The Mass–Ratio Distribution of Short–Period Binaries

Abstract

Abstract We present a new algorithm to derive the mass-ratio distribution of an observed sample of spectroscopic binaries. The algorithm replaces each binary of unknown inclination by an ensemble of virtual systems with a distribution of inclinations. We show that contrary to a widely held assumption the orientations of each virtual ensemble should not be distributed randomly in space. A few iterations are needed to find the true mass-ratio distribution. Numerical simulations clearly demonstrate the advantage of the new algorithm over the classical method. We have applied the new algorithm to the recent large sample of G-dwarf spectroscopic binaries, and got a uniform or perhaps a slightly rising linear mass-ratio distribution. This result suggests that the mass-ratio distributions of short-period and long-period binaries are substantially different. It also indicates that the mass distribution of the secondary stars is not the same as that of the single stars.