Cluster Color-Magnitude Diagrams

The lab below uses online color-magnitude diagrams served from the UW Astronomy Education Clearinghouse Server.

It is an adaptation of a lab written by Julianne Dalcanton and updated by Oliver Fraser.

Also attached at the bottom of the page are paper-based labs

• • ages_clusters_cmd.pdf is a paper-based lab originally written by Ana Larson and Brian Stephani. It has been refined and published in Learning Astronomy by Doing Astronomy by Stacy Palen and Ana Larson.

  • ages_cmds_tutorial.pdf is a paper-based lecture-tutorial originally written by Ana Larson and Brian Stephanik

  • CMDs_of_Clusters.docx is a paper-based short lab written by Oliver Fraser

  • clustercmdlab-extrainfo.docx is supplemental information originally written by Julianne Dalcanton

The Distances and Ages of Star Clusters

Very few stars are born isolated. Instead, most stars form in small groups, known as clusters. The stars in a cluster form when a single cloud of cold gas collapses to form many individual stars with a wide range of masses. Because all the cluster stars form from the same gas cloud, they all have a common age and distance. As you will see in this lab, stellar clusters are particularly useful for studies of the age and distances of stars.

Introduction

You will use Color-Magnitude Diagrams (CMDs) to derive the relative distances and ages of several star clusters. Ideally we study stars using Hertzsprung-Russell (H-R) diagrams, a plot of the luminosity of stars against their spectral types or temperatures, but for clusters of stars we can take a shortcut and instead use CMDs. In that case we plot brightness versus color, which are much easier to measure!

Because all of the stars in a cluster are at very nearly the same distance from us, the relative brightness of stars in a cluster correspond to their relative luminosities. Even better, since all main sequence stars have similar luminosities regardless of which cluster they’re in, differences in the apparent brightnesses of the main sequence will indicate which cluster is more distant.

We use color because the color of stars are a rough measurement of their temperature, but to do this we need a way to standardize color. This isn't as easy as it may sound. Astronomers do this by measuring the brightness of a star through many different filters--this is apparent magnitude--and then comparing the brightness of a star in one filter to its brightness in a different one. The difference between these magnitudes is a number which we can use to describe the star's color in a way that allows us to give “color” a more universal and precise meaning.

The filter combination we will use is B−V: the difference between the star's brightness in a blue filter (B), and in a yellow filter (V, historically for “visual”). The important thing to know is that the larger the B−V number for a star, the redder that star is--and the smaller the B−V number is, the bluer the star is.

In this lab, you will measure the relative distances of two different globular clusters using the relative brightnesses of their main sequence stars. Then you will derive the ages of several different open clusters by identifying the mass of their turn-off stars. There is a unique relationship between the mass of a star and the duration of the time it spends on the main sequence. Thus, you can derive the age of a cluster from the mass of the turn-off stars that are just now leaving the main sequence.

There are 10 questions in this lab, scored at 2 points per question. You're welcome to use any tool for your answers, but please submit something Canvas can open (plain text, Microsoft Word, or a pdf).

Relative Cluster Distances

For these questions, refer to the CMDs of the globular clusters M12 and M71.

Distance Questions:

• 1. In which cluster (M12 or M71) does the main sequence appear brighter?

  2. Which cluster is more distant?

  3. Now we'll answer the same question quantitatively. Imagine a line through the center of the main sequence stars in each cluster. Using the interactive plot, what is the magnitude of the center of the main sequence at B−Vs of 0.5, 0.6, & 0.7? Record these values for each cluster in a table like the one below:

• 1. Using the data in your table, find the average difference in the apparent magnitudes. Which cluster is more distant?

  2. The following table shows the difference in magnitude between two stars, if one star was some number of times fainter than the other. (For example, if one star is 1 magnitude fainter than another, its luminosity is 2.5 times fainter.)

• • 1. Using this table and your answer for the previous question, estimate how much brighter the stars in the nearer cluster appear to be than the stars in the more distant cluster (i.e. by a factor of two? of five? of twenty? etc.). If the magnitude difference between comparable main sequence stars in the two clusters does not exactly correspond to an entry in the table, try your best to estimate the difference in brightness from the table. For example, if you derived a magnitude difference of 0.3, you would estimate that the stars in the more distant cluster were a factor of 1.3 times fainter. (The stars in ______ appear to be ______ times fainter than the stars in the nearer cluster.)

• 1. The apparent brightness of a star falls off with distance like an “inverse square law” (i.e. brightness is proportional to 1/distance²). Thus, if the distances to two otherwise identical stars are different by a factor of 3, their apparent brightnesses will be different by a factor of 9 (= 3²). How many times further away is the more distant cluster than the nearer cluster? (The stars in ______ are _____ times further away than the stars in the nearer cluster.)

Cluster Ages

For these questions, refer to the CMDs at the end of this lab. Superimposed on each CMD is a diagonal line showing where main sequence stars lie; tick marks along this line indicate where main sequence stars of different masses lie. You will identify the turnoff stars in each diagram, and use the main sequence locus to estimate the mass of the turnoff stars. You will then use the lifetimes of the turnoff stars to estimate the ages of the clusters.

The lifetime of the stars of this mass can be estimated from the following plot, which shows a logarithmic plot of a star’s mass versus its main sequence lifetime. The dashed line shows that a star with a mass of ~1.6 M_Sun has a lifetime of ~2 Gyr (a Gyr is 10⁹ years).

Cluster Age Questions

• 1. For each cluster:

     1. • First identify the brightest stars that are still on the main sequence—these are the turn-off stars. Compare the location of these stars to the sequence of main sequence star masses and estimate the masses of the turn-off stars for each cluster. Record your answers in a table like the one below.

        • Then use the Main Sequence Lifetime versus Mass plot to estimate the age of the turnoff stars for each cluster. Record your answers in the table.

        • Decide whether each of the clusters contains red giant branch stars, and record your answer in the table.

• 1. Based on your results, how old must a cluster be before it shows a red giant branch?

  2. Based on your answer to the previous question, only stars with masses less than _____ form red giants.

  3. Which cluster is the most distant? How can you tell?