ASTR 217 Lab Name:

(Based on a University of Washington Astronomy Department online exercise.)

Color-Magnitude Diagrams and the Age of Star Clusters

Summary

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

Background and Theory

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 you 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 (next page) 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, so just like the O-M spectral class sequence, it goes from hotter stars to cooler stars.

Procedure

1.  Plot the BV versus magnitude on a piece of graph paper or using a spreadsheet program such as Microsoft Excel.

2.  Draw a different chart for each cluster.

3.  Your x-axis is the color (BV). Your divisions on the x-axis should be about 0.2.

4.  The y-axis is the apparent magnitude, and is different in each case.

5.  Do not forget that magnitudes are backwards, so that smaller numbers mean brighter stars!!!!
You should put the y-axis values, the apparent magnitude numbers, IN REVERSE ORDER on your Excel chart vertical axis scale.

6.  Answer the written questions on the last page.

Star Cluster 47 Tuc / Star Cluster M45
Star Number / Color (BV) / Magnitude / Star Number / Color (BV) / Magnitude
10012 / 0.76 / 19.6 / 133 / 1.28 / 14.4
10170 / 0.98 / 20.6 / 165 / 0.12 / 7.6
10200 / 1.05 / 21 / 345 / 0.84 / 11.6
10206 / 0.96 / 21 / 522 / 0.9 / 11.9
10278 / 1.23 / 21.6 / 697 / 0.35 / 8.6
10335 / 1.31 / 22 / 804 / 0.2 / 7.9
10359 / 1.23 / 22.2 / 950 / -0.1 / 4.2
10489 / 1.33 / 22.6 / 1040 / 1.44 / 15.8
10610 / 1.45 / 23 / 1103 / 1.47 / 14.8
20028 / 0.53 / 17.6 / 1234 / 0.02 / 6.8
20034 / 0.58 / 17.7 / 1266 / 0.36 / 8.3
20049 / 0.57 / 18 / 1305 / 1.18 / 13.5
20070 / 0.6 / 18.4 / 1309 / 0.47 / 9.5
20104 / 0.65 / 18.8 / 1355 / 1.23 / 14
20130 / 0.69 / 19.1 / 1432 / -0.09 / 2.9
20185 / 0.83 / 19.8 / 1454 / 1.16 / 12.8
20210 / 0.88 / 20.1 / 1516 / 1.31 / 14
20239 / 0.93 / 20.4 / 1766 / 0.47 / 9.1
20335 / 1.1 / 21.4 / 1797 / 0.56 / 10.1
20364 / 1.2 / 21.6 / 1924 / 0.62 / 10.3
30014 / 1.1 / 13.5 / 2168 / -0.08 / 3.6
30103 / 0.82 / 15.5 / 2181 / -0.08 / 5.1
40002 / 1.45 / 12 / 2209 / 1.47 / 14.4
40022 / 1.25 / 12.6 / 2406 / 0.76 / 11.1
40043 / 1.14 / 12.9 / 2425 / -0.05 / 6.2
40130 / 0.99 / 14 / 2588 / 1.22 / 13.1
40135 / 0.69 / 14 / 2601 / 1.55 / 15
40144 / 0.79 / 14 / 2655 / 1.36 / 15.5
40164 / 0.59 / 14 / 2870 / 1.07 / 12.5
40351 / 0.85 / 14.9 / 2881 / 0.86 / 11.8
40628 / 0.73 / 16.2
40821 / 0.73 / 16.6
41051 / 0.7 / 16.9
41107 / 0.58 / 17
41456 / 0.51 / 17.2

Answer the following questions. Staple your two charts (graphs) to this page when finished.

1.  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?)

2.  On your plot for 47 Tuc, locate the red giant stars. Why are these stars so much brighter than main sequence stars of the same color?

3.  Which cluster is closer to the earth? (Hint: think about the method of spectroscopic parallax. Compare the apparent magnitudes for the same spectral types.)

4.  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!

Table 2: Main Sequence Lifetimes
Spectral
Type / Color
B-V / Lifetime
(years)
O / -0.4 / < 106
B / -0.2 / 3 X 107
A / 0.2 / 4 X 108
F / 0.5 / 4 X 109
G / 0.7 / 1 X 1010
K / 1.0 / 6 X 1010
M / 1.6 / >1011

5.  Why don't we see O and B type stars on these diagrams (color < -0.2)?

ASTR 217 Star Cluster Ages Lab Exercise p. 1 - 1 -