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Imaging the Universe A Laboratory Manual for Introductory Astronomy Modern Astronomy 29:050 Fall 2007 Edition Robert Mutel University of Iowa Acknowledgments We wish to thank the Iowa Robotic Observatory observers whose assistance in the preparation of this manual have helped to make it possible. Thanks to the Modern and General Astronomy students and Teaching Assistants past and present, for their valuable input and insight. We also thank Elwood Downey, whose programming expertise and patience have astonished us all. Contributors Jessie Allen John Armstrong Andrew Helton Stacy Palen Lynn Reitzler Peter Kortenkamp Michael Wilson Steven Spangler Table of Contents INTRODUCTION................................................................... 1 1. 2. 3. 4. 5. INTRODUCTION TO ASTRONOMY USING COMPUTERS............................ 3 IMAGE ANALYSIS: BASIC TECHNIQUES................................................ 13 LABORATORY SPECTROSCOPY .......................................................... 19 SPECTRAL CLASSIFICATION OF STARS (CLEA)................................... 26 THE AGE AND DISTANCE OF A STELLAR CLUSTER............................... 32 APPENDICES..................................................................... 39 6. 7. APPENDIX A: PLANNING OBSERVATIONS ............................................ 39 APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM ......................... 43 INTRODUCTION—1 Introduction Introductory astronomy laboratories have historically been a disappointing experience for the average student. The reason is simple: the student looks forward to viewing and photographing celestial objects firsthand, possibly with a quality telescope and camera. Unfortunately, the traditional photographic camera techniques and manually operated telescopes used in undergraduate labs have been too cumbersome, time-consuming, and insensitive to allow useful observations to be made. Given this, most astronomy lab curricula have evolved into rather tedious workbook exercises. Starting about 1990, two innovative technologies became available, at modest cost, which have made possible the development of an entirely new laboratory curriculum. The first was the charge-coupled device (CCD) which is about one hundred times as sensitive to light as photographic film and which can be connected directly to a computer for immediate image display and analysis. The second was powerful robotic interface systems and software for precise computer control of moveable instruments. By allowing the student to command a robotic telescope by computer, the student can quickly and efficiently acquire images of the selected object(s) without the need to search by hand with finding charts, often a lengthy procedure even for an experienced observer. For several years, the University of Iowa has been developing a CCD-based computer laboratory to teach the principles of observational astronomy to introductory students. This manual is a user’s guide for the laboratory. Since the lab facility and equipment are still undergoing development, the manual is in a draft state. We need your input about which parts of the curriculum work and which don’t. We also need your ideas about how the curriculum could be improved. These exercises have been designed to be both challenging and fun, and to give you a taste of what real astronomical research is all about. Along with helping you learn the facts and concepts presented during the class lectures and in the textbook, they will teach you to plan and analyze your own observations using a computer controlled telescope and CCD camera. While studying the solar system, you will investigate the height of lunar features, explore the surface of Mars, determine the mass of Jupiter, study solar rotation and solar flares, and follow the motion of asteroids. Moving into stellar research, you will measure the surface temperature of stars, study the size of the envelopes of dying stars, and study the properties of star clusters. There are even projects to study distant galaxies and quasars. Lab Notebooks and Calculators Each student is required to bring a notebook to each laboratory period in which notes, calculations, and data analysis is written. The notebook should be a 3-ring binder so that images, graphs, and other printed handouts can be added. All pages should be dated and clearly labeled with the project title at the top. All students must bring a scientific calculator to each laboratory session. The calculator functions should include logarithms, powers (xy), and scientific notation (EXP or EE button). Lab Report Format For most labs, completing the worksheet is sufficient. However, a number of times during the semester you will be required to write a formal lab report. Neatness counts: a neat report will receive more credit than a sloppy hand written report. The write-up must include the following sections, although it is often possible to combine sections in the interest of making the report more readable: INTRODUCTION—2 PURPOSE: This is a short description of the exercise and should not be a word-for-word copy of what is written in the lab manual. An example from an exercise in this manual might be: “We used a computer simulation of images of Jupiter and its moon Europa in order to find Jupiter’s mass. This was done using data obtained by examining Europa’s orbit in conjunction with Kepler’s Third Law.” PROCEDURE: Explain what you did and why you did it, in detail. In many cases you’re told which buttons to push and which numbers to record, but you should try to figure out the reasoning behind these operations for the stated purpose. This will become more important in the cases where you’re not explicitly told what to do in a step-by-step fashion. Many of the early labs teach procedures which will be used repeatedly, and you will find detailed procedures for these early labs extremely useful to refer to later when completing other labs. Everything in this section should flow logically toward the goal stated in the Purpose section. DATA: When you report data, don’t just write down numbers. Explain what those numbers are, what quantities they represent. When possible, express your data and calculations in chart form. This helps to organize your data and makes it easy for the reader to see at a glance what information you’ve gathered. RESULTS: Give your results, including any calculations, pictures, worksheets and graphs. Also be sure to discuss the uncertainties of all derived results. These do not include things like “human error”, “mistakes in measurement”, or “I forgot how to work my calculator,” because these are all things which can be fixed with little or no trouble, and which should be fixed by you as you work through the exercise. Uncertainties do include things like limitations on the measurements being made (e.g., nebulae don’t have hard edges, so it’s necessary to average a number of measurements to determine the diameter of one), approximations made in order to simplify calculations (for example, Kepler’s Third Law is changed a bit in the Mass of Jupiter exercise) and what effect removing those approximations would have, and estimations of how far away from the “real answer” you think you may be in terms of percent (as well as an explanation of how you arrived at those percentages). CONCLUSION: Sum it all up. Answer the questions posed in the procedure, along with any general principles you can infer from these answers. Report your result(s), paying particular attention to whether or not you achieved the goals laid out in the Purpose section. Explain any accompanying uncertainties, and discuss any difficulties you met with and how they might be minimized if you were to do the exercise again. Templates for the lab reports can be found in the folder labimages/template. INTRODUCTION TO ASTRONOMY USING COMPUTERS—3 Introduction to Astronomy Using Computers Level: Introductory Learning Goals: The student will acquire basic computer skills, learn the locations and acquire a working knowledge of the software and mathematics which will be used in future labs. Software: Starry Night, MaxIm, Netscape, Internet Explorer Image Directory: proj-01_Intro_Computers Image List: chapel.jpg, image02.fts – image20.fts Other: Math Worksheet Summary This exercise introduces the student to the software which will be used in the undergraduate astronomy laboratory. Procedure All Programs 1. This section is just a way to get you started with the software we shall use. For more detailed information on these programs, please check the appropriate appendix section. 2. The PCs in the lab use the Microsoft Windows operating system and are networked to ‘server’ computers with shared disks and printers. Along one edge of the screen is a bar called the ‘task bar’. This task bar shows you all the programs which are currently being run. In addition, shortcuts to many programs will sit in the taskbar. To start a program, either find its icon on the desktop and double click it, or find the icon on the taskbar and single click it. In the future, we shall refer to this process simply as ‘Run.’ (Note: If you cannot find a program, check with your lab instructor) The command ‘Run MaxIm’ for example should be interpreted as: ‘Click on Start, then on Programs, then Astronomy, and finally MaxIm’. Unless the instructions specify otherwise, all clicking is with the left mouse button. 3. All images in the lab are located in one directory with sub-folders pertinent to each lab. MaxIm should open directly to either this main directory or one of the subfolders. If it opens elsewhere, ask your lab instructor for help returning to them (if necessary). 4. Archived images for observation project labs are located in a separate directory. Your lab instructor will help you find them if it becomes necessary. Web Browser 1. While we are assuming that most who take this class will be at least passably familiar with the internet, not everyone will be. If you are not familiar with it, one of your classmates or your lab instructor can help you out. The computers in the lab are equipped with two popular web browsers, Internet INTRODUCTION TO ASTRONOMY USING COMPUTERS—4 Explorer and Netscape. Which you use is a matter of personal preference, but both should open to the Department of Physics homepage or the course web page for Modern Astronomy. 2. In class you will mainly use the internet to check the lab schedule and, later in the semester, to request images of your own for a research project. 3. From the Physics Dept. page, you can follow numerous links to information. By following the Course Web Pages link, then the Modern Astronomy link on the following page, you will get to info that is specific for the lab. If the browser opens to the Modern web page first, the previous instructions do not apply. Starry Night 1. Run Starry Night Pro. When the program starts, it will show a row of menu items at the top. This is typical of many of the programs you will be using in this lab. This is a sky display program which shows the positions of stars, planets, galaxies, etc. for any time of year at any location. You should see a window displaying various tools, including location, and another window displaying the current date and time. The date and time will be set to current system time, which may or may not match actual time, do not worry about this. At the bottom of the screen, you will see a status bar showing your current location, date, and time. 2. Now find out where Jupiter is. Click on the Find icon (shown in Figure2; an icon is a box with a picture which graphically represents a program or command) under the menu, and a new window will appear. Next to the box labeled Name contains, type in “Jupiter.” Click on Find. Jupiter will become centered in the window and a red arrow labeled “Jupiter” will appear next to the planet. (Note: You may get a warning that Jupiter is below the horizon. If so, just hit the Reset Time button on the warning window, and Jupiter will then center.) If you move your cursor over Jupiter, some basic info will appear in a window. Click on Selection on the menu and choose Get Info from the pull-down menu to get a color image of Jupiter, as well as some other useful information about the planet. 