How Do Astronomers Determine the Distance to a Star Cluster?

[~Sam~]

Homework Statement

An astronomer measures B and V for a large number of stars in a particular star cluster. (All stars in a given star cluster are at essentially the same distance from the Earth.) She then corrects B and V for interstellar absorption, and plots the resulting value of V for each star against its (B-V) colour index.
She then finds a standard CM diagram of MV vs. intrinsic colour index, (B-V)0, that all stars obey (RH and upper scales in Fig. 16.5), and overlays her observed diagram on the standard diagram. Each star's corrected (B-V) equals its intrinsic (B-V)0, so she lines up the plots so the (B-V) and (B-V)0 scales are equal, and then slides the observed diagram vertically to find the best fit with the standard diagram. At the position of best fit, V = 11.0 on the LH scale lines up with MV = 4.4 on the RH scale. What is the distance to the cluster?
(The technique described here is called cluster fitting, and provides an accurate way of finding the distance to a star cluster because it averages out the observational variations in the individual stars.)

Homework Equations

The Attempt at a Solution

I'm somewhat lost, I know I need to find the distance, but not sure how. Does it involve distance modulus? m-M=5logD-5?

 

[anathema]

Yes, you are correct. The distance modulus equation, m-M = 5logD-5, can be used to find the distance to the star cluster. In this case, m is the apparent magnitude of the stars in the cluster, and M is the absolute magnitude. However, since the astronomer has already corrected for interstellar absorption, the observed V magnitude can be considered equivalent to the absolute magnitude, MV. So the equation can be rewritten as V-MV = 5logD-5.

In the forum post, it states that at the position of best fit, V = 11.0 on the LH scale lines up with MV = 4.4 on the RH scale. Plugging these values into the equation, we get 11.0-4.4 = 5logD-5, or 6.6 = 5logD-5. Solving for D, we get a distance of 10^(1.32) = 20.9 parsecs. Therefore, the distance to the star cluster is approximately 20.9 parsecs.