2007ApJ...670..747K

We constrain the properties of massive binaries by comparing radial velocity data on early-type stars in Cygnus OB2 with the expectations of Monte Carlo models. Our comparisons test several popular prescriptions for massive binary parameters. We explore a range of true binary fraction, F, a range of power-law slopes, α, describing the distribution of companion masses between the limits q_low and 1, and a range of power-law slopes, β, describing the distribution of orbital separations between the limits r_in and r_out. We also consider distributions of secondary masses described by a Miller-Scalo type IMF and by a two-component IMF that includes a substantial ``twin'' population with M<sub>2</sub>≃M<sub>1</sub>. Several seemingly disparate prescriptions for massive binary characteristics can be reconciled by adopting carefully chosen values for F, r<sub>in</sub>, and r<sub>out</sub>. We show that binary fractions F<0.7 are less probable than F≥0.8 for reasonable choices of r<sub>in</sub> and r<sub>out</sub>. Thus, the true binary fraction is high. For F=1.0 and a distribution of orbital separations near the canonical ``Opik's law distribution (i.e., flat; β=0), the power-law slope of the mass ratio distribution is α=-0.6 to 0.0. For F≃0.8, α is somewhat larger, in the range -0.4 to 1.0. In any case, the secondary star mass function is inconsistent with a Miller-Scalo-like IMF unless the lower end is truncated below ∼2-4 M_☉. In other words, massive stars preferentially have massive companions. The best-fitting models are described by a Salpeter or Miller-Scalo IMF for 60% of secondary star masses with the other ∼40% of secondaries having M₂≃M₁, i.e., ``twins.'' These model parameters simultaneously predict the fraction of Type Ib/c supernovae to be 30%-40% of all core-collapse supernovae, in agreement with recent observational estimates.