3. Dismiss the info window by clicking OK. Now, try adding labels. Select Guides, then select Constellations, then Boundaries. This shows constellation boundaries on the sky. What constellation is Jupiter presently in? You can turn labels on from the same menu.) (Hint: 4. Before leaving Starry Night Pro, look at the motion of Jupiter’s moons. In order to do this, you need to change the field of view. The field of view is how much space in the sky you can see. While Jupiter is still selected, right click on the box labeled in degrees in the as shown in Figure 3. A pull down menu will appear, select the choice labeled 15’, which represents 15 arcminutes. The display shows the four large moons of Jupiter first discovered by Galileo in 1610, both from above the ecliptic plane and from the viewpoint of Earth (bottom). You will need to turn off the horizon. Click Sky, then de-select Horizon from the pull-down menu. Press on the Time window and you will see Jupiter moving along its orbit and the moons orbiting the planet. How long does it take the innermost moon (Io) to complete one orbit around Jupiter? Note: If the screen shows daylight, you can turn off the daylight option with menu selection Sky -> Daylight option. 5. Close Starry Night Pro. Choose Don’t Save if the program brings a window up asking you to. INTRODUCTION TO ASTRONOMY USING COMPUTERS—5 MaxIm 1. Run MaxIm. Click on the option File, then Open. A new window will open in the MaxIm window. The space next to the words “Look in” will expand to show the drive and directory structure when you click on the down arrow at the right-hand side. Use this space to select the drive where the Proj01_Intro_Computers directory is located, as indicated by your instructor. Double-click on the Intro folder, and open the first image in the Intro directory by double-clicking on the name. 2. In a few seconds you will see a color image. Many of the images in the Intro directory have been taken by various telescopes and spacecraft. Examine several of the images named image##. To get to the next image, again choose File/Open, then select the next image name. Identify the objects in each of the images. The remaining images have been taken with one of the automated telescopes the University has operated (ATF, IRT or Rigel), which are part of the University of Iowa astronomy lab. Examine the menu bar along the top of the screen. Try a few things on the images that you have, just to see what they do. For example, try clicking on Color on the menu and selecting Pseudo Color from the pull-down menu. This will give you several options for changing the colors of the images. Try out some of these options. In later labs we will use this program extensively, so it would be wise to take a few minutes to play with it now. 3. Image comparison and image scale are two important concepts in astronomy. You will often be asked to compare one image against another to see if there are any changes between them. Sometimes this is simply a question of whether or not something has moved out of the image in question (for instance when planet or asteroid hunting). Other times, you will be comparing images of the same object taken through different filters to see the differences. Image scale is important because every image has some sort of scale in order to translate size in the image into real size. All image scales will be given in fractional units, for instance feet/pixel (feet per pixel). While the majority of images in astronomy will have scales of some unit per pixel, do not be surprised to see image scales of inches/centimeter or other “odd” units 4. For this exercise, we need to open chapel.jpg. The image scale of this picture is 0.05 meters/pixel (0.17 feet/pixel). First, you will need to measure the height in pixels of the image. To do so, put your cursor at the bottom of the building. Then, keeping the x-value constant, move the cursor to the top of the building. The difference in the numbers is your height in pixels. Calculate the actual building height in: feet : ____ meters:_____ 5. Close MaxIm by clicking on the × button on the upper right corner. Math 1) The last exercise in this lab is to complete the following mathematics worksheet. INTRODUCTION TO ASTRONOMY USING COMPUTERS—6 Math Worksheet For many people, the major impediment to learning astronomy is the mathematical background which is expected. This worksheet is designed to help you either catch up, or remember the math that you were supposed to have learned in high school. Do not be intimidated by this worksheet! Most of what follows is the sort of math that you use in your everyday life, when calculating tips, or balancing your checkbook- it has just been formalized. Two important pieces of advice: first, always check to see if your answer makes sense. For example, if you calculate the height of the dust pillars in the Eagle nebula, and get 0.04 meters, this can not be right, because you could barely see 0.04 meters from a 100 meters away, much less from many parsecs. The second piece of advice has to do with the magnitude of numbers. Calculations in astronomy nearly always yield immense numbers. One way to deal with this (which will probably help you remember things) is to always translate your answers into something you can comprehend. The actual height of the dust pillars in the Eagle nebula is 16 trillion miles (about 32 trillion kilometers). This is the same as 16,000,000,000,000 miles. But for most of us, numbers above 10 become simply “many”. To give this number meaning, you could try comparing it to the national debt (the same incomprehensible number). Or you could try comparing it to the number of grains of sand on the planet (another incomprehensible number!). Or you could imagine each person on the planet (you, your family, your friends and all of their friends, and so on), walking all of the way from New York to California- a journey of over a year by foot. Stack all of those journeys end to end, and you will be just shy of 16,000,000,000,000 miles. Be creative. Whatever helps you to imagine these numbers will help you to imagine astronomy. You should try to do as many of the following problems as you can without using your calculator. However, you may want to use your calculator for some of these problems. Different companies label the buttons on their calculators differently but scientific notation is probably labeled one of two ways on your machine. 3.15×106 is entered into your calculator as 3.15<EXP>6 or 3.15<EE>6. Your calculator (and many computer applications) also display scientific notation differently. The ×10 doesn’t appear on the display. Instead, 3.15×106 will appear as 3.156 or 3.15E6 or 3.15e6, while 3.15×10-6 will appear as 3.15-6 or 3.15E-6 or 3.15e-6. Write the following numbers in correct scientific notation 1) 0.001=_____________ 2) 5300=______________ INTRODUCTION TO ASTRONOMY USING COMPUTERS—7 Round the following numbers to 2 significant digits. Remember, if the first digit you drop is greater than or equal to 5, round up. 3) 2,770 = __________ 4) 3.42218 = _________ 5) 34.821 = _________ Combining Numbers Multiplying numbers written in scientific notation: The numbers in front of the power terms are multiplied together and the exponents are added together to get a new exponent; e.g.: Dividing numbers written in scientific notation: The numbers in front of the power terms are divided, and the exponents are subtracted. For example: Significant Figures Your answer should have only as many significant figures as the measurement with the least number of significant figures. Apply the rules for combining of numbers to the following problems. Don’t forget to report your answer with the correct number of significant figures. Try to do the first problem without your calculator. 6) 7) Order of operations If you are mixing operations together, powers are performed first, multiplications and divisions next, and additions and subtractions last, unless parentheses dictate otherwise. (Operations enclosed in parentheses are to be carried out first.) Apply these rules to the following problems: INTRODUCTION TO ASTRONOMY USING COMPUTERS—8 8) 9) 10) Units Just as numbers which appear both in the numerator and denominator of a fraction cancel, units which appear in the numerator and denominator of a fraction cancel. Apply this rule to find the simplest units to express the following: 11) 12) 13) Hint: a Newton(N)=kg·m/s2 Logarithms Any number can be written as 10x if we let x be a real number, not necessarily an integer. (Integers are ...,-3,-2,-1,0,1,2,3,...) For example 4=100.6, or 0.6=log(4). The log function is defined such that log(10x) =x. The function log(y) is easily calculated using a calculator; enter y, then press the log key. Try the following, first without your calculator, then with your calculator: 14) log(100) = _________ 15) log(1) = ___________ 16) log(42 ) = __________ Ratio Problems Many times in astronomy, we wish to compare one object to another. This often simplifies the math, and makes the constants drop out (so we don’t have to worry about remembering them!). Most of the problems that you will do in this course can be done as ratio problems. Following is a detailed ratio problem. The first part is worked both ways, without ratios, and with ratios. The second part is left for you to try. A piece of paper has a height of 11 inches, and a width of 8.5 inches. How much larger is the angular height of the paper one foot from you than ten feet from you? INTRODUCTION TO ASTRONOMY USING COMPUTERS—9 Without ratios: The formula relating angular size, θ (arcseconds), linear size, d, and distance, D, is: θ = 206265 ⋅ d D where d and D are measured in the same length units (e.g., km). To find the angular height at the near location (one foot), set d=11 inches, and D=12 inches (d and D must be in the same units so that the units will cancel). This gives: θ = 206265 ⋅ 11in 12 in The inches will cancel out, and so θ = 189,076". This number is very large, and not intuitively obvious. So, convert to degrees by multiplying by 1/3600 (1’/60", then by 1°/60’). Thus the angular height of the piece of paper is 52.5°. To calculate the angular height at the far location (ten feet), set d=11 inches, and D=120 inches. This gives: θ = 206265 ⋅ d 11in = 206265 ⋅ = 18908′′ = 5.25 D 120in Again the inches cancel out, and θ=18,908”. Again this number is difficult to understand. If we convert to degrees as above, we find that θ=5.25°. To find out how much larger the paper appears at one foot than at ten feet, we must divide the angular size at one foot by the angular size at ten feet. Therefore the size at one foot is 52.5/5.25=10 times larger than at ten feet. With ratios: The formula relating angular size, linear size, and distance holds true for all objects and all conditions. If we use subscripts to label the one foot distance and the ten foot distance, we can write two equations: and If we divide these two equations, (left side by left side and right side by right side), we can see that the 206,265” factor will cancel out as will the actual height d (this does not change). Thus, INTRODUCTION TO ASTRONOMY USING COMPUTERS—10 θ1 D1 = θ 2 D2 And, doing almost no math at all, we see that D1/D2=10, and that the angular size is 10 times larger at one foot than at ten feet! 17) Try the same calculations as above using d=8.5 inches. Calculate the angular width of the paper from distances of 12 inches and 120 inches. What is the ratio of the two angular widths? What is the ratio of the two distances? Note: Use 3 significant figures in all answers Use the math skills you have learned above to do the following problems. Don’t forget about units and significant figures. 