Project 7: "The Colors of the Stars in Open Clusters"

by Blake Bartosh

Level: Intermediate

Requirements: Filter Wheel, Photometry, Color Magnitude Diagram

 

Objective

This is an extension of Project 6, which applies techniques learned to determine the magnitude, color, temperature and mass of stars in open clusters.

 

Background

We saw in Project 6 that a Color Magnitude Diagram for many nearby stars follows a straight line, the so called Main Sequence. What are the Color Magnitude characteristics of stars at larger distances? In order to place a star on the Color Magnitude Diagram, we need its absolute magnitude and Color Index. It was parallax, physics and the measurement of apparent brightness that yielded the absolute brightness of nearby stars. One problem that arises in making measurements on stars that are very distant is that parallax methods cannot be used to determine distance, which means we cannot make an accurate measurement of absolute magnitude.

Magnitude measurements are proportional to light intensity and distance. If we can assure that two stars being measured for magnitude are at the same distance, then the ratio of their light intensity (magnitude) should be the same regardless of their distance from us. The effect of the unknown distance is simply to shift all the magnitudes up or down, but the shift is the same for all stars at the same distance.

Fortunately, stars often are found in nature grouped together, perhaps because they were formed in same portion of the universe, and have moved together as a group throughout space. These groups of stars are known as clusters. Clusters can be "open" or "globular." In the Northern Hemisphere the best known open star cluster is the Pleiades, while M13 in Hercules is a prominent globular cluster.

When the apparent magnitudes of stars in an open cluster are measured, the diffrences of their apparent magnitudes must also be the differences of their absolute magnitudes.

Thus we can make apparent magnitude and B-V measurements of several stars in an open cluster, and plot them on a Color Magnitude Diagram without necessarily knowing anything about their distance or absolute magnitude.

 

Discussion of Work

For this project it is possible to take one image of an open cluster and find several stars that may be measured. Select suitable test stars for measurement and comparison of their Color Index. Try to select stars of different spectral classification, or color. Be sure to choose at least one blue star and one red star in the group. 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.

Select a reference star that will appear in the image whose absolute or apparent magnitude is known. If the magnitude is not known, enter "0"--the differences in magnitude between the reference star and the test stars will still be valid. The resulting Color Magnitude Diagram will just be shifted up or down, but the slope will be correct. If the reference star's B-V value is listed, then the reference star can also be placed on the Color Magnitude Diagram.

Use the procedure developed in Project 6 to gather images of stars with the B and V filters in place, and to measure the B and V magnitudes of the test stars.

As in Project 6, be sure to use the same exposure times for the B and V images, and be sure to select the same reference star in each image. The reference star's magnitude may be input as "0" if its B and V apparent magnitudes are not known.

In addition, use the V image to deduce the absolute magnitudes of the test stars from the photometry software. Input the known absolute or apparent magnitude of the reference star. This can be done because the stars are all roughly at the same distance, and therefore the relative apparent magnitudes (which is only what can be measured with the CCD camera) will actually be the absolute magnitudes. See the sample chart below, created from SkyPro data. You may wish to prepare a similar chart to help with the organization of the data.

Enter the S/N (signal to noise) ratio in the chart for each measurement. This will validate the accuracy of the measurements upon later examination. 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.

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.)

This chart shows the comparison of data for three stars, each of different spectral types. Because these stars are located within an open cluster, their distances to Earth are about equal, and therefore their apparent and absolute magnitudes should be of the same ratio.

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

*Apparent magnitude (measured using SkyPor Photometry software) = Absolute magnitude

Plot the absolute magnitude of the test stars on the vertical axis, and the B-V value on the horizontal axis. This is the Color Magnitude Diagram for the test stars. Do the values fall on a straight line?

Do some research to determine which of the stars are more massive, based on their position on the Color Magnitude Diagram. You may wish to add data taken from Project 6 to the diagram.

 

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