over it in the small image in the upper right corner (see below). Matching up the x-ray and optical images: 7. With the frame on the right still chosen, go to Frame>Match Frames>WCS. 8. Click the frame on the left. Adjust the contrast and bias to better see the point x- ray sources using Colors>Colormap Parameters (suggested settings, Contrast– 4.4, Bias–0.25). 9. Contour lines may help define these x-ray sources. Go to Analysis>Contours and then Analysis>Contour Parameters. In the new window, use these settings: Contour levels–10, Contour Smoothness–1, Low–0, High–550 and then click Generate, Apply and Close. 10. To explore where these x-rays sources are located in the optical image, choose Edit>Crosshair and Frame>Lock Crosshairs>WCS. Move your cursor (while holding the left click) over the x-ray point sources. Note their locations on the optical image. Determining the size of the ring: 11. Go to Edit>Pointer. Click the right frame. Left click (hold this down) in the center of the Cartwheel Galaxy and drag a circular region around the galaxy. The region should be just big enough to enclose the entire ring. Once you have drawn the region, if you left click on it again, green squares will appear in the corners of the region. You can left click in the center and drag the circle to the correct spot if it is slightly off-center or change the size by left-clicking on one of the green squares at the corner and dragging. 12. Click on the left frame. Go back to Edit>Crosshair. Move the crosshairs on the x-ray image to determine the diameter of the region you drew in #11 in the optical image. Record the physical x- and y-coordinates (see upper left corner of the window) of two points on opposite sides of the circle. 151 (x 1 , y 1 ) = ( ________ , ________ ) (x 2 , y 2 ) = ( ________ , ________ ) Find the distance in pixels between these points using 13. In a Chandra observation, 1 pixel = 0.5 arc sec. Also, 1 radian = 206,265 arc sec. Convert your answer from #12 to radians. 14. Use the small angle formula below to determine the size of the ring in light years. The distance to the Cartwheel Galaxy is ~380 million light years. How does the size of the ring compare to that of the Milky Way Galaxy (~100,000 light years in diameter)? angular size in radians= (actual size of object) / (distance to object) Conclusions and Analysis: The gravitational disruption of a smaller intruder galaxy passing through the Cartwheel Galaxy compressed the interstellar gas and dust – causing a wave of star formation to move out from the impact point like a ripple across the surface of a pond at ~200,000 mi/hr. The wave of new star formation from the head- on collision has produced the ring-like structure seen in the optical image to the right. Cartwheel Galaxy (Hubble) 1. In the Hubble image above, the bright blue knots represent areas of new star formation. How do the locations of the majority of X-ray sources compare to these areas? 2. Using the information above and your answer to #14, determine how long ago the collision of galaxies may have occurred. (1 light year = 5.87849981 × 10 12 miles) 152 The supermassive black hole at the center of an Active Galaxy is called an Active Galactic Nucleus or AGN. Galaxies that contain an AGN emit enormous amounts of radiation (radio, optical, X-rays, gamma rays) and particle jets and are highly variable. X-rays from AGNs are produced when in-falling matter from the surrounding disk Chandra AGN Illustration is heated to temperatures of millions of degrees as it swirls toward the supermassive black hole. Some of the in-falling material escapes as a hot wind that is blown away from the disc at speeds as high as a tenth of the speed of light. 3. From your comparison of the x-ray and optical images of the Cartwheel Galaxy, does it seem to have an AGN? Explain. 4. Use your knowledge of stellar evolution, your ds9 analysis, and the chart of stellar life spans below to explain what types of objects each of the X-ray sources might be. You may have different answers depending upon the location of the X- ray source (i.e. along the ring, within the ring, outside the ring). Star Mass (solar masses) Time (years) Spectral Type Color 60 3 million O3 bluest 30 11 million O7 bluest 10 32 million B4 bluish 3 370 million A5 blue-white 1.5 3 billion F5 white 1 10 billion G2 (Sun) yellow 0.1 1000’s billion M7 red 5. Compare your findings to those published in the paper, Nonnuclear Hyper/Ultraluminous X-Ray Sources in the Starbursting Cartwheel Ring Galaxy, Yu Gao, 1 Q. Daniel Wang, 1 P. N. Appleton, 2 and Ray A. Lucas 3 , The Astrophysical Journal Letters, 596:L171–L174, 2003 October 20. http://www.iop.org/EJ/article/1538-4357/596/2/L171/17541.html 153 Extensions: Suggestions for further investigations of colliding or starburst galaxies using ds9. 1. The Antennae: Chandra Locates Mother Lode of Planetary Ore in Colliding Galaxies http://chandra.harvard.edu/photo/2004/antennae/ 2. M82: Images From Space Telescopes Produce Stunning View of Starburst Galaxy http://chandra.harvard.edu/photo/2006/m82/index.html To load the images into ds9, go to Analysis>Virtual Observatory>Chandra-Ed Archive Server. In the new window that comes up, scroll down to the bottom of the page and click Unofficial Chandra Public Archive. In the next window enter the OBS ID given in “Fast Facts” section of the links above. Click Search and then the link that comes up under Title. In addition to the type of analysis you have done in this activity, you can analyze the spectra of these galaxies. Instructions for analyzing spectra are in the ds9 activity, X-Ray Spectroscopy of Supernova Remnants. Answers for Star Formation and U/HLXs in the Cartwheel Galaxy ds9 Activity Determining the size of the ring: 12. The diameter of the ring is ~170 pixels. 13. 170 pixels (0.5 arcsec / 1 pixel)(1 rad / 206,625 arc sec) = 0.00041 rad 14. (0.00041 rad)(380 ly) = 160,000 ly Conclusions and Analyses: 1. Most of the X-ray sources are along the lower part of the ring where Hubble observed bright blue knots that are gigantic clusters of newborn stars. 2. Using the expansion rate given in the background material and the distance the ring has moved from the center (half your answer to #14): (200,000 mi/h) / (5.88 X 10 12 mi/ly) X (24 h/day) X (365.25 days/y) = 0.0003 ly/y v = d/t so t = d/v = (80,000 ly) / ( 0.0003 ly/y) = 300 million years 3. No, there is no X-ray source corresponding to the galactic nucleus as seen in the optical image. 4. Answers may vary, but X-ray sources along the ring could be supernova remnants, neutron stars or black holes because the lifetime of a massive star is less than 300 MY which is approximately when the galaxy collision occurred and new star formation was triggered. 154 5. From Nonnuclear Hyper/Ultraluminous X-Ray Sources: A. “It has been argued on observational and theoretical grounds (Appleton & Struck- Marcell 1996; Bransford et al. 1998) that the triggering of newly formed stars in ring galaxies occurs approximately simultaneously as the wave propagates out through the disk—the outer ring representing the most recently formed stars, with representative ages < 10 7 yrs. In this picture, the ring represents the outermost progress of a wave that began at the disk-center some 300 Myrs previously, created by the central perturbation of the intruder, either G3 or G1.” B. “Almost all the X-ray emission in the Cartwheel originates from point-like sources within the southern quadrant of the outer ring. The sources are nearly coincident with the strong H , radio continuum emission and blue super-star clusters (SSCs).” C. “The companion galaxy G1 (spiral) contains 6 point-like X-ray sources, and the early-type spiral G2 is seen as a fainter diffuse source (Fig 1). The farthest companion galaxy G3 is also significantly detected, with one ULX in the eastern edge of its disk. In addition, a faint, diffuse X-ray envelope which includes the Cartwheel, G1 and G2 is marginally detected.” D. “The absence of any point-like X-ray source in the nuclear region of the Cartwheel rules out the existence of AGN.” E. “A point-like source 31, 10 kpc north of G2, is likely a background galaxy or AGN as it has a faint optical counterpart in the HST image.” F. “The two most likely sources of X-ray emission associated with massive young star-forming regions are probably supernovae (SNe) or extremely young SN remnants (SNRs) and the high-mass X-ray binaries (HMXBs). We can almost rule-out low-mass X-ray binaries (LMXBs) to be the significant sources for H/ULXs along the Cartwheel narrow ring, although intermediate mass black holes (IMBHs, see review by Miller & Colbert 2003) are likely viable. It is conceivable that LMXBs and/or background sources could be responsible for the three ULXs interior to the ring. Three “ULXs” outside the Cartwheel with faint optical counterparts are likely background galaxies. “ The Cartwheel Galaxy Image URL’s The Cartwheel Galaxy http://chandra.harvard.edu/photo/2006/cartwheel/ The Intruder Galaxy http://apod.nasa.gov/apod/ap970224.html U/HLX’s Cartwheel Galaxy http://chandra.harvard.edu/photo/2006/cartwheel/cartwheel_xray.jpg Hubble Optical http://chandra.harvard.edu/photo/2006/cartwheel/cartwheel_opt.jpg Chandra Illustration AGN http://chandra.harvard.edu/resources/illustrations/quasar2.html#accret_reddisk X-Ray Spectroscopy of Supernova Remnants. http://chandra.harvard.edu/edu/formal/snr/ds9.html 155 156 Ds9 Image Analysis