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

Maxwell Moe, Rosanne Di Stefano

Published 2016-06-16Version 1

We compile observations of early-type binaries identified via spectroscopy, eclipses, long-baseline interferometry, sparse aperture masking, adaptive optics, lucky imaging, and common proper motion. We combine the samples from the various surveys and correct for their respective selection effects to determine a comprehensive nature of the intrinsic multiplicity statistics of O-type and B-type stars. We find the properties of companions to massive 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 $\langle$q$\rangle$ = 0.5, 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 = 200-5,000 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 primaries, taking into account that (30$\pm$10)% of single-lined spectroscopic binaries likely contain white dwarf companions instead of low-mass stellar secondaries. The mean frequency of stellar companions with q > 0.1 per primary increases from 0.48$\pm$0.04 for solar-type primaries to 2.1$\pm$0.3 for O-type primaries. We fit joint probability density functions f(M$_1$,q,P,e) $\neq$ f(M$_1$)f(q)f(P)f(e) to the corrected distributions, which can be incorporated into binary population synthesis studies.