We constrain the properties of massive binaries by comparing radial velocity data on 114 early-type stars in the Cygnus OB2 Association with the expectations of Monte Carlo models .
Our comparisons test several popular prescriptions for massive binary parameters while highlighting the sensitivity of the best-fitting solutions to the adopted boundary conditions .
We explore a range of true binary fraction , F , a range of power-law slopes , \alpha , describing the distribution of companion masses between the limits q _ { low } and 1 , and a range of power-law slopes , \beta , 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 initial mass function ( IMF ) and by a two-component IMF that includes a substantial “ twin ” population with M _ { 2 } \simeq M _ { 1 } .
Several seemingly disparate prescriptions for massive binary characteristics can be reconciled by adopting carefully chosen values for F , r _ { in } , and r _ { out } .
We show that binary fractions F < 0.7 are less probable than F \geq 0.8 for reasonable choices of r _ { in } and r _ { out } .
Thus , the true binary fraction is high .
For F = 1.0 and a distribution of orbital separations near the canonical Öpik ’ s Law distribution ( i.e. , flat ; \beta = 0 ) , the power law slope of the mass ratio distribution is \alpha = -0.6 – 0.0 .
For F \simeq 0.8 , \alpha is somewhat larger , in the range -0.4 – 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 \sim 2–4 M _ { \odot } .
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 \sim 40 \% of secondaries having M _ { 2 } \simeq M _ { 1 } , i.e. , “ twins ” .
These best-fitting 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 .