18) A photon travels at the speed of light ( c = 3.00×108 m/s). How long does it take for a photon to travel the distance between the Earth and the Sun (1 AU = 1.5×1011 m)? Express your answer in minutes. INTRODUCTION TO ASTRONOMY USING COMPUTERS—11 19) Distance and Magnitudes: The distance (d) to a star in parsecs can be written: d = 101+ ( m − M ) /5 where m is the star’s apparent magnitude and M is the absolute magnitude. Taking the log of both sides and solving for m gives The Sun has an absolute magnitude M=4.7. If a star of equal absolute magnitude has an apparent magnitude m=6.0, how far away is it in parsecs? If the sun were moved to a distance of 10 pc from us, what would its apparent magnitude be? INTRODUCTION TO ASTRONOMY USING COMPUTERS—12 20) Small angle formula: Given that Jupiter is 5 A.U. from Earth, and has an angular size of 43 arcseconds, what is its linear size in km? Use the small angle formula: d= D ⋅θ 206265′′ where d is the linear size of the object, D is the distance to the object (both d and D in the same units), and θ is the angular size in arcseconds. 21) The formula for percent error is: Suppose you have calculated the distance to the moon to be 3.81×105 km. The accepted value is 3.84×105 km. What is your percent error? IMAGE ANALYSIS—13 Image Analysis: Basic Techniques Level: Introductory Learning Goals: The student will become familiar with the image analysis programs used in lab, and also will develop an understanding of the size and age of planetary nebulae. Terminology: ADU count, color palette, coordinates, histogram, nebula, pixel, pseudo-color image Software: MaxIm Image Directory: proj-04_Image_Analysis Image List: chapel.fts, m42.fts, m57.fts Summary A number of basic concepts of image analysis are introduced, including ADU count, histogram adjustment, angular distance measurement, convolution, and image arithmetic. Background and Theory Obtaining useful scientific results from an image often requires the application of image analysis tools. Many of the most commonly used tools are illustrated in this exercise using one terrestrial image and two astronomical images. The following is intended only as a brief summary of the basic concepts. A CCD image consists of a rectangular array of cells called pixels, each of which is assigned a number (the Analogue to Digital Unit or ADU count) which is proportional to the brightness of the image at that location. For the images in this exercise, the range of ADU values is 0 to 65536 or 216; i.e., there are 16 bits assigned to hold the value of each pixel. A single image is inherently monochromatic (‘black and white’) so that the display program normally converts the ADU counts to shades of gray, a so-called ‘grayscale’ image. Since most computer video systems can only display 8 bits of grayscale (256 shades), it is necessary to select the minimum and maximum ADU counts corresponding to the black and white levels, respectively. This can be done either by adjusting the contrast/brightness control or by using the histogram tool. The histogram is a plot of the number of pixels at each ADU level. The user adjusts the minimum and maximum level using the mouse and the arrows at the bottom of the histogram. The x and y coordinates of individual pixels can be read directly by moving around the image with the mouse. One can display multiple images at the same time, and rotate, expand and contract selected images. Images may also be added, subtracted, multiplied, and divided by either constants or other images. The grayscale representation of an image can be converted to a pseudo-color image by changing the color palette, i.e. the mapping of ADU levels to a sequence of colors. These are not true colors in the sense that of a color photograph, but it is sometimes useful to choose a color palette to emphasize small intensity differences, particularly in extended objects such as nebulae. The lab uses three sample images to illustrate some of these image analysis tools. The images of M42 and M57 were taken with the Rigel telescope in Arizona, while the Chapel image was taken with a regular digital camera. Chapel.fts is an image of the Danforth Chapel near the Iowa Memorial Union. M42.fts is an image of the well known star formation region M42 (The Great Orion Nebula) in the sword of Orion. It is about 400 pc distant. The total mass of the nebula is about 106 solar masses. The central part of the nebula containing the 4 Trapezium stars is overexposed and cannot be seen clearly. IMAGE ANALYSIS—14 M57.fts is an image of the Ring Nebula, a famous example of a planetary nebula. 1 The object consists of a central hot star and a surrounding cloud of gas. The gas is glowing because of ionization from ultraviolet radiation from the central star. The Ring Nebula, shown in Figure 1, is one of the brightest of all planetaries, but imaging it with small telescopes is difficult, since it is quite small and the central star is very faint (V=15). The distance to the Ring Nebula is about 700 pc. Procedure 1. Run MaxIm. 2. Load the image chapel.fts (located in directory misc). To do this, click on File in the menu bar at the top of the screen. Then choose Open from the pull-down menu. Choose the image drive from using the box next to the words “Look in”, as described in the Intro to Astronomy Using Computers lab. Ask your instructor if you can’t remember which drive contains the laboratory images. Open the misc folder. Now double-click on the file name chapel.fts. 3. The image you are seeing is composed of individual pixels arranged in a rectangle, with dimensions 800 × 600 or 480000 pixels altogether. The image display program reads each ADU value and converts it into a gray level, with larger values being more nearly white and smaller values more nearly black. The position and ADU count of the individual pixel under the cursor can be read at the bottom of the screen. The ADU count (the i:) is given next to the set of (x,y) coordinates at the bottom right corner of the screen. Notice that the counts in adjacent pixels are often different from one another, even if the pixels look equally bright. Because of the nature of photons; the change in the number of photons has to be fairly large before a brightness change is obvious. Can you tell the difference between pixels with high ADU counts and those with low ADU counts? 4. It is sometimes convenient to adjust the image display gray levels in order to enhance faint features in the image. This is known as adjusting the histogram. To do this, use the Screen Stretch window (shown at right) which should have been displayed upon starting the program. If not, select View from the menu and Screen Stretch Window from the pull-down menu. To adjust the display, move the green and red arrows under the main window. The red arrow adjusts the black background and the green adjusts white levels. Moving the arrows close together produces a high contrast. The histogram is adjusted automatically as you move the arrows. Continue to adjust the histogram until you find a setting that brings out a maximum amount of detail. As you adjust the histogram, you are adjusting the 256 shades of gray scale to cover the desired range of brightness within the image. Including the entire range of brightness within the 256 gray-scale levels can sometimes make it difficult to detect fine differences. Including a small range of brightness hides a lot of information off of the edges of the scale. 5. You may also adjust the contrast and brightness of the image by clicking in the smaller window on the right side of the Screen Stretch. When you click and hold in the window, your cursor will change to a cross. Moving your cursor vertically will adjust the brightness and moving horizontally will adjust the 1The reason the name planetary nebula was coined is probably because these objects are similar in appearance to faint planets when viewed with modest-sized telescopes -- both look like fuzzy disks. IMAGE ANALYSIS—15 contrast. Note that the green and red arrows will also move as you move your mouse in this small window. As before, the adjustments will occur automatically. Continue to adjust the histogram until you feel you have the most detail possible. Adjusting the histogram optimally takes a lot of practice. Don’t be frustrated if you spend fifteen minutes doing what your lab instructor does with just a few clicks. 6. To examine the image more closely, especially the variation in pixel intensity (ADU count), select the Zoom from the menu, it will start out reading 100%. You may also press the + and – buttons next to the zoom pull down. Select a reasonable zoom level for examining the image. This level will change from image to image. For the chapel image, you will need to select a zoom of at least 400%, perhaps larger. 7. While the original image is reasonably clear, we can highlight small scale features using a convolution mask. 2 Click on Filter and choose Unsharp Mask. A new window will open. Don’t worry about any of the options, just use the default values for now. Click OK and you should be able to see more detail in the vehicles in the background. 8. Now repeat an exercise from chapter 1. Measure the height of the building in pixels by putting the cursor at the bottom of the building, and mark down the coordinates (x,y) shown. Keeping the x value constant, move the cursor to the top of the building and record the number. Subtract the first y value from the second to get the height of the building on the image in pixels. Calculate the actual height of the building in both feet and meters using an image scale of .17 feet/pixel and .05 meters/pixel, respectively. 9. Discard the chapel image by clicking on the small × in the upper right corner of the image window. 10. Load the image m42.fts by clicking on File/Open. Click on m42.fts in the image list box, and click on Open. Adjust the histogram. Faint nebulae can often be seen better by producing a negative image. Try this by reversing the positions of the red and green arrows. That is, put the red arrow to the right of the green arrow. Readjust the histogram. 11. Astronomers are often interested in the order of magnitude of a calculation. That is, do we expect to see millions of stars in a region, or just a few? As an example, we can estimate the number of solar-mass size stars that may be formed from the glowing gas of M42. To do this, you must first find the radius of M42. Move the cursor over a point near the center of the nebula. Mark down the coordinates (x,y) shown. Next move the cursor to a point on the edge of the nebula and mark those coordinates The process of convolving an image involves manipulating its ADU counts according to some predetermined mathematical function. You can think of convolving an image as applying one of several special filters to it. 2 IMAGE ANALYSIS—16 down. From these sets of coordinates, you can find the radius (in pixels) using the distance formula: where r is the radius and the x’s and y’s are the coordinates you measured. 12. Take at least 3 more measurements of radius and then take the average of them to get your radius (in pixels). Convert this into arcseconds using the scale of 3 arcseconds per pixel. 