and Stellar Evolution: The two investigations in this section also have a pencil and paper versions which can be used if computers and/or the internet is not available. C. Estimating the Age of Supernova Remnants – ds9 Version Purpose: To use the observed size of the Cassiopeia A supernova remnant (SNR) from its X-ray image and an estimated rate of expansion to calculate its approximate age. Background: There is controversial evidence that the British astronomer John Flamsteed observed and recorded the Cas A supernova event in his journal on the evening of August 16 th , 1680. He observed a star that was near the position of Cas A, not observed by anyone else, and was never seen again – it could have been the explosion that produced Cas A. The Cas A remnant is ~11,100 light years away, and if John Flamsteed did observe the catastrophic Cassiopeia A: Chandra’s 1 st Light collapse of the massive star August 19, 1999, NASA/CXC/SAO ~330 years ago, the supernova event occurred approximately 11,430 years ago. There are some scientific methods of analyzing supernova remnants to try and determine Historia Coelestis, 1725 their age; this activity utilizes ds9 image analysis software and Chandra X-ray observational data. Ds9 allows users to download a toolbox onto their desktop and remotely access dedicated Linux servers which process the analysis commands .The download instructions to install the ds9 toolbox on your desktop are located at http://chandra-ed.harvard.edu/install.html . The introduction at http://chandra- ed.harvard.edu/learning_ds9overview.html describes the overview and purpose of the software and gives a short summary of the Chandra mission. The tutorial for using the ds9 software is located at http://chandra-ed.harvard.edu/learning_ds9.html. NOTE: It is not necessary to read the tutorial before beginning the Estimating the Age of Supernova Remnants activity. Complete instructions to use the image analysis tools in ds9 are given in the following procedure. All necessary equations and conversion factors are listed at the end of the activity. Procedure: How Big is Cas A? 1. Install ds9 if it is not already on your computer. 2. Open ds9. Go to Analysis>Virtual Observatory. Choose any of the servers from the menu that appears. 157 3. Choose Obs ID 114, ACIS OBSERVATION OF CAS A from the menu that appears. The Cas A image should appear in your ds9 window. 4. To better view the edges of Cas A, choose Scale>Square Root and Color>Invert Colormap. 5. Left click on the black dot (neutron star) in the center. Holding the left click button down, drag a circular region around the edges of the supernova remnant. Exclude the jet in the upper left from the region—the dynamics of this jet formation are different that those of the overall expansion of the SNR. 6. Left click in the center of the green region to select it. Adjust the radius of the region by positioning the pointer over one of the square boxes in the corner and left clicking and dragging the pointer. Adjust the position of the region by putting the pointer in the middle, left clicking and dragging. 7. Select Region>Get Info… Record the radius of your region (and of Cas A) in pixels and also the x- and y-coordinates of the center of the region – you will need the radius in #10 below. Make sure it says “physical” next to each of these. 8. To find the radius of Cas A in meters, use the small angle approximation. Imagine the lines of sight from Cas A to Earth. These lines form an angle, θ. On a Chandra image, 1 pixel corresponds to 0.5 arc seconds of angle. Find the angular size of the radius of Cas A in arc seconds and convert to radians. 9. The lines of sight are the radii of an imaginary circle with Earth at the center and Cas A on the circumference. The radius of this circle is the distance to Cas A. For very small angles, the radius of Cas A is approximately equal to the arc length transcribed by these lines of sight. Therefore, the small angle formula is as follows, where θ is in radians: θ = (radius of Cas A) / (distance to Cas A) Using the small angle formula and a distance to Cas A of ~11,100 light years, find the radius of Cas A in meters. What is the rate of expansion of Cas A? The average amount of energy released in a supernova explosion is ~10 44 Joules, and approximately one quarter of the energy drives the expansion of the remnant. Although the initial explosion ejects the outer layers of the star, most of the gas in the remnant is not from the star itself. As the ejected material expands outwards, it encounters and intermingles with the interstellar medium and propels it outward, building up the outer shock wave. The volume through which the remnant has expanded and the density of the interstellar medium determine the amount of material in the shell. On average this density is approximately 10 -21 kg/m 3 . 10. The Cas A SNR is basically a sphere. Determine the mass of the gas within the remnant using the radius previously calculated in #7 above. 158 11. Calculate the velocity of the gas (the expansion velocity of Cas A). 12. Use the expansion velocity and the radius of Cas A to estimate its age. Convert from seconds to years. 13. What is the displacement of the remnant from the center of the SNR? 14. In the center of the remnant, you can see a dot that is the remaining core of the collapsed star. Find the physical x- and y-coordinates of the core by moving the pointer over the core remnant (this will appear as a dark gray dot towards the center of the remnant with Invert Colormap). The box in the upper right corner gives you a close up view of where your pointer is. With the pointer over the core remnant, record the x- and y-coordinates next to “Physical” in the table at the top left. 15. Use the coordinates of the center of the region (from #7 above) to find the displacement of the stellar core from the center. 16. Find the average velocity of the stellar core for this displacement. 17. Using this average velocity, find its kinetic energy. Evidence indicates the core is a neutron star with a typical mass of about 1.4 solar masses. Conclusions and Analysis: 1. How does your estimated age for Cas A compare to 330 years? Does it have the same order of magnitude? 2. What approximations and assumptions were made in this method of estimating the age of a supernova remnant? How might these affect the results? 3. Could Cas A be the supernova observed by John Flamsteed in 1680? Why or why not? Extensions: 11. Use the same age determination method for other supernova remnants. Find scientific papers and historic accounts of these supernovas and compare your calculated results to the ages found in your research. Distances to many SNR and the Obs IDs necessary to load the image into ds9 are located in the Chandra Photo album at http://chandra.harvard.edu/photo/category/snr.html Some suggestions: Try G11.2-0.3 (Obs IDs 780, 781, 2322) (could this be the “Guest Star” of 386 AD, witnessed by Chinese astronomers?) or Tycho's Supernova Remnant (Obs IDs 115, 3837) (note: this is a type Ia supernova event and does not have a core remnant). 159 If the Obs ID for the SNR you decide to investigate is not in list in the internal browser window, scroll to the bottom of the page and click on Unofficial Chandra Public Archive. Enter your Obs ID and click “Search” – then click on the Title of a returned observation to load it into ds9. 12. Research other methods of determining the ages of supernova remnants and describe your findings. Resources: The Three-dimensional Structure of the Cassiopeia A Supernova Remnant http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1995ApJ...440..706R The “Guest Star” of 386AD http://www.geocities.com/perry_science/chandra_activities/Supernova_G11_Activit y.doc Chandra X-Ray Observations of G11.2-0.3: Implications for Pulsar Ages http://www.iop.org/EJ/abstract/0004-637X/560/1/371 Finding the Age of Supernova Remnant N157B http://imagine.gsfc.nasa.gov/docs/features/news/25feb98b.html Survivor Found From Tycho's Supernova http://www.universetoday.com/am/publish/tycho_supernova_survivor.html A VLA Study of the Expansion of Tycho's Supernova Remnant http://www.iop.org/EJ/abstract/0004-637X/491/2/816/ 160 Equations and Conversion Factors Conversion Factors/constants: 60 arc sec = 1 arc min 60 arc min = 1 deg 360 deg = 2π rad 1 light year = 9.46 × 10 15 meters mass of the sun = 2.0 X 10 30 kg Small Angle Formula: angle in radians (θ) = [arc length (s)] / [radius (r)] therefore, for astronomical objects with small angular sizes: angular size as viewed from Earth (θ) = (actual size of object) / (distance to object) Additional Equations: density = mass/volume volume of a sphere = 4/3 π r 3 kinetic energy = ½ (mass)(velocity) 2 velocity = distance/time distance between 2 points = sqrt [ (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 ] 161 Estimating the Age of Supernova Remnants – Pencil and Paper Version Purpose: To use the observed size of the Cassiopeia A supernova remnant (SNR) from its X-ray image and an estimated rate of expansion to calculate its approximate age. Background: There is controversial evidence that the British astronomer John Flamsteed observed and recorded the Cas A supernova event in his journal on the evening of August 16 th , 1680. He observed a star that was near the position of Cas A, not observed by anyone else, and was never seen again – it could have been the explosion that produced Cas A. The Cas A remnant is ~11,100 light years away, and if John Flamsteed did observe the catastrophic Cassiopeia A: Chandra’s 1 st Light collapse of the massive star August 19, 1999, NASA/CXC/SAO ~330 years ago, the supernova event occurred approximately 11,430 years ago. There are some scientific methods of analyzing supernova remnants to try and determine Historia Coelestis, 1725 their age; one method is using ds9 image analysis software and Chandra X-ray observational data. Procedure: How Large is Cas A? 1. Record the radius of Cas A in pixels given in the “Circle” information box on the ds9 screenshot shown in Fig. 1. Note that the jet in the upper left has been excluded from the region surrounding Cas A – the dynamics of this jet formation are different that those of the overall expansion of the SNR. Record the x- and y- coordinates of the center of the region to use in #8 below. 