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

Abstract This note 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 calculate the probability density function (pdf) of the magnitude at a given photometric color, including the effects of binarity. An expression is developed which employs 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. The expression for the pdf is dependent on σ , the fractional variation of primary and secondary, and A , the fraction of stars that are binaries. The expression 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.