13. We can determine the linear size of the object from the angular size and the distance, using the small angle equation: where d and D are in the same units, and θ is in arcseconds. The distance from the Earth to M42 is approximately 400 pc. Find the linear size of M42 in pc. Convert this result to meters. (1 pc = 3×1016 m) 14. Spectral lines indicate that the cloud is made mostly of hydrogen, and that there are roughly 1010 atoms per cubic meter (n = 1010 m-3). Since we know the mass of hydrogen, the mass density, ρ, of the nebula can be obtained by3: ρ = n⋅mH = 1010×1.6×10-27 ≈ 1.6×10-17 kg/m3 15. Multiplying the density by the volume yields the total mass of hydrogen in the nebula. If we assume that the nebula is approximately spherical, the mass can be calculated using the following formula (where r is the linear size, actually the radius, from step 13): M = ρ⋅V = ρ(4/3)πr3 16. How many solar mass stars can be created by the gas in M42 if it all collapses to form solar mass stars? (See Appendix H for the mass of the sun.) 17. Discard M42.fts and load M57.fts. Adjust the histogram so that the ring is not so glaringly bright – use your best judgment to determine when the ring shows the most detail. 18. Notice the star at the center of the nebula 4. This is the star which is shedding its outer atmosphere to produce the nebula. Find the diameter of the nebula (in pixels). Convert this diameter to arcseconds using the image scale of 0.5 arcseconds per pixel. 19. Find the diameter of M57 in a.u. (Hint: the distance to M57 is also given in the background section.) 20. You may have noticed that the length you measured is neither the longest nor the shortest diameter of M57, but is rather an average diameter. Divide this average diameter by two to get an average radius of the nebula. If the sun were to produce a nebula of the same size as M57, would the Earth be inside or outside of it? 3 ρ is the Greek letter rho, pronounced “row.” 4 There is another star inside the ring, offset from the center. This is a foreground star and has nothing to do with the nebula IMAGE ANALYSIS—17 21. Convert the radius of M57 from a.u. to km. 22. The average expansion speed of the gas in the nebula is 20 km/s. If it is assumed that the nebula has been expanding at this speed for its entire lifetime (not a very sound assumption, but it is OK as a rough estimate), it is fairly simple to estimate the nebula’s age, since r = v⋅t, where r is the distance traveled, v is the velocity, and t is the time. The gas from the nebula began expanding from the star at the center of the nebula. Use this to estimate the nebula’s age in seconds and convert the answer to years. For a solar type star, is the planetary nebula phase a small or large fraction of its lifetime? IMAGE ANALYSIS—18 Image Analysis Worksheet Chapel Image Calculate the height of the chapel in: Feet:__________ Meters:___________ M42 Image Calculate the equivalent number of solar mass stars: a. Average pixel radius = ___________ pixels b. Angle θ = ______________” c. Radius (d) = ___________pc. = ________________meters d. Mass of nebula =_______________ kg e. Number of solar mass stars that could be created:______________ M57 Image Calculate the age of the nebula: b. Average pixel diameter = ____________pixels c. θ = _______________ “ d. Average diameter: _________________AU e. Average radius: _________________AU f. Radius: _________________km g. Would the Earth be: inside or outside of the ring? __________________ h. Age of nebula: __________________ i. Is this a small or large fraction of a star’s life? ____________________________ LABORATORY SPECTROSCOPY -- 19 Laboratory Spectroscopy Level: Intermediate Learning Goals: This lab illustrates some of the capabilities of spectroscopy using sophisticated spectroscopic equipment. In particular, the temperature of the Sun is measured. Terminology: Wien’s Law, Kirchoff’s Laws, continuous spectrum, emission line spectrum, absorption line spectrum Software: Ocean Optics OOI Base 32 for Windows Summary There are a number of steps to this lab, intended to give a clear idea of what a spectrometer is doing, and the information that can be gained by studying the spectrum of a light source. First, the spectra of different types of objects in the lab will be studied and wavelengths of spectral lines will be measured. Then measurements of the spectrum of gas discharge tubes and the Sun will be made. Background and Theory Spectroscopy is the measurement of the intensity of light at many different wavelengths, and the interpretation of those measurements using theories of physics. Spectroscopy is absolutely crucial to astronomy. With few exceptions, such as the study of rocks returned from the Moon or data from Mars landers, almost everything we know about the universe comes from analysis of light from astronomical objects. From spectroscopy we have learned the temperatures, luminosities, and chemical compositions of the stars. Spectroscopy is also of importance in other fields of science and technology. It can be used to measure the chemical and physical state of ocean water, glucose levels in human blood, and in industrial procedures. Spectroscopy is one of the better examples of a field of physics that has significantly impacted society. Most spectrometers are fundamentally simple in design. A thin beam or ray of light passes through, or is reflected from an object which spreads out, or disperses the light according to wavelength. An easy way of visualizing this is to think of a prism which spreads out light into all the colors of the rainbow. The dispersing element (a prism or diffraction grating) sends the violet light in one direction, the yellow light in a slightly different direction, the red light in still a different direction, and so on. This dispersed, polychromatic light is then focused onto a surface which acts as a detector. In lecture demonstrations, this is just the overhead LABORATORY SPECTROSCOPY -- 20 projector screen, and your eye is the detector that sees that the different colors have different intensities. For much of twentieth century astronomy, the detector was a photograph plate. Photographic plates are still used in some spectroscopic applications. Modern instruments use a CCD (charge-coupled device) in which an electronic wafer builds up an electrical charge when light shines on it. This charge is later read out and measured by a computer. The spectrometer which is used in this exercise is a USB4000 device manufactured by Ocean Optics. It is an amazingly compact device which has one input (a fiber optics cable which shines the light into the spectrometer) and a USB port to send data to the analysis computer. Software provided with the spectrometer permits display and analysis of the spectra. A diagram of the USB4000 is shown in the figure below. Light comes in from the fiber optics cable through the SMA connector (labeled 1) and goes through a slit (labeled 2). The size and dimensions of the slit control the amount of light allowed into the spectrometer and also the spectral resolution of the device. Next, the light passes through a filter (labeled 3) to restrict the wavelengths that continue on. Light is then reflected a collimating mirror (labeled 4) on the far wall of the spectrometer, and then strikes the diffraction grating (labeled 5), where it is dispersed, or spread out according to wavelength. The focusing mirror (labeled 6) then focuses the dispersed light onto the CCD array detector (labeled 8). There is a relation between position on the detector and the wavelength of light. The intensity of light as a function of position on the detector therefore corresponds directly to intensity as a function of wavelength, which is the spectrum. Not shown are the electronics which read out the charge on the detector, digitize the signal, and format it for the USB port. All of this is crammed in a box the size of a deck of cards! When the spectrometer is connected to the computer, and the control program is running, there are a number of simple controls the user has over the display and analysis of the spectrum. • The vertical cursor measures the wavelength of observation and gives the intensity of light at that wavelength. It is controlled by the mouse. The wavelength and intensity reading are shown in the lower left corner of the screen. • Right above the spectrum are a number of data boxes that can be set by the user. The one at the far left gives the integration time, or the length of time the device averages the signal before readout. The units are milliseconds. The longer the integration time, the larger is the signal recorded. Next to it is the number of spectra that are averaged before display. The larger the number of spectra averaged, the clearer and less noisy the spectrum will appear. You will find it helpful to manipulate these control parameters when studying the spectra of the gas discharge tubes and the spectrum of the Sun. • Finally, at the top of the screen will be a set of standard Windows menu bars. The one labeled “View” can be used to set the scale of the spectrum. If you bring up the dialog box, you can set the range of the abscissa (x coordinate) and ordinate (y coordinate). This is a very useful feature for making precision measurements of spectral lines, or examining the shape of spectral lines. Procedure Part A: Spectra of Light Sources LABORATORY SPECTROSCOPY -- 21 1. The computer will probably be in the Windows desktop when you arrive. Double click on the OOI Base 32 icon to start the program. Look around on the lab table and identify the USB4000 unit, the fiber optics cable connected to it, the stand for holding the fiber optics cable, and the USB cable connected to the computer. You’re ready to start. 2. There is a black box on the lab table with several small LED light bulbs on the edge (see image at right). The light bulbs light up when the switch is turned on. The first light bulb is not “dead”; it emits in the infrared at a wavelength to which your eye is not sensitive (you can check us out on this!). For each of the light bulbs, measure the central wavelength (wavelength at which the light bulb is brightest), and the range of wavelengths over which the light emits significant amount of light. Record your data in the worksheet below. Part B: Spectrum of a Continuous Source 1. Shine the light from an overhead projector into the fiber optics cable. The overhead projector bulb is a regular incandescent light. Make a reasonably accurate sketch of the spectrum you see on the axes provided in the worksheet below. 2. Now calculate the temperature of the filament, using Wien’s Law. Here is a chance to apply an equation you have learned about in class to a real physical situation. Remember that Wien’s Law is a relationship between the temperature of an object and the wavelength at which it is brightest. The relationship is where T is in degrees Kelvin and λmax is the wavelength (in meters) at which the object emitting the radiation is brightest. 3. Carry out the calculation in the space above the spectrum in the worksheet. 4. With the data you have, and have shown above, what is an uncertainty that limits the degree of precision to which you can measure the temperature T? Part C: Spectra of Gas Discharge Tubes 1. Kirchoff’s second law of spectroscopy says that a hot, tenuous gas emits a spectrum which consists of isolated, bright emission lines. The wavelengths at which these lines occur are a unique fingerprint of the gas that is being excited. Each lab table will have two discharge tubes, one of hydrogen and the other of helium. Turn on the hydrogen lamp and bring the optical fiber up to the light. LABORATORY SPECTROSCOPY -- 22 2. Draw the spectrum of hydrogen on the axis provided with the worksheet, taking care to make the spectrum as accurate as possible. 