2. To find the radius of Cas A in meters, use the small angle approximation. Imagine the lines of sight from Cas A to Earth. These lines form an angle, θ. On a Chandra image, 1 pixel corresponds to 0.5 arc seconds of angle. Find the angular size of the radius of Cas A in arc seconds and convert to radians. 3. The lines of sight are the radii of an imaginary circle with Earth at the center and Cas A on the circumference. The radius of this circle is the distance to Cas A. For very small angles, the radius of Cas A is approximately equal to the arc length transcribed by these lines of sight. Therefore, the small angle formula is as follows, where θ is in radians: θ = (radius of Cas A) / (distance to Cas A) 162 Using the small angle formula and a distance to Cas A of ~11,100 light years, find the radius of Cas A in meters. What is the rate of expansion of Cas A? The average amount of energy released in a supernova explosion is ~10 44 Joules, and approximately one quarter of the energy drives the expansion of the remnant. Although the initial explosion ejects the outer layers of the star, most of the gas in the remnant is not from the star. As the ejected material expands outwards, it encounters and intermingles with the interstellar medium and propels it outward, building up the outer shock wave. The volume through which the remnant has expanded and the density of the interstellar medium determine the amount of gas in the shell. On average this density is approximately 10 -21 kg/m 3 . 4. The Cas A SNR is basically a sphere. Determine the mass of the gas within the remnant using the radius previously calculated in #1. 5. Calculate the velocity of the gas (the expansion velocity of Cas A). 6. Use the expansion velocity and the radius of Cas A to estimate its age. Convert from seconds to years. What is the displacement of the core remnant from the center of the SNR? 7. A dot located in the center of the remnant is the remaining core of the collapsed star. Use figure 2 to find the physical x- and y-coordinates of the core. 8. Use the coordinates of the center of the region (from #1 above) to find the displacement of the stellar core from the center. 9. Find the average velocity of the stellar core for this displacement. 10. Using this average velocity, find its kinetic energy. Evidence indicates the core is a neutron star with a typical mass of about 1.4 solar masses. Conclusions and Analysis: 4. How does your estimated age for Cas A compare to 330 years? Does it have the same order of magnitude? 5. What approximations and assumptions were made in this method of estimating the age of a supernova remnant? How might these affect the results? 6. Could Cas A be the supernova observed by John Flamsteed in 1680? Why or why not? 163 Extensions: Research other methods of determining the ages of supernova remnants and describe your findings. Resources: The Three-dimensional Structure of the Cassiopeia A Supernova Remnant http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1995ApJ...440..706R The “Guest Star” of 386AD http://www.geocities.com/perry_science/chandra_activities/Supernova_G11_Activit y.doc Chandra X-Ray Observations of G11.2-0.3: Implications for Pulsar Ages http://www.iop.org/EJ/abstract/0004-637X/560/1/371 Finding the Age of Supernova Remnant N157B http://imagine.gsfc.nasa.gov/docs/features/news/25feb98b.html Survivor Found From Tycho's Supernova http://www.universetoday.com/am/publish/tycho_supernova_survivor.html A VLA Study of the Expansion of Tycho's Supernova Remnant http://www.iop.org/EJ/abstract/0004-637X/491/2/816/ 164 Figure 1. Finding the radius of Cas A 165 Figure 2. Locating the core remnant (physical coordinates) 166 Equations and Conversion Factors Conversion Factors/constants: 60 arc sec = 1 arc min 60 arc min = 1 deg 360 deg = 2π rad 1 light year = 9.46 × 10 15 meters mass of the sun = 2.0 X 10 30 kg Small Angle Formula: angle in radians (θ) = [arc length (s)] / [radius (r)] therefore, for astronomical objects with small angular sizes: angular size as viewed from Earth (θ) = (actual size of object) / (distance to object) Additional Equations: density = mass/volume volume of a sphere = 4/3 π r 3 kinetic energy = ½ (mass)(velocity) 2 velocity = distance/time distance between 2 points = sqrt [ (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 ] 167 Investigating Supernova Remnants with X-ray Spectroscopy Introduction and Background: RCW 86 is a supernova remnant that was created by the destruction of a star approximately two thousand (2000) years ago. This age matches observations recorded by the Chinese and the Romans in 185 A.D. RCW 86 is 8200 light years away in the direction of the constellation Circinus and is considered to be the earliest recorded observation of a supernova event. Supernova explosions are relatively rare in the Milky Way Galaxy, occurring about once every one RCW 86 (Chandra, XMM-Newton) hundred (100) years. The last supernova explosion in the Milky Way Galaxy took place in the mid 17 th century. Because supernovas are rare within any galaxy, obtaining a good sample of supernovas to study requires regular monitoring of many galaxies. In the Large Magellanic Cloud galaxy, one hundred and sixty thousand (160,000) light years away, a supernova explosion took place in 1987. Astronomers and spacecraft have been monitoring this event (SN 1987A) continuously as it changes over time. The movie clip on the right is a composite image showing the effects of the powerful shock wave moving away from the explosion. Bright spots of X- ray and optical emission arise where the shock collides with structures in the surrounding gas. These structures were carved out by the wind from the progenitor star. Hot- spots in the Hubble image (pink-white) now encircle Supernova 1987A and the Chandra data (blue-purple) reveals multimillion-degree gas at the location of the optical hot-spots. These data greatly increase our Chandra Time-lapse Movie of SN1987A understanding of the processes involved as a supernova remnant expands into the surrounding interstellar medium. Type II Supernovae There are several scenarios that can result in a supernova event; however, supernovas are classified by the type of triggering mechanism that initiates the destruction. Type II supernovas are produced by the core collapse of a massive star – RCW 86 and SN 1987A mentioned above are Type II events. Thermonuclear fusion in stars with masses between ~0.8 and 8 solar masses produces the outward radiation pressure to counterbalance gravitational forces for approximately ten billion years. When the core hydrogen has been converted to helium and fusion stops, gravity SNR G292.0+1.8 (Chandra) Type II takes over and the core begins to collapse. The layers outside the core collapse also - the layers closer to the center collapse more quickly than the ones near the stellar surface. As the layers collapse, the gas compresses and heats up. The core temperature becomes high enough for helium to fuse into carbon and oxygen, with hydrogen to helium fusion continuing in a thin layer surrounding the core. The outer 168 layers expand to an enormous size and the star is now called a red giant. The star brightens by a factor of 1,000 to 10,000, and the surface temperature of the extended envelope drops to about 3,000K - 4,000K, giving the star its reddish appearance. A strong wind begins to blow from the star's surface, carrying away most of the hydrogen envelope surrounding the star's central core. During the final shedding of its envelope, when the mass loss is greatest, the star pulsates - the surface layers expand and then contract in repeating cycles with periods ranging from several months to more than a year. The material ejected by the star forms a planetary nebula which expands into the surrounding interstellar medium at ~17-35 km/hr. The core of the star left in the center of the planetary nebula is called a white dwarf. The planetary nebula is very tenuous, and becomes so thin that after ~50,000 years it is no longer visible. A white dwarf can not create internal pressure and its complete collapse is prevented by quantum mechanics. Two electrons with the same “spin” are NGC 6543 Planetary Nebula not allowed to occupy the same energy level. Since there are only (Chandra, Hubble) two ways an electron can spin, only two electrons can occupy any single energy level; this is called the Pauli Exclusion Principle. In a normal gas, this is not a problem; there are not enough electrons floating around to completely fill up all the energy levels. In