On the Mass‐Ratio Distribution of Spectroscopic Binaries

In this paper we derive the mass-ratio and secondary-mass distributions of a large, well-defined, complete sample of 129 spectroscopic binaries with periods between 1 and 2500 days. The binaries, whose orbits were published recently, were detected by a systematic radial-velocity survey of a sample of more than 1400 large proper motion stars. Three features stand out in the mass-ratio distribution: a rise as the mass ratio goes down to q ~ 0.2, a sharp drop below q ~ 0.2, and a smaller peak at q ~ 0.8. Another way to characterize the results is to state that the distribution includes two "populations," one with a high asymmetric peak at q ~ 0.2 and another with a smaller peak at q ~ 0.8, while the minimum between the two populations is centered at q ~ 0.55. The size of the binary sample allows us to divide it into two subsamples and look for differences in the mass-ratio distributions of the two subsamples. We performed two different divisions: one into Galactic halo versus disk populations, and the other into high- and low-mass primary stars (above and below 0.67 M☉). The former division yields differences with moderate statistical significance of 88%, while the latter is more significant at a level of 97%. Our analysis suggests that the rise toward low mass ratios does not appear in the mass-ratio distribution of the halo binaries. The other separation shows a broad peak at mass ratio of q ~ 0.8-1 for the subsample of binaries with low-mass primaries but no corresponding peak in the subsample with high-mass primaries. We discuss our findings and their application to theories of binary formation.