3. Measure the wavelengths of the six most prominent lines (if you can find six), and record the data in the table on the worksheet. Remember to increase the sensitivity of the spectrometer by increasing the integration time, or the number of cycles to average. Also, when measuring the wavelength of a line, take care to position the cursor exactly in the middle of the line. Otherwise, a significant and avoidable error will result. 4. When you have completed your observation of hydrogen, repeat 1-3 with helium. Part D: Solar Spectrum 1. Use the ring stand to hold the entrance to the fiber optic cable at the window of the lab room. Direct sunlight is not necessary, and even on a relatively cloudy day, the light will be bright enough. The spectrum of this light will be the spectrum of sunlight. 2. Adjust parameters such as integration time, number of cycles to average, and scale of the spectrum to give you a good display that is convenient for making measurements. 3. Draw an accurate sketch of the spectrum on the axis in the worksheet. 4. How would you characterize the solar spectrum in terms of the types of spectra described in Kirchoff ’s laws, i.e. a continuous spectrum, an emission line spectrum, or an absorption line spectrum? 5. Using data from your plot (and with the help of the cursor measurer), and applying Wien’s law, measure the surface temperature of the Sun. Put your calculations in the space below the plot. 6. Measure the wavelengths of some of the strongest spectral lines in the spectrum of the Sun. Record them in the table below. Which of them can you identify from Part C. above? If you can identify it, indicate what element is responsible for it. You have thereby demonstrated that this element is present in the Sun. 7. When you have completed your table, check with your teaching assistant for the accepted table of lines in the solar spectrum. LABORATORY SPECTROSCOPY -- 23 Laboratory Spectroscopy Worksheet A. Spectra of LED Light Sources Bulb Nr Color Central Wavelength B. Spectrum of a Continuous Source Range of Wavelengths Comment LABORATORY SPECTROSCOPY -- 24 C. Spectra of Gas Discharge Tubes Wavelength Line Strength Hydrogen Spectrum Wavelength Line Strength Helium Spectrum LABORATORY SPECTROSCOPY -- 25 D. Solar Spectrum Wavelength Strength Identification SPECTRAL CLASSIFICATION OF STARS —26 Spectral Classification of Stars (CLEA) Level: Introductory Learning Goals: This lab teaches the basic techniques and criteria used in the Morgan-Keenan system of spectral classification. Terminology: absorption line, emission line, continuum emission Software: CLEA Stellar Spectra for Windows Summary In this lab, the student examines and classifies the spectra of 25 stars. The behavior of absorption lines throughout the spectral sequence is also examined. Background and Theory Classification lies at the foundation of nearly every science. We are all aware that biologists classify plants and animals into subgroups called genus and species. Geologists also have an elaborate system of classification for rocks and minerals. Scientists develop classification systems based upon perceived patterns in and relationships among natural objects. Astronomers are no exception. They classify planets as terrestrial or Jovian, galaxies as spiral, elliptical or irregular, and stars according to the appearance of their spectra. In this exercise you will study the method that astronomers use to classify stars, which is called the MK Spectral Classification system. M and K are the initials of the founders of this system, W. W. Morgan and P. C. Keenan. A spectrum of a star is composed of its continuum emission, as well as a number of ‘lines’ which can be either emission or absorption lines. The continuum emission is a product of the blackbody radiation of the star. It varies smoothly with frequency (or wavelength), and has a peak at a frequency determined by the temperature of the star. Emission lines are excesses of radiation at specific frequencies, caused by electrons in atoms dropping down into lower energy levels. They can also be caused by molecular transitions to lower energy levels. This sort of line appears brighter compared to the region of the spectrum around it. Absorption lines cause holes in the continuum emission where the radiation is removed from the continuum emission. This is caused by atoms (or molecules) absorbing radiation, and moving to a higher energy state. This process causes the lines to look darker when compared to the region of the spectrum around them. Stars come in a wide range of sizes and temperatures. The hottest stars in the sky have temperatures in excess of 40,000 K, whereas the coolest stars that we can detect optically have temperatures on the order of 2000 - 3000 K. As you might guess, the appearance of the spectrum of a star is very strongly dependent on its temperature. For instance, the very hottest stars (called O-type stars) show absorption lines due to ionized helium (He II) and doubly and even triply ionized carbon, oxygen and silicon. On the other hand, the coolest stars (M-type stars) show lines produced by molecules. Morgan and Keenan (and their predecessors) based their spectral classification system on this dramatic change in the appearance of the spectrum with temperature. Morgan and Keenan built on the Harvard classification system, developed by Annie Cannon and her associates. The Harvard classification system is a spectral sequence starting with the hottest stars, type O, and running through intermediate classes (B, A, F, G, K) to the very coolest stars (type M). Each class can be divided into subtypes running from 0 to 9 (for instance, A0, A1,...,A8, A9). To make certain that every astronomer around the world would be able to classify stars using their system, they set up a sequence of standard stars. For instance, Vega is the standard for A0, and the sun is the standard for G2. Hence, to classify the spectrum of a star, an astronomer must first obtain spectra of all of the standards with her telescope. The unknown spectrum can then be classified by the simple process of visually comparing it with the standard spectra. Because standards have not been defined for all of the subtypes, interpolation is sometimes necessary. SPECTRAL CLASSIFICATION OF STARS —27 Morgan and Keenan added another dimension to this classification system− a luminosity dimension. The luminosity classes are represented by Roman numerals and are as follows: main sequence (also called dwarf) (V), subgiant (IV), giant (III), bright giant (II), supergiant (Ib), bright supergiant (Ia). Hence, the full spectral type of a star requires both a temperature type and a luminosity type. For example, the sun is classified as G2 V, Vega is A0 V, Rigel is B8 Ia, and Betelgeuse is M2 Ia. In this lab you will be classifying only in the temperature dimension (Luminosity classification is much more difficult than temperature classification.), and all of the stars you will be considering are main sequence (V), but keep in mind that a full classification requires a luminosity class as well. Procedure 1. There are two discharge tubes located in the laboratory. They should be labeled with the name of the gas that they contain. Use the spectroscope at your workstation to look at each tube. Notice that the colored lines that you see inside the tube are different for the two tubes. This is because the elements in the tubes are different, and therefore absorb and emit at different wavelengths. The lines in the tubes are emission lines, because there is no background continuum source to cause the gas to absorb emission. The spectral lines of stars are usually absorption lines because the lines are formed in the photosphere, which is above the hotter stellar interior. 2. Run Stellar Spectra in the CLEA Labs folder on your desktop. Log-in to the exercise, and click on OK. SPECTRAL CLASSIFICATION OF STARS —28 3. Choose Run from the File menu at the top of the window to begin the program. Two options then appear. Choose the second option, Classify Spectra. 4. The window is now filled by three graph windows and a set of options along the right hand side. In order to use these options, you must first load a set of standard spectra. To do this, choose the File menu at the top of the window, and then choose Atlas of Standard Spectra. For this exercise, the Main Sequence atlas will be sufficient. You will now need to move the atlas out of the way, so that you can see the main window again. To do this, you must ‘grab’ it with the mouse by clicking on the blue bar where it says ‘Main Sequence’, and then, holding down the mouse button, move it to the right, and out of the way. The buttons labeled up and down in the main window may be used to scroll through the main sequence spectra. Notice that the spectra show absorption lines, or places where the level of the intensity of the spectrum is unusually low (a ‘trough’). Each line is created by a specific type of atom or molecule in the star which absorbs emission from the star at a specific wavelength. A few of the unknown spectra you will be classifying also show emission features, which are places where the intensity is unusually high (a ‘peak’). These lines are due to the presence of atoms or molecules which emit at those wavelengths. 5. Scroll down through the list of Standard (Main Sequence) spectra, using the scroll bar on the right side of the window. Notice that the depth of the absorption lines as well as the overall slope of the line, changes as you move through the list. 6. Choose an absorption line from one of the standard spectra. Describe this line on the worksheet by its approximate location, and the spectral type in which it appears. Also write down anything special that you notice about the line; for example, the line is much deeper than any of the others. For example; ‘The deep absorption line at the far left edge of spectral type G0.’ Load the spectral type in which your line appears into the graph windows by double clicking on it. Then determine the name of this specific line (as well as the element which produced it), by selecting the Spectral Line Table from the File menu. Now click on the line you want to know about. The name of the line will be outlined by two dashed red lines in the Spectral Line Identification window. If you do not have a name bracket in the table, move your mouse slightly and click again until you do. Record the name of the line and the wavelength on the question sheet. From the name of the line, determine the element which formed it. If you are unsure of which element the abbreviation stands for, consult a periodic table or ask your instructor. 7. Now use the standard spectra to answer the other questions on the question sheet. 8. Now select File, then Unknown Spectrum, then Program List. Load the first unknown spectra on the list, HD 124320. The unknown spectrum appears in the middle window, with two main sequence spectra in the top and bottom windows. 