Astronomy 201: Cosmology, Fall 2013 Professor Edward Olszewski and Charles Kilpatrick Lab 3, Cluster Hertzsprung-Russell Diagrams and the Age of Stars Due October 22, Worth 32 points You may work in groups of two (2) if you wish. Hand in one writeup with both of your names on the paper. Do NOT hand in THIS entire document. 1 Introduction In this assignment, we are going to measure the age of stars in star clusters. This exercise is modeled after labs invented at the University of Washington and the University of Michigan. Before you get started, study up on the Hertzsprung-Russell (HR) diagram. 2 Background Thus far in the course, we have learned how to determine many characteristics of the stars: distance (from parallax), intrinsic luminosity (from brightness with distance effect removed or using the HR diagram once its calibrated), surface temperature (from the color or spectrum), composition (from the spectrum), mass (from binary stars and the laws of gravity, or using calibrated HR diagram if you also know its a main sequence star) and radius (from the laws of light or eclipsing binary stars). 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, the HR diagram plots the spectral type of a star determined from its spectrum against the star s intrinsic luminosity. It turns out that stars of different spectral type have different colors. We can measure a star s color by determining its apparent brightness through two different (color) filters, say a blue filter and a yellow filter. We can then plot the color of a star against its apparent brightness as a way of building an HR diagram without taking the star s spectrum. Astronomers like to measure brightness in terms of magnitude. The magnitude of a star is proportional to the logarithm of its brightness and is defined in such a way that faint objects have LARGER magnitudes than brighter objects. You would think it would be the other way around. Some astronomers like this quaint system, which was invented by the ancient Greek astronomer Hipparchos (Greek: Iππαρχoς) 2000 years ago. Others think it is hopelessly old-fashioned, and should be abandoned. In any case, for the time being we are stuck with it. In the plots below we plot magnitudes which are the apparent magnitudes, or apparent brightnesses of the stars. An HR diagram with color versus magnitude instead of spectral type (OBAFGKM) versus magnitude is generally called a color-magnitude diagram. This method is particularly useful with star clusters where taking the spectrum of thousands of closely-spaced stars would be impossible. To understand a color-magnitude diagram, just remember the following rules: 1
Brighter stars are found towards the top of the plot. If apparent or absolute magnitudes are used to measure the brightness, then smaller numbers will be at the top of the plot. The magnitude system is backwards, such that brighter objects have smaller magnitudes. Redder colors and cooler temperatures are found towards the right side of the plot Astronomers derive a numerical value for a stars color by measuring the difference between a stars apparent magnitude when it is viewed through a blue filter and then through a redder filter. With this system, larger numbers for the color indicate redder colors and lower temperatures. The data in this lab uses the blue (B) filter and greenish-yellow (V) filter to measure a color referred to as B-V. B-V is a measure of the color, or temperature, of a star. It is the difference between the star s magnitude in a blue filter and a yellow filter. The important thing to know is that larger B-V values are redder and lower values are bluer. 3 The Ages of Clusters To understand how stars evolve and change throughout their lifetimes, it is critical to know the properties of stars of different ages. Unfortunately, it is extremely difficult to determine the age of any random star. An old 1 M main sequence star looks nearly identical to a young 1 M main sequence star, making it difficult to distinguish between them even if one is many billion years older than the other. (Note: is the ancient Egyptian symbol for the Sun. The symbol M means solar mass i.e. mass of the Sun). While it is difficult to measure the age of an individual star, it is relatively straightforward to measure the age of a cluster of stars. If all of the stars in a cluster were born at the same time, then they are the same age. Thus, if the age of just one of the stars can be determined, then the age of all the stars will be known. Fortunately, there is one class of stars for which it is quite easy to determine an age. Stars that have just used up the hydrogen in their cores will begin to brighten, and will pull off the main sequence to higher luminosities. These stars are known as turnoff stars, because they are in the process of turning off the main sequence (changing their structure so that their properties plotted on the HR diagram change). Stars of different masses leave the main sequence at different times, because the main sequence lifetime of a star depends sensitively on the mass of the star. Thus, for a cluster of stars with similar ages, stars of only one particular mass will have just the right lifetime to be leaving the main sequence at the time the cluster is observed. Stars that are more massive than the turnoff mass will have already evolved into red giants or supergiants, and stars that are less massive will still be sitting on the main sequence. To find the age of stars in a cluster, you (1) identify the turnoff stars, (2) estimate their masses, and (3) look up (from models of stars) what the main sequence lifetime is for a star with the mass of the turnoff star. 2