a white dwarf, all of the electrons are forced close together, and all the energy levels in its atoms are filled up with electrons. If all the energy levels are filled, and it is impossible to put more than two electrons in each level, then the white dwarf has now become degenerate. Since a white dwarf is degenerate, gravity cannot compress it any more because quantum mechanics tells us there is no more available space. The complete collapse of the white dwarf is prevented because it is held in equilibrium with gravity by electron degeneracy pressure. The white dwarf is extremely dense, ~200,000 times more dense than the Earth. The mass limit for a white dwarf to remain in equilibrium between gravity and electron degeneracy pressure is 1.4 solar masses - the Chandrasekhar limit. Over hundreds of billions to a trillion years the white dwarf will radiate its remaining heat away and become a black dwarf - a cold, dark mass of electron degenerate matter. Stars with masses greater than eight solar masses continue nuclear fusion beyond that of core helium. The carbon-oxygen core more massive stars acquired during the core helium fusion contracts and heats. After all of the helium in the core is gone, carbon and oxygen begin to fuse. Their fusion yields neon, magnesium, silicon, and sulfur. Eventually, silicon and sulfur fuse in the star's core to form iron, nickel, and other elements of similar atomic weight. The star's structure now resembles an onion. The central core of the onion consists of iron. Surrounding it is a shell in which silicon and sulfur fuse, adding more iron to the iron core. In additional shells further out, lighter elements fuse - oxygen, carbon, helium, and hydrogen. The iron core is very compact and cannot induce further nuclear fusion. Nuclear fusion is possible only if the reactions release energy. The fusion of iron with other nuclei to make still heavier nuclei requires an input of energy - it is an endothermic nuclear reaction. The energy required to produce elements heavier than iron becomes available only during the imminent catastrophic collapse of the star's core and the violent explosion of the star's outer envelope. Cas A Type II Supernova Remnant (Chandra) 169 The mass of the star’s iron core approaches 1.4 solar masses due to the continued silicon And sulfur fusion in the thin layer adjacent to the iron core, and the continued fusion of iron requires more energy than is available. Radiation pressure is no longer able to support the core against gravity and the iron core collapses. In less than a second, the core collapses from a diameter of ~8000 kilometers to ~19 kilometers - the collapse happens so rapidly that the outer layers have no time to react or collapse along with the core. The energy released during core collapse is unimaginable - more energy than is produced by 100 stars like the Sun during their entire lifetimes of more than 10 billion years. Most of the energy released during collapse is carried off into space by neutrinos; a small fraction of the energy triggers the accompanying supernova explosion. The core collapses so fast that it momentarily goes past its equilibrium point at nuclear density and instantaneously rebounds. The innermost layers of the star are still in-falling and meet the rebounding core, creating a super strong shock wave that runs outward through the layers towards to the star's surface. The shock wave heats the outer layers, inducing explosive nuclear fusion, and ejects the outermost layers in excess of speeds of ~16 million kilometers per hour. The energy released by the shockwave produces elements heavier than iron. When the shock wave reaches the star's surface, it heats the surface layers and brightens them - within a day or two the exploding star becomes brighter than a billion Suns. The expanding gaseous shell, referred to as a supernova remnant, plows into the surrounding interstellar medium (ISM), and pushes, compresses, and intermingles with it. A forward and a reverse shock are created when the supernova Cas A Type II Supernova Event shock wave interacts with the ISM. The forward shock continues Movie to expand into the ISM, and the reverse shock travels back into the freely expanding supernova ejecta – heating the material to millions of degrees Kelvin and producing thermal X-ray emissions. This is a Type II supernova event - the core collapse of a massive star. The end product within the remnant depends upon the initial mass of the star, and is a neutron star, pulsar, magnetar, or black hole. Type Ia Supernovae A white dwarf is not always the end product in the collapse of a mid-sized (~.8 – 8 solar masses) star if it is in a contact binary system. Suppose two stars, one with one solar mass and the other with five solar masses are in a binary system. The five solar mass star runs out of hydrogen faster than its less massive companion, becomes a red giant, shrugs off a planetary nebula, and collapses into a white dwarf. Eventually the companion star runs out of hydrogen and enters the red giant stage. The outer layers of the red giant are loosely held by the star, and the extreme gravitational field of the white dwarf starts pulling the material from the red giant into Tycho Type Ia Supernova Remnant (Chandra) an accretion disk around the white dwarf. The mass transfer continues, with the material orbiting the white dwarf in the accretion disk. Magnetic friction slows the matter's orbital motion, which causes the matter to spiral through the disk down to the surface of the white dwarf. The falling and spiraling of the matter towards the white dwarf releases large amounts of gravitational 170 energy and heats the accretion disk. The white dwarf accretes matter from its companion relatively rapidly at the Langarian point – the point where the Roche lobe of the white dwarf and red giant make contact. The Roche lobe is the region of space around a star in a binary system within which orbiting material is gravitationally bound to that star; the red giant’s outer atmospheric layers are easily transferred by the strong gravity of the white dwarf. Consequently, the white dwarf grows in mass. When the accretion has raised the white dwarf's mass to the critical mass of 1.4 solar masses, the density and temperature in the center of the white dwarf become so severe that carbon starts fusing explosively. Within one second the fusion moves from the center to the surface and the white dwarf undergoes a thermonuclear explosion and is completely destroyed. Only the remnant remains. All of the core’s matter – the products of nuclear fusion (iron, nickel, silicon, magnesium, and nickel, silicon, magnesium, and other heavy elements) plus unfused carbon Mira Red Giant & White Dwarf and oxygen - are ejected into the interstellar medium at Companion speeds upwards of ~48,000,000 km/hr. This type of event is called a Type Ia supernova. Type II and Type Ia Supernovas Type II supernova events – core collapses of massive stars – are more common than Type Ia events – the thermonuclear explosion of white dwarfs. The progenitor stars for Type II supernovas exist for a much shorter length of time. The initial mass of a star determines its evolutionary history; the more massive the star the more rapidly the core hydrogen is fused into helium – and when all the core hydrogen is fused the stage is set for the eventual collapse of the star. The entire process takes from ~70 million years for a six (6) solar mass star to ~500 million for a two (2) solar mass star. Type Ia supernovas occur when a white dwarf exceeds Chandrasekhar’s Limit. A white dwarf is the end product of a mid-sized star such as the sun, and from protostar to white dwarf takes ~10 billion years. The universe is ~13.7 billions years old; therefore fewer mid-sized stars have had time to evolve into white dwarfs than massive stars have had to collapse into neutron stars, pulsars, magnetars or black holes. The composite X-ray (red and green)/optical (blue) image of DEM L316 reveals an image produced by the remnants of two exploded stars in the Large Magellanic Cloud galaxy. The upper remnant is a Type Ia event and the lower remnant is a Type II event. It takes billions of years to form a white dwarf star, whereas a massive young star will collapse in a few million years. The disparity of ages for the progenitor stars for these two remnants means that it is very unlikely that the two DEM L316 (Chandra/NOAO) events happened in close proximity. The apparent closeness of the two remnants is most likely the result of a chance alignment resulting in an optical illusion. 