Main Sequence Fitting

Main sequence fitting also determines distances using the HR Diagram but is always applied to clusters of stars. These stars are gravitationally bound, all located at the same distance, and formed at the same time from the same cloud of gas and dust. It is assumed that the members of a cluster will be found at the same locations as stars in general on the HR diagram. Thus, 90% of the cluster stars are on the main sequence.

Main sequence fitting compares 1) the location of the main sequence for the cluster stars placed on the HR Diagram where apparent magnitude is used as the y-axis variable to 2) the location of the main sequence for nearby stars whose distances are well-known from parallax where absolute magnitude is used as the y-axis variable. Any difference in position between the main sequences must be due to the distance of the cluster. The vertical position of the cluster main sequence is adjusted vertically that it lines up with the main sequence of nearby stars. The amount of vertical adjustment gives the distance modulus which in turn gives the distance.

Figure 1: The difference between the apparent magnitude of the cluster and the absolute magnitude of the main sequeunce line is the distance modulus used in the main sequence fitting technique.

There are some complications with main sequence fitting. When cluster stars run out of hydrogen fuel in their cores, they will leave the main sequence and evolve towards the upper right. Thus, these stars are really a distraction to the fitting process and the older a cluster is, the less of the main sequence you have to work with. A second problem is "blue stragglers". These are stars that are likely members of binary systems and have received mass from their companion. Thus, they can appear to the left of the cluster turn off point because they didn't always have this much mass. The third problem is that one is not always confident regarding membership in the cluster – a few non-member stars are likely to be found in the same direction in the sky and end up included in the cluster photometry. Foreground main sequence stars will appear brighter and above the cluster main sequence stars, similar in appearance to stars becoming red giants. Background main sequence stars appear fainter and below the cluster main sequence stars.