Project 6: "The Colors of the Stars"

by Blake Bartosh

Level: Intermediate

Requirements: Filter Wheel, Photometry, Color Magnitude Diagram

 

Objective

The Student/Amateur is to utilize advanced techniques, including filter wheel and photometry, to measure the color index (B-V, V-R, etc.) of stars using the TIE telescope system. A Color Magnitude Diagram is created from the measured data. Apparent and absolute magnitudes, stellar mass, temperature, color index, spectral classifications and Color Magnitude Diagrams are studied.

 

Background

Stellar evolution is studied by astronomers to learn about the processes that goon deep within a star's core. Unfortunately, most stars evolve quite slowly, and astronomers must examine many stars to gain an adequate understanding of how stars work. It is also important to realize that we don't have access to a star in a laboratory, so astronomers must make use of measurements of distant stars recorded by instruments and then analyze those measurements and formulate theories about stellar evolution and makeup. The first instruments used to gather information about the stars were our eyes.

Measuring Star Brightness: Star magnitudes were originally assigned very simple degrees of measurement. Stars of the "first magnitude" were the brightest, as determined by the naked eye, and stars of the "sixth magnitude" were the faintest, barely visible to the naked eye. Astronomers now have electronic instruments for measuring light intensity and measurements of magnitude have evolved to today's current logarithmic method.

Apparent vs. Absolute Magnitudes: Because we view stars at many varying distances from us, the magnitudes measured directly from the emitted light is really an apparent magnitude. Astronomers need to know the absolute magnitude of the stars to carry out meaningful research. We can apply simple physics concerning the way light dissipates over distance, and measure the distance to stars through trigonometric "parallax" (a purely geometrical measurement of star distance), to determine the absolute magnitude of the star. Absolute magnitude is basically the apparent magnitude adjusted for distance. Astronomers have chosen a standard distance of 10 parsecs which is used to compute the absolute magnitude of stars, and allows the accurate comparison of stellar light output from star to star. Apparent magnitudes are designated "m" while absolute magnitudes are designated "M."

Stellar Colors: Stars emit a broad range of light frequencies which we perceive as color. If you examine several stars in the night sky with the naked eye, binoculars or a telescope, you will notice that stars do have color. Vega and Sirius are distinctly blue, while Antares and Betelgeuse are distinctly red. While we can say that a star is red or yellow or blue, astronomers must accurately measure a star's color in a way that allows comparison to other stars. That measurement is known as a star's Color Index.

The Color Index: The Color Index is the ratio of light energy measured in two frequencies, or wavebands, of light. In particular, astronomers have chosen to measure the ratio of blue light relative to the amount of visual (yellow-green) light to quantify a star's color. A star's light energy, or apparent magnitude, is measured with the use of filters designed to block all but specific frequencies from getting to the detector, in this case the TIE CCD camera.

The Filter Wheel: The TIE CCD camera contains a built-in Filter Wheel outfitted with filters of the type just described. The Filter Wheel places blue, red or yellow-green (visual) filters in front of the CCD just before taking an image of a star. By comparing the intensity of a star's light output through the different filters, a Color Index can be determined which identifies and quantifies the color of the star being examined. Color Indices can then be related to stellar temperature, and help locate the star on the Color Magnitude Diagram, described below.

Determination of B-V: Because star magnitudes are logarithmic, the ratio of light intensities can be easily determined from the measurements of apparent star magnitudes in the blue (mB) and visual (mV) bands by using the filters described above. Once a star's blue and visual magnitudes are measured, astronomers compute a simple difference, mB-mV, of the star's magnitudes. This Color Index, mB-mV, is abbreviated B-V. A positive B-V value means a redder (and cooler) star. Why? A positive B-V value means that the B value must be greater than the V value. Remember, light intensity of magnitude 2 is fainter than magnitude 1, hence a positive B-V value really means the intensity of blue light is less than the intensity of red light.

It can be shown that B-V, derived from the apparent magnitudes of a star using the B and V filters, is the same as B-V derived from the absolute magnitudes. Thus there is no need to correct for distance to achieve a true Color Index. This is an important fact which validates the use of the TIE CCD camera in this project to make meaningful measurements.

Astronomers are now using several other Color Indices, including V-R. These measurements can be investigated as well with the method described below.

The B-V, V-R and other Color Index measurements give the astronomer important tools to compare stars and determine their temperature and mass, and help to locate stars on the Color Magnitude diagram.

The Color Magnitude Diagram: Astronomers have found an interesting relationship between the absolute magnitudes of stars and their B-V Color Index. It appears that many near stars with the same B-V value have the same absolute magnitude.

When plotted on a graph of absolute magnitude versus B-V value, the measurements fall along a line. Astronomers call this plot the Color Magnitude Diagram, and the line the Main Sequence. Apparently, there is a simple relationship between intrinsic brightness and color--it depends on one factor for stars that fall in the Main Sequence. Astronomers have determined that this factor is the mass of the star.

 

Discussion of Work

Select several suitable stars for measurement and comparison of their Color Index. Try to choose stars of different spectral classification, or color. Within each star field, ensure a reference star is included whose B-V is known or can be computed. Also, choose stars fainter than magnitude 3 and brighter than magnitude 10 to ensure the ability to take an image without encountering saturation of the CCD's pixels or a poor signal to noise ratio. Record their absolute magnitudes as noted in one of the references.

The TIE CCD camera system includes a Filter Wheel. The Filter Wheel mechanically places a colored filter in front of the CCD array. The filter blocks most of the light except at the pass band (the color) of the filter. Thus, a blue filter blocks all but blue light. The Filter Wheel has a "B", "V" and "R" filter which can be alternately placed in front of the CCD array remotely by the user.