171 How do scientists determine if a supernova remnant is the result of a core collapse of a massive star or the thermonuclear destruction of a white dwarf? In DEM L316 one indicator is the large amount of iron in the upper Type Ia remnant compared to the amount of iron in the lower Type II remnant. The composition of supernova remnants is determined by analyzing their spectra. The elements and their relative abundances are different for Type Ia and Type II remnants because the Cas A Distribution of Elements progenitors are different. Type Ia remnants – from white dwarfs – usually show relatively strong Si, S, Ar, Ca, and Fe, and weak O, Ne, and Mg lines; Type II remnants – from massive stars – generally have the reverse pattern. In addition to the composition of the ejecta, spectroscopy can show how much of the stellar material was convectively mixed during the supernova event by calculating the density and temperature of the ionizing gas that generates the spectral lines. However, spectroscopy of supernova remnants is not clear cut and drawing conclusions is complicated; it is sometimes difficult to determine if a remnant is Type II or Type Ia. The Chandra and XMM-Newton missions have inaugurated the era of true spatially resolved X-ray spectroscopy. For supernova remnants, this means the capability to measure, for the first time, the detailed distribution of the ejecta and the spectra of ejecta at different positions in the remnant. This capability is greatly increasing our knowledge of the dynamics and processes involved in stellar catastrophic events. Chandra has detected numerous pulsars and their associated pulsar nebulas. These discoveries are proving to be one of the best ways to identify supernova remnants produced by the core collapse of a massive star, and distinguish them from Type Ia supernova remnants. X-Ray Radiation and Spectroscopy The animation above shows the distribution of elements in the Cas A supernova remnant. The X-ray spectrum to the left shows the abundances of those elements. The Cas A spectrum is typical of X-ray spectra, and differs from optical spectra – which is what is we are most familiar with. The cataclysmic spectral image below is an emission spectrum – showing the composition of a star in the optical part of the spectrum. To accurately measure the wavelengths of the emission lines, a spectral plot is constructed. On a spectral plot, the emission Cas A X-Ray Spectra (Chandra) lines appear as sharp peaks. On the X-ray spectra above, the emission lines produced by the elements also show as peaks; the higher the peak, the stronger the emission line. However on the X-ray spectra the emission lines are superimposed on top of a large curve. This curve is Cataclysmic Spectral Image – Optical produced by the acceleration of electrons as they are deflected by positively charged atomic nuclei and is called Bremsstrahlung (breaking) radiation. Bremsstrahlung is also referred to as free-free radiation. This refers to radiation that arises as a Cataclysmic Spectral Plot – Optical 172 result of a charged particle that is free both before and after the deflection (acceleration) that caused the emission. When a free-ranging electron is accelerated by the electric field of a proton, the photons emitted can have a wide range of energies that depends on how fast the electrons are moving and how much they are accelerated. The distribution of photon energies due to this process is called a continuous spectrum, and is graphed as a smooth curve as in the Cas A spectrum above. In addition, emission lines can appear superimposed on the Bremsstrahlung Radiation Bremsstrahlung radiation curve corresponding to the ejection of K and L shell electrons knocked out of atoms in collisions with the high-energy electrons. Higher energy electrons then fall into the vacated energy states emitting X-ray photons and producing the emission lines. The energies of these emission lines can be used to identify the elements in plasmas such as supernova remnants. A hot gas or plasma will produce a spectrum composed of many emission lines due to the various elements that are present. Image Analysis of Supernova Remnants An activity – X-Ray Spectroscopy of Supernova Remnants – has been developed so students can examine the spectra of several supernova remnants; determine the elements that are present and their relative abundances, and decide if each remnant is from a Type II core-collapse event or the Type Ia thermonuclear destruction of a white dwarf. This activity uses ds9 – an image analysis software package. Ds9 allows the user to download a toolbox onto their desktop and remotely access dedicated Linux servers which process the analysis commands. The ds9 image analysis software allows educators, students, amateur astronomers and the general public to perform X-ray astronomy data analysis using data sets from the Chandra X-ray Observatory, the ds9 image display program, and astrophysical software analysis tools. The program uses the same analysis process that an X-ray astronomer would follow in analyzing the data from a Chandra observation. The download instructions to install the ds9 toolbox on your desktop are located at http://chandra- ed.harvard.edu/install.html . The introduction at http://chandra- ed.harvard.edu/learning_ds9overview.html describes the overview and purpose of the software and gives a short summary of the Chandra mission. The tutorial for using the ds9 software is located at http://chandra-ed.harvard.edu/learning_ds9.html. NOTE: It is not necessary to read the tutorial before beginning the X-ray Spectroscopy of Supernova Remnants activity. All ds9 educational activities are constructed to use one or two specific software tools, and complete constructions to use the tools are given within the individual activities. If a computer activity is not available as an option, a paper and pencil version of this activity is also provided. Screen shots of the necessary spectra from ds9 are included with the activity, and the only additional materials required are pencils and rulers. 173 D. X-ray Spectroscopy of Supernova Remnants Activity – ds9 Version Purpose: To determine types of supernovas by examining Chandra X-ray Observatory images of supernova remnants (SNRs) and by identifying the elements in their energy spectra. Figure 1. Tycho’s SNR, Type Ia Figure 2. SNR G292.0+1.8, Type II Credit: NASA/CXC/Rutgers/J.Warren & J.Hughes et al. Credit: NASA/CXC/Rutgers/J.Hughes et al. Tycho’s Supernova Remnant In the year 1572, the Danish astronomer Tycho Brahe observed and studied the sudden appearance of a bright “new star” in the direction of the constellation Cassiopeia. Now known as Tycho’s supernova remnant, the event created a sensation in Tycho’s time because until then stars were thought to be unchanging. Tycho’s observations of this event marked the beginning of the study of astronomy as a science. This object is a Type Ia event – the thermonuclear destruction of a white dwarf. Information about this object is located at http://chandra.harvard.edu/press/05_releases/press_092205.html SNR G292.0+1.8 The Type II core collapse of a massive star that produced this supernova remnant ~1600 years ago is located in the direction of the constellation Centaurus. SNR G292.0+1.8 is interesting because it is one of only three oxygen-rich remnants and one of the primary sources of the heavy elements necessary to form planets and people. Although considered a “textbook” case of a supernova remnant, the intricate structure shown here reveals a few surprises. Information about this object is located at http://chandra.harvard.edu/photo/2007/g292/ Tycho’s Supernova Remnant (Type Ia) and SNR G292.0+1.8 (Type II) are representative of the two supernova types. Follow the procedure below to analyze their spectra and determine the elements present in the remnants and their relative abundances. The same procedure will be used to study other remnants, compare the results to Tycho and SNR G292.0+1.8, and determine if they are Type II or Type Ia supernova events. 174 Procedure: Install the software and load the FITS file (data/image file): 15. Download and install ds9 according to the instructions on the Chandra-Ed web site. http://chandra-ed.harvard.edu/install.html 16. Open ds9. From the menus, choose Analysis>Virtual Observatory>Chandra- Ed Archive Server. 17. In the new window that comes up, click “ObsID 115 – ACIS OBSERVATIONS OF TYCHO AND KEPLER”. Do not close this window – you will need it later. 18. When the image is loaded, go back to the SAOImage ds9 window. Plot the spectrum of Tycho’s SNR: 19. Click in the center of the Tycho SNR and drag a circular region completely around the whole remnant. 20. Choose Analysis>Chandra Ed>CIAO: Sherpa Spectral fit. For “Model Type”, choose “bremsstrahlung” (when you click on “power law”, a menu will appear). It may take a few minutes for the plot to appear. NOTE: If this takes to long, or you are unable to get the plot, try Analysis>Chandra Ed>Quick Energy Spectrum Plot. Note that the unit on the x-axis on this plot is eV rather than keV. 21. On the graph window that comes up, choose Graph>linear-log. Maximize the screen by clicking the square in the upper right corner. 22. Print the graph by using the Print Scrn button on the keyboard and then pasting it into a PowerPoint or Word document and printing from there. Identify the emission lines in Tycho’s SNR: 23. To get the energy of each emission line, create a zoom box on the graph by holding the left mouse button down and dragging a box around the area of the emission line (peak). When you click again, a close-up of that area will appear. Right clicking the mouse returns you to the original graph. (See Fig. 6) Fig. 6 Zoom in on an emission line 175 24. Record the energies and identify the elements for each X-ray emission line/peak in the Data section and on your printed graph, using Table 1. If you have lines whose energy is not close to that of one of the elements in the chart, leave those lines unidentified. Plot the spectrum of G292.0+1.8 and identify the emission lines: 25. On the arvard-ed.cfa.harvard.edu window, click the back arrow to go back to the previous page. “Obs ID 126 – G292.0+1.8 A REMARKABLE OXYGEN- RICH SUPERNOVA REMNANT”. Again, do not close this window. 