Are the majority of Sun-like stars single?

Abstract

It has recently been suggested that, in the field, $\sim 56\%$ of Sun-like stars ($0.8{\mathrm{M}}_{{}_{\odot }}\lesssim M_{\star }\lesssim 1.2{\mathrm{M}}_{{}_{\odot }}$) are single. We argue here that this suggestion may be incorrect, since it appears to be based on the multiplicity frequency of systems with Sun-like primaries, and therefore takes no account of Sun-like stars that are secondary (or higher-order) components in multiple systems. When these components are included in the reckoning, it seems likely that only $\sim 46\%$ of Sun-like stars are single. This estimate is based on a model in which the system mass function has the form proposed by Chabrier, with a power-law Salpeter extension to high masses; there is a flat distribution of mass ratios; and the probability that a system of mass $M$ is a binary is $0.50+0.46{\log }_{{}_{10}}\left(M/{\mathrm{M}}_{{}_{\odot }}\right)$ for $0.08{\mathrm{M}}_{{}_{\odot }}\le M\le 12.5{\mathrm{M}}_{{}_{\odot }}$, $0$ for $M<0.08{\mathrm{M}}_{{}_{\odot }}$, and $1$ for $M>12.5{\mathrm{M}}_{{}_{\odot }}$. The constants in this last relation are chosen so that the model also reproduces the observed variation of multiplicity frequency with primary mass. However, the more qualitative conclusion, that a minority of Sun-like stars are single, holds up for virtually all reasonable values of the model parameters. Parenthetically, it is still likely that the majority of {\it all} stars in the field are single, but that is because most M Dwarfs probably are single.

arXiv comment6 pages. Accepted by MNRAS

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