Student Name: Lab Partner Name: Lab TA Name: Background A1101, Lab 8: Distances and Ages of Star Clusters Lab Worksheet Here are a few important things to remember about stellar evolution and star clusters for this Lab: A star spends most of its lifetime on the main sequence, fusing hydrogen into helium in its core. After exhausting its core hydrogen, a star expands and becomes a luminous, cool, red giant. After the end of the red giant phase, the envelope of the star expands out into space, and the core remains behind as a white dwarf, slowly cooling off over time. (Massive stars explode as supernovae and leave behind neutron stars or black holes.) On the main sequence, higher mass stars are hotter and much more luminous. As a result, they use up their hydrogen fuel more quickly than lower mass stars, even though they have more fuel to begin with. Massive stars live fast and die young. The Sun is about 4.5 billion years old, roughly halfway through its lifetime as a main sequence star. The stars we see over the sky with the naked eye or a small telescope have a wide range of masses, luminosities, distances, and ages. The stars in a star cluster appear close together on the sky, and they are all at nearly the same distance from the Earth. The stars in a star cluster were all born at nearly the same time, so the stars in a given cluster are all nearly the same age today. However, different star clusters may have very different ages. For reference: the Sun has a surface temperature of about 6000 degrees and a color index of 0.62.
Part 1: The HR Diagram and Color- Brightness Diagram On page 1 of the graph handout, there are four plots. The upper left plot shows the Hertszprung- Russell (HR) diagram for stars within 100 light years of the Sun, where parallax has been used to determine distance and thus convert apparent brightness to luminosity. The upper right plot contains the same stars, but now the vertical axis is showing the apparent brightness of the stars instead of their luminosity. 1. Why is the distribution of stars in the upper right plot blurrier than the one in the upper left plot? Which plot better conveys the intrinsic characteristics of the stars? We could call the upper right plot a color- brightness diagram. The lower left plot shows a color- brightness diagram for stars in a small patch of the sky that contains a star cluster known as NGC188. Because it is a small patch of sky, even the brightest stars in it are 1000 times fainter than α Centauri (i.e., all stars in this patch have a brightness relative to αcen that is 10-3 or smaller). These observations didn t collect enough light to measure stars fainter than 10-8 relative to αcen; longer observations or a bigger telescope could detect fainter stars. The lower right plot is like the lower left, but it contains only stars whose motion on the sky is very close to the average motion of the NGC 188 cluster. 2. Referring to these plots: (a) Why does the lower left plot have a well defined main sequence of stars but also a wash of stars above and below this main sequence? (b) For the lower right plot, what is the advantage of selecting stars that have the same motion as the cluster?
(c) In the top two plots, the one on the right, which shows brightness instead of luminosity, the main sequence is much blurrier than the left plot. In the lower right plot, why does the main sequence of NGC 188 appear so sharp, even though this plot uses brightness instead of luminosity? Part 2: The HR Diagram of the Hyades Cluster On page 2 of the graph handout, the upper plot shows the HR diagram of stars in the Hipparcos catalog, with distances measured from parallax, just like the one you examined in Lab 5. The lower plot shows the HR diagram of stars in a small patch of sky that contains the Hyades star cluster, one of the star clusters closest to the solar system. The brightnesses of stars have been converted to luminosities assuming that all stars in this patch of sky are at the distance of the Hyades cluster, which is about 150 light years. 3. In both plots (top and bottom) (a) Circle the most massive stars that are on the main sequence. Indicate this group with the label LFDY for Live Fast, Die Young. (b) Circle the lowest mass stars on the main sequence. Indicate this group with the label LLSL for Long Life in the Slow Lane. (c) Circle a group of main sequence stars that are likely to be nearly the same mass as the Sun. Indicate this group with the label ST, for Solar Twins. (d) Circle the stars that are likely to be red giants. Indicate this group with the imaginative label RG. How many red giants are there in the Hyades cluster? (e) Circle the stars that are likely to be white dwarfs. Indicate this group with the label WD. (f) In the bottom plot only, circle some of the stars that are likely to be contaminants, i.e., stars that happen to be in the same area of sky as the Hyades but are not really members of the Hyades cluster. Indicate this group with a frowning- face label, as they are getting in the way.
Part 3: Distances to Star Clusters The Hyades cluster is close enough that its distance can be measured from the parallax of its member stars. But one of the most useful things about star clusters is that their distances can be inferred even if they are too far away for parallax measurements. Page 3 of the graph handout has color- brightness diagrams of four star clusters: the Hyades, the Pleiades (a.k.a. Subaru), NGC 188, and Messier 67. (The two latter names are based on the catalogs of objects that the clusters appear in.) 4. Rank these four clusters in order of distance, from closest to furthest. Explain your reasoning. Hint: Circle the group of stars in each cluster that you think are most similar to the Sun. Then compare their brightness. Recall that the color index of the Sun is 0.62. Part 4: Relative Ages of Star Clusters The plots on page 4 of the graph handout show the same four clusters, but now their distances have been used to convert brightness to luminosity. 5. Describe three differences that you notice among the HR diagrams of these four clusters. (a) (b) (c) You may want to refer back to the introductory material on the first page before answering the remaining questions.
6. Rank these four clusters in order of age, from youngest to oldest. Explain your reasoning. If there are clusters you have a hard time ranking relative to each other, note which ones they are and explain why it is difficult to tell which is older. Hint: Live Fast, Die Young. 7. Could you have ranked these clusters in age even if you didn t know their distances, using the plots on page 3 of the graph handout instead of page 4? If so, how? Part 5: Absolute Ages of Star Clusters To get an absolute age of a star cluster, in years, we must compare the observed properties of its stars to theoretical predictions for how long a star can live on the main sequence. 8. Recall that the Sun will spend about 9 billion years on the main sequence (we re halfway through). Is the Hyades cluster older than 9 billion years or younger than 9 billion years? Explain your reasoning. Is the cluster Messier 67 older than 9 billion years or younger than 9 billion years? Explain your reasoning.
9. Up until now, we have been looking at open clusters, relatively loose clusters of stars found in the disk of the Milky Way galaxy. Page 5 of the graph handout shows the HR diagram of the globular cluster Messier 5, a very dense cluster of more than 100,000 stars in the outer regions of the Milky Way. (a) Which of the open cluster HR diagrams does the Messier 5 HR diagram most resemble? (b) What is a difference between the Messier 5 HR diagram and any of the open cluster diagrams? The lower plot on page 5 has the same data points, but overlaid are predictions of stellar evolution theory, calculated using a computer program that OSU Professor Marc Pinsonneault wrote (many years ago, when he was a graduate student at Yale). The topmost curve is the prediction for where stars would lie in the HR diagram if the cluster were 10 billion years old. The next highest curve is the prediction for a 12 billion year old cluster, and so on down to the bottom curve, for 20 billion years. These predictions account for the fact that the composition of globular cluster stars is quite different from that of open clusters, which makes the colors and luminosities significantly different at a given age. 10. Based on comparing these theoretical models to the data, what is your best estimate for the age of the globular cluster Messier 5? What is the plausible range of ages (i.e., it must be more than X but less than Y)?