26. Repeat steps #4-10 for SNR G292.0+1.8. To see the emission lines better, you can zoom in as shown in Fig. 7. Fig. 7 Zoom to magnify emission lines Table 1. Energies of X-ray Emission Lines element Energy (Kev) element Energy (Kev) element Energy (Kev) O 0.18 Mg 1.33 Ar 3.32 Mg 0.25 Mg 1.45 Ar 3.69 Mg 0.27 Fe 1.66 Ca 3.86 O 0.64 Si 1.87 Ca 3.89 O 0.66 Si 1.98 Ca 4.11 Fe 0.80 Si 2.14 Ca 4.95 Fe 0.81 S 2.42 Fe 6.47 Ne 0.92 S 2.44 Fe 6.54 Ne 0.93 S 2.63 Fe 6.97 Ne 1.02 Ar 3.10 Fe 7.80 176 Data: Tycho’s SNR (Type Ia) SNR G292.0+1.8 SNR (Type II) Energy of emission line (KeV) chemical symbol of element Energy of emission line (KeV) chemical symbol of element Conclusions and Analysis: 1. What are the similarities and differences between these two spectra? 2. From your analysis of Tycho’s SNR and SNR G292.0+1.8, what elements are more predominant in a Type Ia supernova? Which are more predominant in a Type II? Are there elements present in one that are not in another? 3. Explain how you might be able to classify a supernova event as type Ia or type II from its spectrum based on your observations of Tycho’s SNR and SNR G292.0+1.8. Sometimes, due to interstellar absorption, emission lines less than 1.5 KeV are not seen. How could this affect your classification of a supernova remnant? Extensions: 1. Analyze the spectra of any three of the following SNRs using the same procedure as Tycho’s SNR and G292.0+1.8. Construct your own data tables. a. Obs ID 117 – ACIS OBSERVATIONS OF W49B b. Obs ID 116 – Kepler’s SNR c. Obs ID 2758 – SNR 0103-72.6: AN UNSUALLY BRIGHT REMNANT IN THE SMC ALTERNATE TARGET d. Obs ID 775 – A SYSTEMATIC STUDY OF LMC SNRS WITH AXAF (this is the SNR called DEM L71) e. Obs ID 114 – ACIS OBSERVATIONS OF CAS A 2. From your analyses, classify these SNR by type. What is the basis for your conclusions? How sure are you of your classifications? What features of the spectra helped with your classifications? What features made it difficult to classify these SNR? 3. Look up these supernovas in the Chandra Supernova Photo Album. How do your results compare with the information in the Photo Album? http://chandra.harvard.edu/photo/category/snr.html 177 Additional Information for X-ray Spectroscopy and Supernova Remnants ds9 Version: 1. Additional information for Tycho’s supernova remnant and supernova G292.0+1.8 OBS ID 115 (Tycho’s SNR) - Type Ia http://chandra.harvard.edu/photo/2002/0005/index.html 178 OBS ID 126 (G292.0+1.8) – Type II http://chandra.harvard.edu/photo/2001/0112/index.html 179 Hughes, et all 2001. Note the higher abundance of O, Ne, and Mg in this Type II spectrum. Use Analysis>Chandra Ed Analysis Tools>Energy Filter in ds9 to view the location of only the high energy or “hard” x-ray photons (a “lo’ of 4 KeV and a “hi” of 8 KeV). in this SNR. You can see the results in the frame on the right. This shows the region that could be the core remnant pointing to a type II supernova from a massive star. 1. Information for the supernova remnants listed in number 1 (a through e) in the Extensions Section. OBS ID 117 (W49B) – Type II; though hard to tell from the spectrum perhaps due to interstellar absorption of lines less than 1.5 keV ( so you can’t see O, Me and Mg lines). From this spectrum it is very difficult to classify the supernova type. Students may say it is a type Ia if they do no further research. http://chandra.harvard.edu/press/04_releases/press_060204.html OBS OD 116 – Type?; Astronomers have studied Kepler intensively over the past three decades with radio, optical and X-ray telescopes, but its origin has remained a puzzle. On the one hand, the presence of large amounts of iron and the absence of a detectable neutron star points toward a Type Ia supernova. On the other hand, when viewed in optical light, the supernova remnant appears to be expanding into dense material that is rich in nitrogen. This would suggest Kepler is a Type II supernova event as Type Ia supernovas do not normally have such surroundings. OBS ID 2758 (SNR 0103-72.6) – Type II; Oxygen and neon are the most abundant elements in the spectrum as in the spectrum of G292.0+1.8. In ds9, using color>bb and scale>square root, you can also see (faintly) a core remnant. http://chandra.harvard.edu/photo/2003/snr0103/ Obs ID 775 (DEM L71) – Type 1a; O and Ne are not evident in the spectrum (which could be due to interstellar absorption BUT there also does not seem to be a core remnant as in a type II). Other elements are similar to those of Tycho’s SNR. http://chandra.harvard.edu/photo/2003/deml71/ Obs ID 114 (Cas A) – Type II; Spectrum has a peak at Ne, but O and Mg are either missing or not very prominent. Spectrum looks very much like that of Tycho’s SNR. A bright core, however, is evident at the center of the image. Interstellar absorption may be responsible for not seeing emission lines less than 1.5 KeV. http://chandra.harvard.edu/photo/2002/0237/ 3. References that can be used for further discussion and study of the classification of supernova remnants. Typing supernovae from their remnants http://articles.adsabs.harvard.edu//full/1995ApJ...444L..81H/L000084.000.html X-ray Spectroscopy of Young SNR – Imagine! The Universe http://imagine.gsfc.nasa.gov/docs/features/topics/snr_group/spectroscopy.html An X-Ray Study of the Supernova Remnant G290.1-0.8 http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v564n1/54479/54479.text. html 180 The X-Ray Line Emission from the Supernova Remnant W49B http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v532n2/50112/50112.text. html 0103-72.6: A New Oxygen-Rich Supernova Remnant in the Small Magellanic Cloud http://www.journals.uchicago.edu/ApJ/journal/issues/ApJL/v598n2/17768/17768.tex t.html Iron-rich Ejecta in the Supernova Remnant DEM L71 http://www.journals.uchicago.edu/ApJ/journal/issues/ApJL/v582n2/16886/brief/168 86.abstract.html HST Observations of SNRs in Magellanic Clouds. II. http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v537n2/50874/50874.text. html ASCA X-Ray Spectroscopy of Large Magellanic Cloud Supernova Remnants and the Metal Abundances of the Large Magellanic Cloud http://www.journals.uchicago.edu/ApJ/journal/issues/ApJ/v505n2/38033/38033.pdf Young Supernova Remnants in the Magellanic Clouds http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3Aar Xiv.org%3Aastro-ph%2F0102377 Hughes Presentation on X-ray studies of SNR http://constellation.gsfc.nasa.gov/documents/mission/fst/2003May/hughes.pdf 181 X-ray Spectroscopy of Supernova Remnants – Pencil and Paper Version NOTE: The introduction and background, along with additional supporting information, is included with the ds9 version of this activity preceding this version. Purpose: To determine types of supernovas by examining Chandra X-ray Observatory images of supernova remnants (SNRs) and by identifying the elements in their energy spectra. Figure 1. Tycho’s SNR, Type Ia Figure 2. SNR G292.0+1.8, Type II Credit: NASA/CXC/Rutgers/J.Warren & J.Hughes et al. Credit: NASA/CXC/Rutgers/J.Hughes et al. Tycho’s Supernova Remnant In the year 1572, the Danish astronomer Tycho Brahe observed and studied the sudden appearance of a bright "new star" in the direction of the constellation Cassiopeia. Now known as Tycho's supernova remnant, the event created a sensation in Tycho's time because until then stars were thought to be unchanging. Tycho’s observations of this event marked the beginning of the study of astronomy as a science. This object is a Type Ia event – the thermonuclear destruction of a white dwarf. Information about this object is located at http://chandra.harvard.edu/press/05_releases/press_092205.html SNR G292.0+1.8 The Type II core collapse of a massive star that produced this supernova remnant ~1600 years ago is located in the direction of the constellation Centaurus. SNR G292.0+1.8 is interesting because it is one of only three oxygen-rich remnants and one of the primary sources of the heavy elements necessary to form planets and people. Although considered a "textbook" case of a supernova remnant, the intricate structure shown here reveals a few surprises. Information about this object is located at http://chandra.harvard.edu/photo/2007/g292/ 182 Tycho’s Supernova Remnant (Type Ia) and SNR G292.0+1.8 (Type II) are representative of the two supernova types. Follow the procedure below to analyze their spectra and determine the elements present in the remnants and their relative abundances. The same procedure will be used to study other remnants, compare the results to Tycho and SNR G292.0+1.8, and determine if they are Type II or Type Ia supernova events. Procedure: 1. Examine Figure 6, the bremsstrahlung spectrum of Tycho’s SNR. 2. On Figure 6, number the emission lines (peaks) you have decided to identify. 3. To get the energy of each emission line, measure the distance between 1 and 2 keV to the nearest tenth of a centimeter (mm). This gives a scale in cm/keV. Measure the distance in cm (with as much precision as possible) from 1 keV to the center of each peak (X- ray emission line). Make this distance negative if the peak is before 1 KeV and positive if it is after 1 keV. Record in the data table. 4. Divide the distance to each peak (cm) by your scale (cm/keV) and add to 1 KeV to get the energy (keV) of each emission line. Record in the data table. 