Broadening of the Main Sequence of a Star Cluster by Undetected Binaries

Abstract

This paper is concerned with the spread in apparent magnitudes (or absolute magnitudes) of main-sequence stars in a star cluster. I specifically consider the effect of binary stars in broadening the main sequence. I present analytic and semi-analytic expressions for the probability density function (pdf) of the magnitude at a given photometric color, including the effects of binarity. The expressions obtained employ plausible models for the pdfs of the magnitudes of the primary and secondary stars, as well as the distribution of secondary-to-primary mass ratio. A crucial parameter is the fraction of stars in the star cluster that are binaries. The resultant formulas can be used to determine the fraction of binaries in a sample of stars taken from a star cluster, or to limit long term variations in the luminosity of solar type stars.