Cluster Color-Magnitude Diagrams and the Age of Stars

Summary

The student will find the ages of two clusters by plotting stellar data on a color-magnitude diagram.

Background and Theory

Thus far in the course, we have learned how to determine many characteristics of the stars: distance, intrinsic luminosity, surface temperature, composition, mass and radius. In order to study the life cycle of stars, we would like to know the age of the stars we observe. Stellar clusters give us an opportunity to determine the age of their member stars.

Normally, a Hertzsprung-Russell (H-R) diagram plots the spectral type of a star against the star's intrinsic luminosity. As we have seen, a star's spectral type corresponds to the star's color. We can measure a star's color by determining its brightness through two different filters, say a blue filter and a yellow filter. We can therefore plot the color of a star against its brightness (measured in magnitudes) as a way of building an H-R diagram without taking the star's spectrum. This type of diagram is generally called a "color-magnitude" diagram", which is really a type of H-R diagram. This method is particularly useful with star clusters where taking the spectrum of thousands of closely-spaced stars would be impossible.

Today we will be plotting actual data for two star clusters: an open cluster called M45 and a globular cluster called 47 Tuc. Each cluster contains thousands of stars, but we will only plot the data for a representative few. The table below provides the data.

B-V is a measure of the color of a star. (It is the difference between the star's brightness in a blue filter and a yellow filter.) The important thing to know is that the higher numbers are redder and the lower numbers are bluer.

Procedure
1. Plot the B-V versus magnitude on a piece of graph paper. Use a different plot or a different color for each cluster. Your x-axis is the color (B-V), and runs from -0.4 to +1.6 in both plots. Your divisions should be about 0.2. The y-axis is the apparent magnitude, and is different in each case. Check the numbers in the table to see what your maximum and minimum values should be. Don't forget that magnitudes are backwards, so that smaller numbers mean brighter stars!!!!
2. We have always plotted absolute magnitude on the y-axis of an H-R diagram. Why can we plot the apparent magnitude for cluster stars? (Hint: what's the difference between apparent and absolute magnitude?)
3. On your plot for 47 Tuc, identify the red giant stars (just draw an oval around them all). Why are these stars so much brighter than main sequence stars of the same color?
4. Which cluster is closer to the earth? (Hint: think about the method of spectroscopic parallax.)
5. The lifetimes of different spectral types are given in Table 2. Use these lifetimes to estimate the age of 47 Tuc and M45. Explain your reasoning!
6. Why don't we see O and B type stars on these diagrams (color < -0.2)?

Table 1: Data for 47 Tuc and M45 Table 2: Main Sequence Lifetimes
47 Tuc       M45
Star Number Magnitude Color (B-V)   Star Number Magnitude Color (B-V)
10012 19.6 0.76   133 14.4 1.28
10170 20.6 0.98   165 7.6 0.12
10200 21.0 1.05   345 11.6 0.84
10206 21.0 0.96   522 11.9 0.90
10278 21.6 1.23   697 8.6 0.35
10335 22.0 1.31   804 7.9 0.20
10359 22.2 1.23   950 4.2 -0.10
10489 22.6 1.33   1040 15.8 1.44
10610 23.0 1.45   1103 14.8 1.47
20028 17.6 0.53   1234 6.8 0.02
20034 17.7 0.58   1266 8.3 0.36
20049 18.0 0.57   1305 13.5 1.18
20070 18.4 0.60   1309 9.5 0.47
20104 18.8 0.65   1355 14.0 1.23
20130 19.1 0.69   1432 2.9 -0.09
20185 19.8 0.83   1454 12.8 1.16
20210 20.1 0.88   1516 14.0 1.31
20239 20.4 0.93   1766 9.1 0.47
20335 21.4 1.10   1797 10.1 0.56
20364 21.6 1.20   1924 10.3 0.62
30014 13.5 1.10   2168 3.6 -0.08
30103 15.5 0.82   2181 5.1 -0.08
40002 12.0 1.45   2209 14.4 1.47
40022 12.6 1.25   2406 11.1 0.76
40043 12.9 1.14   2425 6.2 -0.05
40130 14.0 0.99   2588 13.1 1.22
40135 14.0 0.69   2601 15.0 1.55
40144 14.0 0.79   2655 15.5 1.36
40164 14.0 0.59   2870 12.5 1.07
40351 14.9 0.85   2881 11.8 0.86
40628 16.2 0.73
40821 16.6 0.73
41051 16.9 0.70
41107 17.0 0.58
41456 17.2 0.51
Spectral
Type