9. By comparing the unknown spectra with the standard spectra, you can determine the spectral type of the unknown spectrum. Scroll through the main sequence spectra, using the up and down buttons until you ‘bracket’ the unknown spectrum between two spectra in the standard spectral sequence. Notice that not all of the spectral types are represented in the atlas. This means that some of the unknown spectra will not exactly match the atlas spectra. However, it is possible to estimate the correct spectral type by comparing the unknown spectrum to the two closest main sequence spectra. For example, if you find that your unknown falls between the A1 and A5 standards, but is closer to A5, you will probably classify it as A3 or A4. It is helpful to use the difference button located to the right of the bottom window. This button changes the lower window, so that it shows you the difference between the upper window and the unknown spectrum. The best match will make the red line in this window nearly straight. Note that, in the difference window, absorption will appear as a peak and emission as a trough, since you are subtracting the spectra, do not let this confuse you. Record the spectral type for the star in the chart at the back of this lab. Also include a comment explaining how you determined the spectral type. When necessary, make sure you also comment on any ‘odd’ features you notice in the unknown spectra, such as more absorption at one wavelength than the matching spectra would indicate. SPECTRAL CLASSIFICATION OF STARS —29 10. Load each of the program stars by selecting Next on List from the Unknown Spectrum menu and determine its spectral type. Warning! A few of the program spectra are ‘peculiar stars’ that do not fit very well into the spectral sequence. Try to describe these peculiar spectra in terms of the standard spectra as well as you can. SPECTRAL CLASSIFICATION OF STARS —30 Spectral Classification Worksheet 1. Description of absorption line:_________________________________________ ________________________________________________________________ Spectral Type:_____________ Name of line:______________ Wavelength:_______________ Element:__________________ 2. At which spectral type does the H I (H delta) line become indistinguishable from the rest of the spectrum? 3. Which spectral type shows the strongest Hγ (H gamma) line? 4. Which spectral type has the most constant continuum emission? Can you explain what you are seeing? Hint: At what part of the spectrum are you looking? 5. What is the wavelength of the Hε (H Epsilon) line? The Hδ (H Delta) line? The Hγ (H Gamma) line? 6. Fill out the chart of unknown spectral types on the next page. If you need more space, feel free to use a separate sheet of paper. SPECTRAL CLASSIFICATION OF STARS —31 Spectral Type Source Name HD 124320 HD 37767 HD 35619 HD 23733 O 1015 HD 24189 HD 107399 HD 240344 HD 17647 BD+63 137 HD 66171 HZ 948 HD 35215 Feige 40 Feige 41 HD 6111 HD 13863 HD 221741 HD 242936 HD 5351 SAO 81292 HD 27685 HD 21619 HD 23511 HD 158659 Comment on how Unusual type was determined Features AGE AND DISTANCE OF A STELLAR CLUSTER -- 32 The Age and Distance of a Stellar Cluster Level: Intermediate to Advanced Learning Goals: The student will learn how to make a color-magnitude diagram using differential photometry. By identifying the main sequence, the distance to the cluster can be found. Also, the relationship between the main-sequence turn-off and the age of a cluster is explored. Terminology: main sequence, turn-off point, absolute magnitude, apparent magnitude, distance modulus, isochrone, differential photometry Software: MaxIm Image Directory: proj-12_Age_Distance_Cluster Image List: m67-i.fts, m67-v.fts Summary The goals of this lab are to determine the photometric magnitudes and color indices of members of the evolved stellar cluster M67 (NGC2682) using images taken with V and I filters. A plot of the V magnitudes versus V−I color index constitutes a color-magnitude (or H-R) diagram which can be used to determine the distance and approximate age of the cluster. Background and Theory Open star clusters are groups of several hundred stars held together by gravity. All of the stars in a cluster are thought to have been born at the same time from a parent cloud of gas and dust. Many clusters are relatively young (less than ~108 years, young for stars!). A plot of apparent magnitude versus surface temperature (or equivalently color index) reveals a characteristic nearly diagonal line called the main sequence. Stars on the main sequence (e.g. the Sun) are still ‘burning’ hydrogen in their cores. However, several clusters are much older, with a large number of stars which have evolved off the main sequence to the giant and supergiant phase. By constructing a colormagnitude diagram of such clusters, we can look for the turn-off point, i.e., the point above which all stars have left the main sequence and have evolved to the giant or supergiant phase. (All stars above the turnoff point are more massive than the stars just leaving at the turnoff, and therefore have evolved faster). Evolutionary models predict the turn-off point as a function of cluster age, so that the age can be determined by measuring the turn-off point on a color-magnitude diagram. The distance to the cluster can also be measured since the main sequence relation is between absolute magnitude ( ) and color index. By adjusting an observed color-magnitude plot with a universal HR AGE AND DISTANCE OF A STELLAR CLUSTER -- 33 diagram (y-axis absolute magnitude) the distance modulus ( ), can be easily found. The distance d in parsecs is simply given by where Δ is the distance modulus. Procedure 1. Run MaxIm. Click on File/Open. Go to the directory Clusters/m67/. 2. Load the V filter image of M67 named m67-v.fts. Click on this filename, and then click on Open. You may need to adjust the histogram. Recall that you do this moving the colored arrows on the Screen Stretch window. 3. When the image is clear, and you are confident that you can see all of the stars, click on View/ Information Window to open the information window, then press the Calibrate button in order to prepare for photometry. You should see a box appear underneath the Calibrate button with several selections that we will later use to calibrate the program. You will be doing differential photometry on this cluster of stars. Differential photometry is done by first making a circle around a star (or asteroid or other (small) bright object) and adding up all of the ADU counts within that circle. The sky background brightness is subtracted from this total, and the resulting ADU counts are set equal to a magnitude. The magnitudes of other stars in the field are determined relative to this star by comparing ADU counts. Fortunately, programs such as MaxIm remove most of the tedium of photometry by doing the arithmetic for you. 4. In order to do photometry properly, you must set up your cursor to check the correct radius. When the information window is active, your cursor will look like a targeting crosshair surrounded by three circles in the active image window. By pressing the right mouse button, you can select the size of the centroid Aperture, Annulus, and Gap Width. The centroid is the area of interest for the cursor. You want to set the Aperture size to be just larger than the largest star you are measuring (note: not necessarily the largest star on the image itself). The Annulus is used to calculate the average background brightness of the image so its size determines how much is averaged. The Gap Width determines how far away from the annulus the background is measured. Scan the image and the finding chart at the end of this lab to determine the largest star you will be looking at. Move the cursor over that star and select an Aperture size. Adjust this until the centroid circle is just larger than that star. You do not want the circle too large, however, as it will then be difficult to accurately record the magnitudes of smaller stars. Consult your instructor if you are unsure if your centroid circle is too large or small. For the purposes of this lab, a Gap Width value of 3 and an Annulus value of 2 are adequate. 5. Now you need to calibrate MaxIm for photometry. In the area underneath the Calibrate button, you have three Magnitude Calibration selections, Intensity, Exposure, and Magnitude. All three are needed, but only one (Magnitude) requires information not found from the image itself. The magnitude of stars for photometry is usually found from finding charts, and here we give you the value. Enter the magnitude given for star 38 in the Magnitude box. Next, click the Set from FITS button next to the Exposure box. This sets the exposure time from the FITS header in the image. Now, click the Extract from image button next to the Intensity box. Use the finding chart again to locate star number 37 in the image and click on star 37 in your image. This extracts the intensity level from the image, and sets the star you clicked on to the magnitude you entered in. Make sure that you enter the V magnitude here. You have now set your reference star. (Note: Make sure you do not adjust anything in the magnitude calibration area again, else you will have to recalibrate and re-measure every star.) To check that you calibrated correctly, check stars numbered 9 or 13 to make sure the value is reasonably close to the given value (it may not match exactly, but it should be very close). 6. Starting with star number 1 at the top of the table in the Worksheet section, find each star, and move the mouse over it. Record the magnitude for each star in the table. AGE AND DISTANCE OF A STELLAR CLUSTER -- 34 7. Repeat steps 2 through 6 for the I filter image. Don’t forget to recalibrate for the reference star (37) first using the I magnitude values! 8. Fill in the third column of the chart (the V-I column). 9. Use the graph in the Worksheet section to plot the V magnitude against the color index (V-I) 5. There should be a clear correlation between the magnitude (V) and the temperature (which is proportional to the color index). This correlation was discovered in the early years of this century by the American astronomer H. N. Russell and independently by the Danish astronomer Ejnar Hertzsprung. The resulting plot is called the Hertzsprung-Russell (H-R) diagram. Stellar evolution models predict that stars which are on the main sequence (the line formed by the magnitude-color relation) are still ‘burning’6 hydrogen in their cores. 10. The main sequence and several evolutionary tracks are plotted on a transparency which fits over your color-magnitude plot. Overlay the transparency, and adjust for best fit of the diagonal line to the Main Sequence. Make sure that you only move the transparency in the vertical direction, so that the vertical axes overlap. 11. The transparency’s HR diagram has a vertical axis in absolute visual magnitude (Mv), whereas your diagram is in apparent visual magnitude. By measuring the difference in the intercepts on the vertical axis, the distance to the cluster (distance modulus) can be found (see Background and Theory). Find the distance to M67 in parsecs. 12. The transparency shows a series of isochrones, (evolutionary tracks of stars with different ages), based on a model of stellar evolution. Compare the model tracks with the measurements to estimate the age of the stars in M67. 13. The relationship between V-I color index and surface temperature is approximately: Find the surface temperature of the hottest and coolest stars you have measured. This formula gives the temperature in degrees Kelvin, a linear scale (like Celsius), for which 0°K=-273°C. How do the temperatures of the hottest and coolest stars compare with that of the sun? A more common color index used in H-R diagrams is B-V (B is blue). Since the CCD camera which acquired these images is much more sensitive in the red and infrared, it is preferable to use the V-I color index. For all but the reddest stars, there is a linear relationship between B-V and V-I, so the color-magnitude diagram can use either. 