ON THE MASS-RATIO DISTRIBUTION OF SINGLE-LINED SPECTROSCOPIC BINARIES

A mathematically rigorous, nonparametric statistical model is derived for the inference of mass ratio distributions from observed mass function distributions of single-lined spectroscopic binaries. The mathematical relation between these distributions is that of a deterministic integral equation, which is shown to be ill-posed and very poorly conditioned. Three nearly equivalent methods of solution of this relation are developed and demonstrated on synthetic datasets. Sampling variations in datasets of reasonable size are shown to greatly limit the precision with which mass ratio distributions can be deduced. The solution methods are applied to three sets of binaries studied in the current literature: those with B dwarf primaries, F and G dwarf primaries, and G and K giant primaries. All three sets show approximately the same form of mass ratio distribution, one rising toward small values of q; but uncertainties arising from poor conditioning, instrumental limitations, and selection effects are so large that the true forms of mass ratio distributions of these classes of binaries remain essentially unknown. Mass ratio distributions inferred from single-line binaries alone currently appear to provide few constraints on binary formation theory. Credible estimation of the binary bass ratio distribution for any class of binaries may require an order of magnitude improvement in the quality and quantity of currently available observational data, and relatively sophisticated data analysis. © 1995 American Astronomical Society.