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

TL;DR

This paper develops analytic models to quantify how undetected binary stars cause the main sequence of a star cluster to appear broader in magnitude, aiding in binary fraction estimation.

Contribution

It introduces new analytic and semi-analytic formulas for the probability density function of stellar magnitudes considering binarity effects.

Findings

Formulas for the magnitude distribution including binary effects

Methods to estimate binary fractions from observed data

Tools to constrain luminosity variations in solar-type stars

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.