5 In stellar astronomy we use the term ‘burning’ to refer to fusion. Stars along the main sequence fuse hydrogen into helium. Stars that have evolved off of the main sequence burn heavier elements such as carbon and oxygen, eventually forming iron. 6 AGE AND DISTANCE OF A STELLAR CLUSTER -- 35 Open Cluster M67 Finding Chart AGE AND DISTANCE OF A STELLAR CLUSTER -- 36 Age and Distance of a Stellar Cluster Worksheet Stellar Magnitudes of Stars in M67 Star V I V-I Star 1 28 2 29 3 30 4 31 5 32 6 33 7 34 8 35 9 10.968 10.650 0.318 V I V-I 10.479 9.409 1.070 12.147 11.582 0.565 36 10 37 11 38 12 39 13 40 14 41 15 42 16 43 17 44 18 45 19 46 20 47 21 48 22 49 23 24 50 51 25 26 52 53 27 54 AGE AND DISTANCE OF A STELLAR CLUSTER -- 37 HR Diagram for M67 1. Distance to cluster: _________________________________ 2. Age of cluster:________________________ 3. Surface temp (hottest): _______________________ 4. Surface temp (coolest): _______________________ AGE AND DISTANCE OF A STELLAR CLUSTER -- 38 5. Compare to the surface temperature of the sun: _______________________________ APPENDIX A: PLANNING OBSERVATIONS -- 39 Appendices Appendix A: Planning Observations Is the object in the night sky? In order to plan an observation, the first task is to determine whether the objects of interest are visible at night. The telescope scheduler assumes that ‘night’ means from astronomical dusk to dawn, i.e. Sun’s elevation –18 degrees (below the horizon). Use a sky display program such as Starry Night or Megastar to see what the rising and setting times are. Make sure you have chosen the Rigel telescope location and the approximate date of observation. How much of the sky can the telescope see? The Rigel telescope horizons is quite low (~5º) except to the north, where the roll-off roof blocks the sky at elevations below 20º. The minimum observable declination is about –53º (5º elevation at transit), although the image quality and sensitivity will be compromised since the telescope is looking through 10 air masses! There are no hour angle limits. Do I have to specify celestial coordinates for an object? In most cases, no. When an object is named in a schedule, the scheduler looks at a large number of catalogs for a corresponding entry. The only trick is to use the same name as the catalog. For example the names M12, Jupiter, NGC682, and UX_Ari are valid names from the Messier, Planet, NGC, and GCVS catalogs. Asteroids are specified by number only, e.g. 4 for Vesta. Click on the Catalog hyperlink on the IRTF Web site (also on the observing request form) to see a listing of all online catalogs. What observing time should I request? Normally the telescope scheduler will choose times near transit automatically. This corresponds to the highest elevation, which minimizes atmospheric extinction. If you have a particular need for observations at another time, use the start time option, specifying either hour angle (HA) or local sidereal time (LST). What filters are available and which should I use? The choice of filter depends on the goal of the observation. For the best sensitivity, always use the clear (C) filter. Use the B, V, R, or I filters for photometry. Above is a list of the available filters. Note that the BVRI filters conform to the Johnson-Cousins photometric standard. Filter Code Center Bandwidth Wavelength (nm) (nm) Clear C - - UV U 350 80 Blue B 450 80 Visual V 550 80 APPENDIX A: PLANNING OBSERVATIONS -- 40 Filter Code Center Bandwidth Wavelength (nm) (nm) Red R 650 80 Infrared I 800 100 What about observing planets? In general, the untraviolet (U) or blue filter (B) is best for observing planets, however, the ‘naked-eye’ planets (Venus, Mars, Jupiter, Saturn), all saturate even at 0.25 sec exposures under the CBVRI filters. Under normal conditions, then, only the U filter is usuable. Using CBVRI filteres the four planets are effectively unobservable (their moons, for those that have them, are observable however). What exposure times should I use? • Extended Objects (Galaxies and Nebulae) For extended objects the exposure time depends on the size of the object. As a general rule only the brightest galaxies and nebulae will be overexposed for exposure times less than 1 minute. We recommend initial exposure times of 30-60 seconds for all galaxies and nebulae for all filters. If this in incorrect, a second submission with a shorter exposure times is appropriate. • Point Like Objects (Stars, Planets, and Asteroids) There is an online exposure time calculator (suitable for point objects such as stars, planets, and asteroids) available on the Observing Request web page. Click ‘Calculate’ to use. The exposure time dialog box looks like this: APPENDIX A: PLANNING OBSERVATIONS -- 41 Simply fill in the apparent visual magnitude of the target object and thecolorindex (B-V) if known. (If the color index is not known, the default value of 0.7 should be adequate unless the object is very red or blue.) Next, click on the desired filter and signal-to-noise ratio (SNR) or on the entire line (Export-all) and all times will be transferred to the main screen. Check the filters needed for the observation. Inany case, do not exceed the saturation time listed for each filter. Note that the SNR calculation assumes a dark (moonless) night, high elevation angle, and good seeing conditions (under 3 arcseconds). What is the sky brightness? Under moonless conditions, the sky brightness is typically 18.5 – 19.0 magnitudes per square arcsec. The moon phase is now available on the Observing Request web page as an icon. Recall that 1st quarter moon is above the horizon in the evening (sets at midnight), full moon is above the horizon all night, 3rd quarter moon is above the horizon between midnight and dawn. What is seeing? Seeing is the astronomical term for the spreading of a point source of light (e.g. a star) due to thermal fluctuations in the Earth’s atmosphere. The seeing is most often near 2.5 arcsec (FWHM) at Winer Obervatory, although at low elevations it is larger ecause the star’s light passes through a larger path in the atmosphere. The seeing-airmass scattering law is: 3 θ = θ0 Z 5 where Z= sec(φ) is the air mass (φ is the zenith angle (90° - elevation angle). APPENDIX A: PLANNING OBSERVATIONS -- 42 What software can I use to display and analyze images? The format of the images is FITS (Flexible Image Transport System), the standard image format in most astronomical observatories. There are numerous FITS viewers available. Here’s a selected list that are used at the University of Iowa. Program OS Comments Camera UNIX Full image display, astrometry, photometry, WCS MaxIm Win-2000/ XP Display, some photometry, image alignment and color combination APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—43 Appendix B: Maxim, An Image Analysis Program For the most up-to-date information, please consult MaxIm’s help file, as certain procedures may change if the program has been updated. Screen Stretch The Screen Stretch window is one of three windows in MaxIm which will be used nearly constantly. It is used to adjust contrast and brightness in an image (histogram adjustment) as well as making an image in inverse (negative). If Screen Stretch window is not visible, you may select it from the View menu. To adjust the histogram: 1. Load an image. 2. To manually adjust the histogram, move the Green Arrow under the graph in the screen stretch window to adjust the brightness that corresponds to full white in the image. Move the Red Arrow to APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—44 adjust the background level (the black) in the image. Moving the arrows close together produces a high contrast and far apart, a low contrast. 3. To “fine tune” the histogram, click and hold in the small box in the upper right (the “quick stretch”). Your cursor will change to a +, and you may move it in any direction within the box. The vertical direction corresponds to brightness and the horizontal to contrast. When the cursor is moved, you will see the red and green arrows also move. 4. To fine tune even farther, you may click the zoom button to put the graph’s limits to the current locations of the green and red arrows. Adjust them again as described in step 2. 5. To automatically adjust the image, choose an appropriate setting from the pull down menu under the quick stretch box (i.e. if you have an image of the moon, choose Moon from the menu). This will adjust the histogram to a preset level. Even after auto-adjustment, you may manually adjust further by moving the arrows. To make an inverse image: 1. Load an image. 2. Reverse the positions of the green and red arrows under the graph. Figure 2: Screen Stretch Window. 3. Adjust the histogram as described above. Information Window The information window provides several types of information on an image, depending on what it is set to display. It will display general information on the image, statistics, as well as information restricted to a specific area that can be designated. Select the appropriate display type from the pull down menu at the bottom of the window. If the Information Window is not visible, you may select it from the View menu. What each selection will display: 1. Aperture is the default display. While your cursor is on the active image, it will display the position of the cursor in (x,y) and the radius of the centroid, or inner ring around the crosshair. It will also display the Pixel value beneath the cursor, as well as the maximum, minimum and median ADU counts beneath the cursor. If calibrated properly, it will display photometric measures of magnitude, intensity, and signal-to-noise ratio (SNR). It will also display the Full Width at Half Maximum (FWHM) of the star (in pixels or arcseconds) and the flatness, a measure of how oblong a star is. 2. Region is a simpler version of Aperture. It will display everything as per above, except for the photometry parts. It will also separate information into Red, Green, and Blue for color images, while displaying Mono for monochrome images. 3. Area will display information about a rectangular section of an image. The default is for the full image, but you may change this by clicking and dragging over a section of screen to draw a rectangle. You may also change the position of your rectangle by moving the cursor to a corner of it, press and APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—45 hold the left mouse button, then drag the area to its new position. Displayed will be the diagonal size of the rectangle, the number of pixels contained, and the average, standard deviation, and maximum pixel values over the entire section. Area will also differentiate between colors as per Region. FITS Header The FITS Header is the last of the three windows that you will refer to often. FITS stands for Flexible Image Transport System, and is a standard format for sharing and transferring astronomical images. The header will have data that is necessary for using the images, such as the time and date the image was taken (both in “normal” time and the Julian Date), the R.A. and Dec., and usually the observatory that took the image, the type of telescope used, and the name of the person who took the image. The most important data for most purposes however will be the date, the location in the sky (RA and Dec.), the filter used, and the exposure time. If an image does not end in the extensions .fts, .fts, or .fth, however, it will not have a FITS header. If the FITS header window is not visible, you may select it from the View menu. Zoom Window The Zoom Window is one more window that may be selected from the View menu. This window shows a close up view a fixed distance around your cursor, and is used to see Figure 4: The FITS Header window. details that may otherwise be unnoticed on the image. Image Processing Auto - Aligning In order to perform many of the operations below, you must first align your images. This will line up the stars so that when you make a blink movie, for example, you will see the moving object change its location, while every other object remains in the same spot. MaxIm is very good at automatically aligning astronomical images. 1. Load two images of the object. Figure 5: The Zoom Window. 2. Select Process from the menu and then Align from the pull down menu. A new window will open with various alignment controls. 