The Mass-Ratio Distribution of Visual Binary Stars

Abstract

The selection effects that govern the observations of Visual Binary Stars are in- vestigated, in order to obtain a realistic statistical distribution of the mass-ratio q = Msec=Mprim. To this end a numerical simulation programme has been developed, which `generates' binary stars and `looks' at them to determine whether an observer on Earth would be able to detect them. The simulations show that for mass-ratios q >0:35, observations are expected to reveal the real q{distribution, while for mass- ratios q <0:35 selection effects begin to play a major part. It is found that the observed mass-ratio distribution for main-sequence systems, derived from the Index Catalogue of Visual Binary Stars (ids), can be explained by a distribution of sec- ondary masses according to the Initial Mass Function (imf), i.e. ø(M) a M- 2:7 . From the Fourth Catalogue of Orbits of Visual Binary Stars (ovb) authors find a q{distribution that peaks strongly for q{values close to q = 1. Itisshownthat this mass-ratio distribution may be the result of a sampling selection effect. Due to this sampling selection effect, the ovb is a considerably more biased sample of the binary population in our Galaxy than the ids. Numerical simulations of biased sampling show that the q{distribution, found from the ovb, is not incompatible with the distribution of secondary masses according to the imf (for q >0:35), found from the ids. Because of the selection effects, it is difficult to establish the real q{distribution for q <0:35. If the real q{distribution departs from ø(q) a q^(-2,7) for q < 0,35, about 36% of all stars are in visual binaries (i.e. if the q{distribution is assumed to be at for 0 < q<0,35); if the distribution attens for q < 0,25, about 60% of the stars must be primaries of visual binaries.