Mind Your Ps and Qs: The Interrelation between Period (P) and Mass-ratio (Q) Distributions of Binary Stars

Abstract

We compile observations of early-type binaries identified via spectroscopy, eclipses, long-baseline interferometry, adaptive optics, common proper motion, etc. Each observational technique is sensitive to companions across a narrow parameter space of orbital periods P and mass ratios q = /M 1. After combining the samples from the various surveys and correcting for their respective selection effects, we find that the properties of companions to O-type and B-type main-sequence (MS) stars differ among three regimes. First, at short orbital periods P ≲ 20 days (separations a ≲ 0.4 au), the binaries have small eccentricities e ≲ 0.4, favor modest mass ratios , and exhibit a small excess of twins q > 0.95. Second, the companion frequency peaks at intermediate periods log P (days) ≈ 3.5 (a ≈ 10 au), where the binaries have mass ratios weighted toward small values q ≈ 0.2–0.3 and follow a Maxwellian “thermal” eccentricity distribution. Finally, companions with long orbital periods log P (days) ≈ 5.5–7.5 (a ≈ 200–5000 au) are outer tertiary components in hierarchical triples and have a mass ratio distribution across q ≈ 0.1–1.0 that is nearly consistent with random pairings drawn from the initial mass function. We discuss these companion distributions and properties in the context of binary-star formation and evolution. We also reanalyze the binary statistics of solar-type MS primaries, taking into account that 30% ± 10% of single-lined spectroscopic binaries likely contain white dwarf companions instead of low-mass stellar secondaries. The mean frequency of stellar companions with q > 0.1 and log P (days) < 8.0 per primary increases from 0.50 ± 0.04 for solar-type MS primaries to 2.1 ± 0.3 for O-type MS primaries. We fit joint probability density functions to the corrected distributions, which can be incorporated into binary population synthesis studies.