3. Choose Auto – star matching, from the pull down box at the top of the window, then click on the Overlay all images button. A preview window will open up that will show the overlain images. (Note: For images that show few or no stars, choose Auto – correlation, for a better match.) 4. After a few moments, the program will align the images according to the star patterns on both images. Examine the preview window to see if any inaccuracies show up. 5. If everything looks right, click on OK. 6. Examine all the images that were aligned. If the results are unsatisfactory, you may need to manually align the images as described below. APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—46 7. You may auto-align more than two images at a time, if necessary. Manual alignment Sometimes, the automatic alignment may be unsatisfactory or too inaccurate for use. In these cases, you may opt to manually align the images instead. 1. Load two images of the object. 2. Select Process from the menu, then choose Align. 3. In the pull down box, there are two choices for manual. Star shift only and Stars. The Stars selection is needed only if rotation of the images must occur to align them. For most purposes, this will not be necessary. 4. With the Use Centroid box selected, click on the star to use as the center point for the image in each image. This star should be recognizable in each image. (For instance, choose the central star of a planetary nebula). Set one image as the reference by clicking Set to Reference. This image will not be shifted, all others will be shifted in relation to it. It will display in the information window which, if any, image is the reference. 5. Select Overlay all Images to determine if the results are satisfactory. Figure 6: The Align Tool. 6. Click OK. 7. You may also manually align multiple images. Blinking Images 1. Align two images as described above. (Note: As with aligning, you may blink more than two images at a time.) 2. Choose View from the main menu, then choose Blink. 3. Select the names of the images you wish to blink, then click the button marked >> in the order you wish them to be shown. Alternatively, you may click the Add All button, and then Move Up or Down buttons to put the images in order. Click on OK. 4. A window titled Blink will open, shown at right. Choose a skip time from the pull down menu, then press the Play button. 5. When you are finished, click the Stop button to stop the movie. Click Close to close the blink window. Measuring Objects Distances within a single image (e.g. the length of a comet’s tail): Figure 7: The Blink Tool. APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—47 1. Place the cursor on the image at one end of the object you wish to measure. Write down the x and y coordinates of that point (x1,y1). 2. Move the cursor to the other end of the object you wish to measure. Write down the x and y coordinates of that point(x2,y2). 3. Calculate the distance between the two points using the Pythagorean theorem: . 4. This is the distance in pixels. To convert to an angular distance, multiply by the image scale (for the IRO this is 1.23 arcseconds/pixel). Angular motion between images (e.g. the motion of an asteroid): 1. Load two images. 2. Align the images (as described above). 3. Place the cursor over the object in the first image. Write down the x and y coordinates of the object (x1,y1). 4. Place the cursor over the object in the second image. Write down the x and y coordinates of the object (x2,y2). 5. Calculate the distance between the two points using the Pythagorean theorem: 6. This is the distance in pixels. To convert to an angular distance, multiply by the image scale (for the IRO this is 1.23 arcseconds/pixel). 7. Find the time elapsed between images from the date-obs and time-obs information obtained by going to View/FITS Header. 8. Divide the angular distance by the time elapsed to find the angular velocity of the object. Using MaxIm to Perform Differential Photometry There are two ways to perform differential photometry within MaxIm. The first is simple and uses the Information Window mentioned above. The second is more complex, and more accurate, but is only very useful for performing differential photometry on a series of images. To do Basic Differential Photometry (appropriate for photometry of a single image): 1. Access the Information Window and press the Calibrate button near the bottom of it. Make sure Aperture is your selection for the window. 2. There are two sections to the photometry window, Magnitude Calibration and Spatial Calibration. Magnitude Calibration is used for photometry, where Spatial Calibration is used convert pixels to arcseconds for display in spatial sizes and FWHM. APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—48 3. First, check your reference star on the image. In order to accurately perform photometry, your reference star cannot be overexposed. Check that the ADU count is no higher than 50,000. If it is, choose a different reference star (if possible) or reschedule observations. 4. You must also select sizes for your Aperture, Annulus, and Gap Width. The Aperture is the size of the inner circle, which represents the boundary of the centroid, the area where the photometry reading will occur. The Annulus is used to calculate the average background brightness of the image, so its size determines how much background is averaged. The Gap Width determines how far away from the annulus the background is measured. 5. Set the value for the Aperture to be just larger than the largest object you will be performing photometry on. If it is too large, photometry on dimmer stars will be less accurate since pixels from other stars will contribute if they are within the centroid. Values for the Gap Width and Annulus are harder to judge, in general, the larger the object you are measuring, the larger the gap width you want, and the brighter the background as a whole, the smaller the annulus you want. Consult with your instructor if you are unsure of which values you should be using. 6. Three quantities are needed to perform accurate photometry, Magnitude, Intensity, and Exposure. Magnitude is determined from a finding chart or other reference source whereas Intensity and Exposure are both extracted from the image itself. 7. Enter the magnitude of your reference star in the box labeled Magnitude. Make sure you use the correct magnitude for the filter your image was taken through. 8. Next, Press the Set from FITS button next to the Exposure box. This will read the exposure time from the FITS header. Naturally, if the image is not a FITS image, you will need to know the exposure time and enter it manually. 9. Press the Extract from image button next to the Intensity box. Once you left click on a star in your image, a value will appear in the Intensity box, and the computer will assign the value in Magnitude to that star. 10. You are now calibrated properly for photometry. 11. To check the magnitude of any other object on the image, move the cursor over the object in question. The program will add up all the pixel values within the area of the target circle, compare to the value you input for the reference star, and give a value for the magnitude of the star. 12. Do not change any values in the Magnitude Calibration or change the sizes of the circles around the crosshair, as this will require you to recalibrate and re-measure everything. For Advanced Differential Photometry (appropriate for multiple images of the same filter): 1. Select Photometry under the Analyze menu. APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—49 2. Two windows will appear, one labeled Photometry – yourimage.fts, a copy of the image(s) which will be used to select stars for photometry, and another labeled Analyze Photometry, which contains the image list and the list of stars you have tagged to perform photometry on. 3. One image in your image list will be highlighted, it will match the name in the image window, and the Figure 8: Basic Photometry with the Information Window image window will change by clicking on a different image name in the list. 4. Set up your Aperture, Gap Width, and Annulus as per basic photometry. 5. To set your reference star, select New Reference Star from the pull down menu underneath Mouse click tags as. Click on the star in your image and green circles matching the orientation of those around your crosshair will appear, tagged (labeled) as Ref1. Enter the magnitude of the star in the box that appears. If you have Act on all images checked, it will set this star and magnitude to Ref1 in all images. If you have Snap to centroid selected, MaxIm will choose the brightest pixel in the star to center on. It is recommended to select Use star matching if you select Act on all images, as MaxIm will use pattern matching to determine the correct star to tag in each image. 6. You may select more than one reference star if needed, and only reference stars allow you to enter a magnitude in. 7. If you require check stars, select New Check Star from the pull down menu, and select as you did the reference star. These stars will be tagged as Chk1, Chk2, and so forth. 8. To select stars to perform photometry on, select New Object from the pull down menu, and select your object(s) as before. Each will be tagged as Obj1, and so forth. 9. If you have a moving object in your images (e.g. an asteroid or comet), you may select New Moving Object from the pull down menu and select as before. Each of these will be tagged with Mov1, and so forth. Act on all images is ignored under selecting moving objects, so you will have to tag the object on APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—50 at least two images for MaxIm to predict the location in all the images (Tagging the object in the first and last image usually works best). 10. To remove a tag, select the tagged object you wish to remove, and click the Untag button. You may Untag more than one object at a time. 11. To see the results, click the View plot… button. This will display a plot of the values for each object, and will be a time-based plot for multiple images. 12. You may print the plot if you wish, or click the Save Data… button in order to save the data as a .csv (comma separated values) file, which can be read by a program such as Microsoft Excel. 13. MaxIm can not do absolute photometry. If you need to do absolute photometry, refer to the Camera section of the appendix. Cropping Images It is often useful to crop images so only the most interesting or useful areas are displayed. To do this: 1. Select Edit/Crop from the menu. 2. A new window will open up displaying the current size of the image, the size to be cropped to, and the x and y offsets. 3. Make a box around the part of the image you wish to crop down to by clicking and dragging with the mouse. If you are unsatisfied with the area, or make a mistake, just redraw the box. 4. If necessary, you may fine-tune the box’s position by clicking the up and down arrows next to the offsets. This will slowly move the box to let you center your image. 5. When done with adjustments, click the OK button. Your image will be re-sized, but not replaced. If you are not happy with the results, discard the image by clicking the X in the upper right corner and not saving. This will allow you to crop the original image again. Figure 9: Advanced Photometry with the Photometry function. APPENDIX B: MAXIM, AN IMAGE ANALYSIS PROGRAM—51 6. Note: You will get better results by aligning images prior to cropping them. This way, you can easily crop “dead” areas where nothing is displayed after the alignment. Figure 10: A Plot of a light curve from an eclipsing binary generated by MaxIm