First, slew the telescope to the selected star. Next, place the B filter in position. Determine a proper exposure time that results in an image that is not over or under exposed. Once the proper exposure time is determined, record the exposure time and save the image file that was taken with this best exposure time. Save the image with a filename that indicates the name of the star and the filter used, i.e. "MegrezB."

Now place the V filter in position. Take another image, again using the same exposure time. Save this image with a filename such as "MegrezV" to indicate the image was taken with the V filter in place.

Repeat this procedure for several star fields.

After the images are taken and the user is off-line:Photometric software can be used to process the images and determine the magnitudes of the stars in question. Photometry software packages may be purchased separately to perform the necessary image processing, and is available from Software Bisque, CompuScope or other sources. Later versions of SkyPro have built-in photometry software, whose functions are described below.

Perform the following procedures using SkyPro if photometry software is not available:

1. Open both the B and V images of the star in question in SkyPro. Adjust the image sizes so that both can be viewed at the same time.

2. In the View menu, click on Select Panel. A vertical toolbar will appear with seven (7) tiles. If only four (4) tiles appear, the version of SkyPro in use does not support photometry measurements. As of this writing, SkyPro Version 2.06 has typically been shipped with the photometry capability. To verify the version, select menu Help, About. Information on the version number, how to contact Software Bisque and their BBS is given in the window.

3. Select the Photometry Setup tile, which is the 5th tile from the top. A window entitled "Photometry Setup" will appear. Enter the following information:

Telescope Diameter: 24 inches (click the "Inches" radio button)

CCD Camera Pixel Size: "Automatic Detect"

Telescope f Number: 3.5

Seeing Conditions: Good

4. Select the Photometry Reference tool, which is the 6th tile from the top. Place the mouse cursor on the image, and the arrow will change to a crosshair. Move the crosshair to the B image and over the selected reference star, different from the one to be measured. A reference star is one whose B-V is documented. The reference star should have sufficient intensity to ensure a high signal to noise ratio. See Below.

If the image is too small to accurately place the crosshair, select the magnification tool "+" Magnifier over the desired star image and click until the star is sufficiently magnified.

Once the crosshair is placed over the desired reference star in the B image, click and a window entitled "Enter Reference Magnitude" appears. If the reference star's apparent B value is known, enter that in the space provided. Otherwise, enter "0" as the reference magnitude, then click OK. Since we are measuring differences in magnitudes, the reference star magnitude is arbitrary.

5. Next, select the Magnitude Measurement tool, the 7th (last) tool from the top. Place the mouse cursor on the desired same star in the B image and click. A window will appear with computations for the Reference Magnitude and the Unknown Magnitude. Record the Unknown Magnitude. If there are other stars in the same image which are to be measured, click on each individually and record their Unknown Magnitudes.

Note on Signal to Noise Ratio: More accurate B-V measurements are made when the signal to noise ratio (S/N) of the star image is high. The S/N can be roughly determined by dividing the Intensity value by the Background value as displayed in the Magnitude Measurement window for both the reference star and test star ("Unknown"). A S/N of 10 is good, and will probably yield an accuracy of ±0.1 magnitude. A S/N of 20 is excellent, and may yield an accuracy as high as ±0.02 magnitude. It is suggested the S/N be entered into the table as shown below. This will validate the accuracy of the measurements upon later examination.

6. Repeat Steps 4-5 for the V image, being sure to choose the same reference star, and entering the reference star's V value if known, or "0" if it is not.

7. Construct a table like the one shown below. In the chart, a reference star was chosen in the image with an absolute magnitude of -1.6 and a color index of -0.2. Star 1 and Star 2 were stars located within the image whose absolute magnitudes were recorded from the literature.

The B-V of each star is computed in the following way. The reference star's B-V is known, and the relative magnitudes between the reference star and the stars in question were measured with SkyPro's photometry software for the B and V images. Solving for the B-V of the star in question:

Computed Star B-V = (Reference Star B-V) + (B Image Mag. - V Image Mag.)

Based on the B-V value, what color is each of the stars in question?

 

10. Images of several different fields can be accumulated, and for each field the color index of the stars in question can be computed.

9. Construct a Color Magnitude diagram. Plot the absolute magnitude of the selected stars on the vertical axis, and the B-V value on the horizontal axis. Do the values fall on a straight line?

Do some research to determine which of the stars are more massive and hotter based on their position on the Color Magnitude diagram. Where would a "White Dwarf" be located on the diagram?

Note: Atmospheric absorption has not been addressed in this project due to the complexity of the correction. The effects of absorption, in which the Earth's atmosphere acts like a filter, can be mitigated by choosing stars that lie in a small field of view very near zenith.

 

References

Colours of the Stars, Malin and Murdin, Cambridge University Press, 1984
Philip's Color Star Atlas, Cox and Monkhouse, Kalmbach Publishing, 1991
Introduction to Stellar Astrophysics, Bohm-Vitense, Cambridge University Press, 1989

 

TABLE OF CONTENTS TIE User Guide TIE USER'S GUIDE CCD ASTRO INTRODUCTION TO CCD ASTRONOMY PROJECT 1 Basic Use of the TIE 24" Telescope System PROJECT 2 Adopt a Constellation PROJECT 3 Adopt a Galaxy--The Search for Supernovae PROJECT 4 A Survey of Deep Sky Objects PROJECT 5

Near Earth Objects--Comet and Asteroid Studies PROJECT 6 The Colors of the Stars PROJECT 7 The Colors of the Stars in Open Clusters PROJECT 8 Advanced Imaging Techniques PROJECT 9 Variable Stars--Keys to the Universe PROJECT 10 Focus on RR Lyrae Stars--The Anatomy of the H-R Diagram PROJECT 11 Variable Star Search PROJECT 12 Asteroid Rotation and NEO Search