Identifying the turnoff stars (1) is relatively straightforward. If you can find the main sequence stars in a cluster, the turnoff stars will be those that are just a bit brighter than the brightest stars that are still on the main sequence. To find the masses of the turnoff stars (2), you can use the fact that main sequence stars of a particular mass always have a particular temperature, and thus appear to have a particular color. Therefore, by measuring the color of the stars that are just now leaving the main sequence, you can estimate the mass of the turnoff stars. Since we know how long stars of any mass can live on the main sequence, we can calculate how old the stars in a cluster might be. For example, suppose the turnoff stars in a cluster had the color of an A-type star (white or bluish white), which has a mass of 2 solar masses (M ). A 2 M star lives on the main sequence for roughly one billion years (1 Gyr) and thus the cluster must be around 1 Gyr old. If the cluster were younger than 1 Gyr, then there would still be stars more massive than 2 M living on the main sequence. If the cluster were older, then all 2 M stars would have already used up the hydrogen in their cores and evolved far from the main sequence. 4 Procedure Open your favorite net browser and go to the link: http://www.astro.lsa.umich.edu/ugactivities/labs/clusters/applet/index.html You must be able to run Java on your web browser. Be patient, it takes a little while for everything to load (maybe even a few minutes, especially if 90 of your best friends are trying to use this website at the same time). The program will load a set of color-magnitude Hertzsprung-Russell (HR) diagrams for eight star clusters in our Milky Way galaxy. Take a look at the plots for each of the eight clusters, using the drop-down menu at the top right of the page. Notice that these are plots of real data, which are a bit messier than the artistic HR diagrams in introductory textbooks. Now, note that the plots are of apparent magnitude (V) versus (B-V) color. Along the top of each plot the axis is labeled as (B-V) 0, which is the color of the star corrected for reddening by interstellar dust. Interstellar dust (like dust on the ground) makes stars appear slightly redder and dimmer than they actually are. For our purposes, we will just assume that the corrections for dust have been made correctly. Note also that smaller values of (B-V) correspond to bluer colors, or hotter stars. Go back to the first color-magnitude diagram and click somewhere on the plot. You should get a blue crosshair, which you can drag around to measure values at any point in the plots. The values are printed in the lower right of the page. Now turn on the ZAMS (zero age main sequence) with the menu in the upper right. This produces a red gridded overlay. The ZAMS line corresponds to where stars will be in the plot when the cluster is first born. As time goes on, stars leave the ZAMS and then have colors and magnitudes that put them in the giant part or white dwarf part of these plots. Moving the slider bars allows you to slide the ZAMS around; clicking the arrows will allow finer adjustments. 3
5 Turnoff Point and Age We can determine the age of a cluster fairly accurately using the turnoff point, the spot where stars begin to deviate from the main sequence. Below the turnoff, stars are still burning hydrogen in their cores, happily living on the main sequence. Above the turnoff point, stars have exhausted their core hydrogen. For a younger cluster, the turnoff point is closer to the blue (high mass, bright) end of the main sequence, and for older clusters, it is closer to the red end of the main sequence. To accurately locate the turnoff point, use the ZAMS overlay. First, match up the upper x-axis of the overlay and the upper x-axis of the diagram at (B-V ) 0 = 0.0 by using the horizontal slider. Then slide the overlay up/down with the vertical slider until you get what you consider to be the best match between the star data points and the ZAMS line. When fitting clusters with a lot of scatter, try to match the narrower parts of scatter to the curve, and generally try to keep the ZAMS to the lower left of the scatter since objects not on the main sequence are probably above and right of the ZAMS. When youve got a match, you will be able to see where the star data peels off from the ZAMS this is the turnoff point. 1. Use the cross-hairs to measure (B-V) 0 of the turnoff for each cluster. Print out the plot with your best fit ZAMS superimposed, and the blue crosshair on the turnoff point, and attach it to your homework. Remember that in detail every student will have a slightly different result, depending on exactly where they put the red overlay on the data. (1 point for each plot) 2. Enter your value of the turnoff color, (B-V) 0 in Table 1, for each cluster. (8 points) 3. Using the turnoff color, you can now estimate the age of the cluster, using the theoretical calculations shown in Figure 1. Figure 1 shows the cluster age as a function of turnoff color, (B-V ) 0. For each cluster, match your measured value of (B-V) 0 on the x-axis and and then follow up to the solid line and read off the age of the cluster on the y-axis. Record the age in Table 1 (turn in the sheet with Table 1 as part of the writeup). (8 points) 4. Question: Why does the HR diagram of each of those clusters in the observed units (apparent brightness and color) look the same as the HR diagram of each of those clusters in intrinsic units (luminosity and color)? While the numbers on the y-axis are different, there has to be something special about star clusters besides the fact that all the stars are the same age. (2 points) 5. Summary Question: While there is some variation in age for the clusters in Table 1, none of them are as old as a globular cluster (you will have to read up on globular clusters). If you were to look at a color-magnitude diagram of a very old globular cluster, what would you expect to see? Draw the color-magnitude diagram you expect for a globular cluster and explain in your own words why it looks different from the clusters listed in Table 1. (6 points) 4
Figure 1: Cluster Age as a function of Turnoff color. 5
Table 1: Cluster Turnoff point and ages. Cluster Name (B-V) 0 at Turnoff Age (years) M67 M45 M44 M25 NGC 752 NGC 6791 NGC 7044 Mel 20 6