What a local sample of spectroscopic binaries can tell us about the field binary population

We study a sample of spectroscopic binaries (SBs) in the local solar neighbourhood (d<= 100 pc and M_V<= 4) in an attempt to find the distributions of the period, P, the primary mass, m₁, and the mass ratio q(=m₂/m₁), as well as the initial mass function (IMF) of the local population of field binaries. The sample was collated using available SB data and the Hipparcos catalogue, the latter being used for distances and to refer numbers of objects to fractions of the local stellar population as a whole. We use the better determined double-lined SBs (SB2s) to calibrate a Monte Carlo approach to modelling the q distribution of the single-lined SBs (SB1s) from their mass functions, f(m), and primary masses, m₁. The totalq distribution is then found by adding the observed SB2 distribution to the Monte Carlo SB1 distribution. While a complete sample is not possible, given the data available, we are able to address important questions of incompleteness and parameter-specific biases by comparing subsamples of SBs with different ranges in parameter space. Our results show a clear peak in the q distribution of field binaries near unity. This is dominated by the SB2s, but the flat distribution of the SB1s is inconsistent with their components being chosen independently at random from a steep IMF.