1 KeV + [(d in cm)/(scale in cm/KeV)] 5. Identify the elements for each X-ray emission line/peak using Table 1. If you have lines whose energy is not close to that of one of the elements in the chart, leave those lines unidentified. Record in the data table. 6. Repeat steps #1-5 for Figure 7, the bremsstrahlung spectrum of SNR G292.0+1.8. Table 1. Energies of X-ray Emission Lines element Energy (Kev) element Energy (Kev) element Energy (Kev) O 0.18 Mg 1.33 Ar 3.32 Mg 0.25 Mg 1.45 Ar 3.69 Mg 0.27 Fe 1.66 Ca 3.86 O 0.64 Si 1.87 Ca 3.89 O 0.66 Si 1.98 Ca 4.11 Fe 0.80 Si 2.14 Ca 4.95 Fe 0.81 S 2.42 Fe 6.47 Ne 0.92 S 2.44 Fe 6.54 Ne 0.93 S 2.63 Fe 6.97 Ne 1.02 Ar 3.10 Fe 7.80 183 Data: Tycho’s SNR (Type Ia) Distance from 1 KeV to 2 KeV: 1 Kev = ________ cm # of emission line distance from 1 KeV (cm) Energy of emission line (KeV) chemical symbol of element SNR G292.0+1.8 SNR (Type II) Distance from 1 KeV to 2 KeV: 1 Kev = ________ cm # of emission line distance from 1 KeV (cm) Energy of emission line (KeV) chemical symbol of element Conclusions and Analysis: 4. What are the similarities and differences between these two spectra? 5. From your analysis of Tycho’s SNR and SNR G292.0+1.8, what elements are more predominant in a Type Ia supernova? Which are more predominant in a Type II? Are there elements present in one that are not in another? 184 6. Explain how you might be able to classify a supernova event as type Ia or type II from its spectrum based on your observations of Tycho’s SNR and SNR G292.0+1.8. Sometimes, due to interstellar absorption, emission lines less than 1.5 KeV are not seen. How could this affect your classification of a supernova remnant? Extensions: 1. Analyze the spectra of any three of the following SNRs using the same procedure as Tycho’s SNR and G292.0+1.8. Construct your own data tables. a. Figure 8. W49B b. Figure 9. Kepler’s SNR c. Figure 10. SNR 0103-72.6 d. Figure 11. DEM L71 e. Figure 12. Cas A 4. From your analyses, classify these SNR by type. What is the basis for your conclusions? How sure are you of your classifications? What features of the spectra helped with your classifications? What features made it difficult to classify these SNR? 5. Look up these supernovas in the Chandra Supernova Photo Album. How do your results compare with the information in the Photo Album? http://chandra.harvard.edu/photo/category/snr.html 185 Figure 6. Bremsstrahlung Spectrum of Tycho’s SNR 186 Figure 7. Bremsstrahlung Spectrum of G292.0+1.8 187 Figure 8. Bremsstrahlung Spectrum of W49B 188 Figure 9. Bremsstrahlung Spectrum of Kepler’s SNR 189 Figure 10. Bremsstrahlung Spectrum of SNR 0103-72.6 190 Figure 11. Bremsstrahlung Spectrum of DEM L71 191 Figure 12. Bremsstrahlung Spectrum of Cas A 192 Analyzing Pulsating Sources This activity uses basic physics principles and equation to analyze varying sources. The background information in this manual on white dwarfs and neutron stars in both the Stellar Evolution and Variable Star sections, as well as in the Introduction for Investigating Supernova Remnants with X-ray Spectroscopy on pages 165 – 169 is useful for understanding this activity. There are both ds9 and pencil and paper versions for this activity. NOTE: All other ds9 activities are posted on the Chandra education website. This activity is not yet posted, though it is expected to be added to the website by the end of 2010. This is a beta version draft of the final activity. E. Analysis of Two Pulsating X-ray Sources – ds9 Version Purpose: To determine if GK Per and Cen X-3 could be white dwarfs or neutron stars by finding the periods of the X-ray emission pulses using data sets from the Chandra X-ray Observatory. Background: ds9 can produce a light curve for data gathered by the Chandra X-ray Observatory. A light curve is a graph of the brightness of an object versus time. For stellar objects which change brightness over time, such as supernovae, novae and variable stars, a light curve can help astronomers classify the object and identify its nature. Accreting White Dwarf illustration of an accretion powered pulsar Credit: CXC/M.Weiss The regularity in the changes in brightness for GK Per and Cen X-3 lead us to believe that there is some periodic mechanism causing this. In the case of rotating variable stars, the brightness in X-rays could change as a “hot spot” rotates in and out of our view. In the case of a white dwarf, such a “hot spot” might occur if a white dwarf with a magnetic field accretes matter from a companion star. The accretion disk is disrupted at small radii by the white dwarf’s magnetosphere. Material leaves the disk and travels along magnetic field lines. At some distance to the surface, a strong shock occurs where freefall kinetic energy is converted to thermal energy. Below this, material settles onto the white dwarf near the magnetic poles. As this material cools, it releases x-rays. If the magnetic axis is 193 offset from the spin axis, the X-ray emission will pulse with the spin period of the white dwarf. A sun-like star eventually becomes a white dwarf when the core, left behind after a red giant puffs off its outer layers, collapses. An object the size of an olive made of white dwarf material would have the same mass as an automobile! The central part of a more massive star will collapse even further to form a neutron star. Electrons are pushed into protons to form neutrons and the result is a tiny star with very little empty space. A neutron star would have the same density as 10 million full-sized African elephants in the space of a thimble. A neutron star in a binary system can become an accretion powered pulsar, producing a pulsing X-ray emission in much the same way as described above for the white dwarf. A neutron star, however, can spin faster (have a shorter period) because its higher mass and smaller size generates a stronger gravitational field that can prevent a fast spinning pulsar from breaking apart. Procedure: 1. Go to http://chandra-ed.harvard.edu/install.html and install ds9 if it is not already on your computer. 2. Open ds9. Go to Analysis>Virtual Observatory>Chandra-Ed Archive Server and click Obs ID 3454 - CHANDRA HETG SPECTROSCOPY OF GK PER IN OUTBURST on the screen that comes up. (Do not close this window – you will be loading another image later.) 3. Regions have been pre-drawn for you. If you wish, play with different Scales and Colors to see the details of GK Per. Go to Analysis>Chandra Ed Analysis Tools>FTOOLS Light Curve and click OK. On the light curve generated, zoom in on an area on the graph by either left clicking and dragging a box around a region of the graph or by changing the x-axis range under Graph>Axis Range until you can determine if there appears to be a periodic x-ray pulse. 4. Go to Analysis>Chandra Ed Analysis Tools>FTOOLS Power Spectrum and click OK. This command does a fast Fourier Transform on the data to search for periodicities. If the data isn’t periodic, you will not see one large peak as you will for GK Per. Zoom in on the peak until you can determine its frequency. Convert the frequency to period (period = 1/frequency). 5. Go to Analysis>Chandra Ed Analysis Tools>FTOOLS Period Fold. This will help you to check the accuracy of the period you found in step 4. Enter the value for this period in the window that comes up and click OK. To understand what this command is doing, picture a drawing of a sine wave on a long piece of paper. Cut this paper into sections, each one period long, and put each cycle on top of the first one, adding all the sine waves together. If your cuts are not exactly every period, when you add the sine waves, parts of the waves would cancel out and your composite wave would have a 194 smaller amplitude. How does your Period Fold graph look? Try it again with a period several seconds different than the one you used before. Which graph is more sine-like and has the highest amplitude? If you need to, try Period Fold again with different periods until you produce the best graph. Record this period. This is equal to GK Per’s spin period as discussed in the background information. 6. Go to “chandra-ed.cfa.harvard.edu” window and hit the back arrow. Click Obs ID 1943 – THE WIND AND ACCRETION DISK IN CEN X-3/V779 CEN. Make a light curve, power spectrum, and period fold for this data to find the period of Cen X-3. Calculations and Interpretations: The acceleration due to gravity (g) on the surface of a star (according to Newton’s Universal Law of Gravitation) is given by g = (GM)/R 2 where G = 6.67 X 10 -11 Nm 2 /kg 2 , M=star’s mass and R = star’s radius Centripetal acceleration (a c ) of an object on the surface of a star at its equator is given by a c = V 2 /R and since V = 2πR/T for an object moving in a circle a c = 4π 2 R/T 2 , where R = star’s radius and T = star’s spin period If the centripetal acceleration on material on the star’s surface for a given period is less than the acceleration due to gravity, the gravitational force would be enough to hold the material on the surface and the star could sustain such a period without disruption. 