# Star Clusters

Hertzsprung-Russell diagrams were developed in the early twentieth century; they consist of individual stars plotted on axes of increasing luminosity–brightness, essentially–versus decreasing surface temperature, for various historical reasons. If the stars are selected exclusively from one group, called a cluster, their graph can be analyzed in various ways to estimate the cluster’s distance and age. Color-magnitude diagrams, also called “observational HR diagrams,” plot apparent magnitude against temperature or color, whereas a Hertzsprung-Russell diagram uses the absolute magnitude scale. In this activity, students will first produce a color-magnitude diagram of their cluster, then calculate its distance to make an HR diagram, and finally use models of stellar life to estimate the age and chemical composition of the cluster.

This Expedition is designed to encourage decision-making. Each bulleted question is tailored to remain open to discussion; that is to say, there are no “correct” answers, and students should choose the option they believe is best. There are also many areas which invite further exploration, so feel free to perform more in-depth investigations as time and interest allow.

## Color-Magnitude Diagrams

Star clusters offer an accessible entry point into producing Hertzsprung-Russell diagrams, since their properties allow us to skip the more complex work that is otherwise necessary to calculate luminosity. This section explores the creation of color-magnitude diagrams, first choosing a cluster and then progressing through data extraction and plotting. If you want to learn more about star clusters and produce your own HR diagram, this is a good place to start.

## The Distance Modulus

Once we have a color-magnitude diagram as produced in the first step, it can be fitted to a graph which has already been calibrated to the absolute magnitude scale: in this case, a theoretical model called an isochrone. This magnitude relationship, called the distance modulus, allows us to convert the color-magnitude plot to a typical Hertzsprung-Russell diagram.

## Isochrone Fitting

After accounting for the distance of the cluster and converting its apparent magnitudes to absolute magnitudes, it becomes possible to estimate further properties of the cluster by comparing it to a variety of isochrones. This is done based upon the shape of the HR diagram’s stellar distribution since in older clusters, a greater fraction of stars have left the main sequence and evolved into red giants.