The mass-ratio distribution of spectroscopic binary stars

In order to determine the mass-ratio distribution of spectroscopic binary stars, the selection effects that govern the observations of this class of binary systems are investigated. The selection effects are modelled numerically and analytically. The results of the models are compared to the data inThe Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars (DAO8) compiled by Battenet al. (1989). The investigations involve binary systems with Main-Sequence primary components only, in order to avoid confusion of evolutionary and selection effects.For single-lined spectroscopic binaries (SBI) it is found that the mass ratios (q=M _sec/M _prim) in general adhere to a distribution _q q ^-2 forq>q ₀, withq ₀=0.3. The observations are consistent with a distribution that is flat forq<q ₀. The turn-over value varies fromq ₀=0.3 for systems with B-type primaries, toq ₀=0.55 for systems with K-type primaries. The semi-major axesa ₁ are distributed according to _a (a ₁)a ₁ ^-a with an average value of _a =1.3. The power varies from _a =1.7 for systems with B-type primaries to _a =0 for systems with K-type primaries. The eccentricitiese of the orbits of SBI systems are distributed according to _e (e)e ^-1.For double-lined spectroscopic binary stars (SBII) it is found that the shape of theq-distribution, as derived from observations, is almost entirely determined by selection effects. It is shown that the distribution is compatible with theq-distribution found for SBI systems. A sub-sample, consisting of the SBII systems from DAO8 with magnitudesm _V 5 ^m , is less hampered by selection effects, and shows the same shape of theq-distribution as the SBI systems, at theq-interval (0.67, 1).It is estimated that 19–45% of the stars in the solar neighbourhood are spectroscopic binary systems.