Download Imaging the Universe Robert Mutel A Laboratory Manual for Introductory Astronomy

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