Determining the distance to a star cluster

How to determine the distance to a star cluster using its H-R diagram?

Background and Need

Having covered the background on Star Clusters, H-R diagram, Main sequence and the need to study star clusters in our previous article on estimating the age of a cluster, we will discuss about ZAMS. Zero-Age Main Sequence (ZAMS) is the locus of all newly formed stars main sequence (MS) stars on the H-R diagram of a cluster – forming a boundary to the lower left of the main sequence.

Idea

All the stars belonging to the same cluster are almost at the same distance from Earth. The difference between apparent magnitude (m) and the absolute magnitude (M) is same for all the stars of the cluster, as it is dependent only on the distance. This difference is also known as the distance modulus.

Concept

An H-R diagram of the star cluster is made using the apparent magnitudes that we directly measure instead of the absolute magnitudes that are normally used for this purpose. The diagram will look the same except that all the points, representing the stars, will be shifted in the vertical direction. The amount of shift that needs to be given to this curve to match it with the theoretical ZAMS is proportional to the distance of the cluster.

This method of distance determination has a certain advantage over other methods, in that it is statistically more robust as it inherently involves observation data from a large number of stars.

References:
[1] Carroll, Bradley W., Dale A. Ostlie, and M. Friedlander. An introduction to modern astrophysics. Vol. 523. New York: Addison-Wesley, 1996.
[2] Kaufmann, William J. "Discovering the universe." New York: WH Freeman, c1993. 3rd ed. 1 (1993).
[3] Böhm-Vitense, Erika. Introduction to stellar astrophysics. Vol. 3. Cambridge University Press, 1992.