1. Find the acceleration due to gravity on the surface of a white dwarf. Let the mass of a white dwarf be approximately one solar mass or 2.0 X 10 30 kg and its radius, approximately that of Earth or 6.4 X 10 6 m. 2. Find the acceleration due to gravity on the surface of a neutron star. Let the mass of a neutron star be two solar masses or 4 X 10 30 kg and its radius be 10.0 km. 3. Assume GK Per is a white dwarf. Calculate the centripetal acceleration of material on the surface of GK Per (using the period you found from the power spectrum). According to your calculations, can GK Per be a white dwarf*? Why or why not? 4. If your answer above is “no”, repeat #3 assuming GK Per is a neutron star. 5. Repeat #3 and #4 for Cen X-3. Is it more likely that Cen X-3 is a white dwarf or a neutron star? Why? *Note: If it is possible that a star is a white dwarf according to the types of calculations you did in this activity, other analysis would be necessary to determine if an object is actually white dwarf, such as examination of its temperature and luminosity 195 Resources: Podcasts: Supernovas: When Stars Die (contains description of a white dwarf) http://chandra.harvard.edu/resources/podcasts/media/pod301006.m4v The Exotic World of Neutron Stars http://chandra.harvard.edu/resources/podcasts/media/pod300407.m4v References: Chandra Education Data Analysis Software And Activities http://chandra-ed.harvard.edu/ Chandra Field Guide http://chandra.harvard.edu/field_guide.html Variable Star Of The Month Nov. '00: GK Persei (Nova Persei 1901) http://www.aavso.org/vstar/vsots/1100.shtml The Encyclopedia of Astrobiology, Astronomy, and Spaceflight - Cen X-3 http://www.daviddarling.info/encyclopedia/C/Centaurus_X-3.html ASTRONOMY AND ASTROPHYSICS YY Draconis and V709 Cassiopeiae http://physics.open.ac.uk/~ajnorton/papers/yydra_v709cas.pdf 196 Analysis of Two Pulsating X-ray Sources Answers: 197 Analysis of Two Pulsating X-ray Sources – Pencil and Paper Version Purpose: To determine if GK Per and Cen X-3 could be white dwarfs or neutron stars by finding the periods of the X-ray emission pulses using data sets from the Chandra X-ray Observatory. Background: A light curve is a graph of the brightness of an object versus time. For stellar objects which change brightness over time, such as supernovae, novae and variable stars, a light curve can help astronomers classify the object and identify its nature. Accreting White Dwarf illustration of an accretion powered pulsar Credit: CXC/M.Weiss The regularity in the changes in brightness for GK Per and Cen X-3 lead us to believe that there is some periodic mechanism causing this. In the case of rotating variable stars, the brightness in X-rays could change as a “hot spot” rotates in and out of our view. In the case of a white dwarf, such a “hot spot” might occur if a white dwarf with a magnetic field accretes matter from a companion star. The accretion disk is disrupted at small radii by the white dwarf’s magnetosphere. Material leaves the disk and travels along magnetic field lines. At some distance to the surface, a strong shock occurs where freefall kinetic energy is converted to thermal energy. Below this, material settles onto the white dwarf near the magnetic poles. As this material cools, it releases x-rays. If the magnetic axis is offset from the spin axis, the X-ray emission will pulse with the spin period of the white dwarf. A sun-like star eventually becomes a white dwarf when the core, left behind after a red giant puffs off its outer layers, collapses. An object the size of an olive made of white dwarf material would have the same mass as an automobile! The central part of a more massive star will collapse even further to form a neutron star. Electrons are pushed into protons to form neutrons and the result is a tiny star with very little empty space. A neutron star would have the same density as 10 million full-sized African elephants in the space of a thimble. 198 A neutron star in a binary system can become an accretion powered pulsar, producing a pulsing X-ray emission in much the same way as described above for the white dwarf. A neutron star, however, can spin faster (have a shorter period) because its higher mass and smaller size generates a stronger gravitational field that can prevent a fast spinning pulsar from breaking apart. Procedure: 1. Figure 3. is a light curve of GK Per obtained from Chandra X-Ray Observatory data. This is a plot of brightness vs time. Does the change in brightness seem to be periodic? Estimate the possible period. 2. Figure 4. is a power spectrum of GK Per’s light curve. A power spectrum indicates the likelihood that certain frequencies (of rotation or other periodic phenomena) are present in the data. Zooming in on the tallest spike (Figure 5.), you can estimate the frequency of the x-ray “flashes” which is also the frequency of the rotation of GK Per. Calculate the period, T, by taking the inverse of the frequency, f (T = 1/f). How does this compare with the period you obtained from the light curve? 3. Repeat steps 1 and 2, using Figures 6, 7 and 8 for Cen X-3. Calculations and Interpretations: The acceleration due to gravity (g) on the surface of a star (according to Newton’s Universal Law of Gravitation) is given by g = (GM)/R 2 where G = 6.67 X 10 -11 Nm 2 /kg 2 , M=star’s mass and R = star’s radius Centripetal acceleration (a c ) of an object on the surface of a star at its equator is given by a c = V 2 /R and since V = 2πR/T for an object moving in a circle a c = 4π 2 R/T 2 , where R = star’s radius and T = star’s spin period If the centripetal acceleration on material on the star’s surface for a given period is less than the acceleration due to gravity, the gravitational force would be enough to hold the material on the surface and the star could sustain such a period without disruption. 6. Find the acceleration due to gravity on the surface of a white dwarf. Let the mass of a white dwarf be approximately one solar mass or 2.0 X 10 30 kg and its radius, approximately that of Earth or 6.4 X 10 6 m. 7. Find the acceleration due to gravity on the surface of a neutron star. Let the mass of a neutron star be two solar masses or 4 X 10 30 kg and its radius be 10.0 km. 199 8. Assume GK Per is a white dwarf. Calculate the centripetal acceleration of material on the surface of GK Per (using the period you found from the power spectrum). According to your calculations, can GK Per be a white dwarf*? Why or why not? 9. If your answer above is “no”, repeat #3 assuming GK Per is a neutron star. 10. Repeat #3 and #4 for Cen X-3. Is it more likely that Cen X-3 is a white dwarf or a neutron star? Why? *Note: If it is possible that a star is a white dwarf according to the types of calculations you did in this activity, other analysis would be necessary to determine if an object is actually white dwarf, such as examination of its temperature and luminosity 200 Figure 3. Light Curve of GK Per Figure 4. Power Spectrum of GK Per 201 Figure 5. Zoom of Power Spectrum of GK Per Figure 6. Light Curve of Cen X-3 202 Figure 7. Power Spectrum of Cen X-3 Figure 8. Zoom of Power Spectrum of Cen X-3 203 Analysis of Two Pulsating X-ray Sources Answers: NOTE: Additional resources for this activity are listed in the ds9 version of this activity on page 194 204 I. Free Resources: The Chandra X-Ray Observatory homepage at http://chandra.harvard.edu/ contains many resources, such as the photo album , and the educational materials. By January 2005,a stellar evolution module will be added to the educational website with information, activities and links that will be especially useful to prepare for this event. The http://chandra-ed.harvard.edu/ site is the homepage for the Chandra DS9 data analysis software - including instructions for downloading and using the software. http://www3.gettysburg.edu/~marschal/clea/CLEAhome.html is the homepage for the CLEA (Contemporary Laboratory Exercises in Astronomy) Project - the labs all include a dedicated computer program, a student manual, and a technical guide for the instructor. The technical guides describe file formats, user-settable options, and algorithms used in the programs. The most advanced CLEA labs run under Windows on PC's, or on color- capable Macintosh computers. All of the software and manuals are free and downloadable. The http://skyserver.sdss.org/dr2/en/ website brings you the entire public database of the Sloan Digital Sky Survey - over 80 million stars, galaxies and quasars. The site includes a variety of tools to view and download SDSS data, and many projects and activities at levels from basic to advanced to learn about spectra, the H-R diagram, and Hubble's law, among others. http://www.astro.washington.edu/labs/clearinghouse/labs/labs_comments.html is a website maintained by the University of Washington astronomy department. It has ~60 introductory astronomy labs organized by type - i.e. the Stellar Evolution and H-R diagram section. http://aavso.org/ is the website for the American Association of Variable Star Observers. It contains a lot of helpful information and activities. It is also link to the variable star activities on the Chandra website at: http://chandra.harvard.edu/edu/formal/variable_stars/ http://www.aavso.org/education/vsa/ is the Variable Star Astronomy curriculum which contains information and activities on variable stars – including light curves, phase diagrams, and O-C diagrams. II. Recommended Resources Available for Purchase: http://store.soinc.org/c-14-new-materials-for-2010.aspx This CD contains all prior astronomy national and state exams and materials, and coaches clinic presentations. These are excellent resources to study for state and national competition. The Stellar Journey board game available from Other Worlds Educational Enterprises at http://stellarjourney.net/ NOTE: This site is off-line until ~May 2010 205