HOMEWORK 4: H-R DIAGRAM

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1 NAME(S) SECTION DAY/TIME ASTRONOMY25 (LLOYD) SPRING 2012 Purpose HOMEWORK 4: H-R DIAGRAM To plot the H-R diagram of a star cluster and estimate its age and distance. Background Magnitude is a measure of the brightness of stars. Bigger numbers mean fainter stars. The faintest stars that can be seen with the unaided eye in a dark sky site are magnitude 6. B is the magnitude in the blue color. V is the magnitude in the yellow color. B V is the difference between these two. A large B V means the star is reddish; a negative B V means the star is bluish. Software Settings In the H-R (Color-magnitude) diagram, the B V color is plotted on the horizontal axis and the V magnitude on the vertical axis. These directions are for Stellarium version See the overview handout for Stellarium to adjust the initial settings if necessary. 1. Set your location to Torrance (if it's not already). 2. Set the time to 21:00 hours (9:00 pm) on Jan Stop the clock [7]. 4. Find Aldebaran. (Click on the magnifying lens or hit [F3].) 5. Zoom in till the Field of View (FOV) is about 5 to 10. (Hold down the shift key and hit page-up or page-down. On some laptops, hold down the fn key as well.) The FOV is displayed above the symbols on the bottom of the screen. Configuration For this exercise, you will need to load extra stars. 1. Open the Configuration window by clicking on the wrench icon or hit F2. 2. Click on the Tools tab. 3. The Star Catalog Updates section is at the bottom. Click on Get catalog 5 of 9. Wait till the new star catalog loads. 4. Click on Get catalog 6 of 9. Wait till the new star catalog loads. 5. Quit and restart Stellarium. Observe the Stars Click on thirty stars in the cluster. Try to have a variety of stars: both bright stars and very faint stairs. You should see some stars as faint as magnitude 9. Zoom to about 2 to see stars as faint as magnitude 11. Also notice that stars have color. Click on some bluish stars and some yellowish or reddish stars. For each star, record 1. the magnitude (this is the V magnitude). 2. the B-V color 3. the Right Ascension (RA). Use the first one (J2000). 4. the Declination (DE). Use the first one (J2000). Plot the magnitude and B-V color on the chart on page 3.

2 ASTRONOMY 25 H-R DIAGRAM P. 2 MAGNITUDE B V R.A. DEC.

3 ASTRONOMY 25 H-R DIAGRAM P

4 ASTRONOMY 25 H-R DIAGRAM P. 4 Age The age of a cluster is determined by the color of the bluest stars on the main sequence, since the blue stars spend the shortest amount of time on the main sequence and quickly turn into red giants. The color of the bluest stars is called the turn-off point. The age can be determined from the turn-off point by using this table: B V Age (millions of years) Distance The inverse square law tells us that the distance to a star is determined by the ratio of its apparent brightness to its absolute brightness (b/b). When using the stellar magnitude scale, the ratio b/b is replaced by the difference between the apparent and absolute magnitudes, (m-m). (The absolute magnitude is the apparent magnitude the star would have if put at a distance of 10 parsecs.) This quantity is called the distance modulus. Once the distance modulus is known, the distance in parsecs can be calculated as follows: x = (m M + 5)/5 distance = 10 x This equation is mathematically the same as the inverse square law.

5 ASTRONOMY 25 H-R DIAGRAM P. 5 Questions 1. Draw a line through the main sequence. What you have plotted is just one end of the main sequence. Is it the blue end or the red end? 2. Mark with an R any stars that appear to be red giants. 3. Circle any stars that appear to be background stars that don't belong to the cluster. 4. What is the B V color of the bluest cluster members? 5. Using the table, estimate the age of this cluster. 6. At what magnitude (m) does your main sequence line cross B V = 0.5? 7. A main sequence star of color B V = 0.5 has an absolute magnitude of M = 4. Calculate the distance modulus (m M) of the star cluster. 8. Calculate the distance to the cluster.round off to the nearest whole number. This is the distance in parsecs. 9. Compare the age of this star cluster with the age of the Galaxy.