Toward Complete Statistics of Massive Binary Stars: Penultimate Results from the Cygnus OB2 Radial Velocity Survey

We analyze orbital solutions for 48 massive multiple-star systems in the Cygnus OB2 Association, 23 of which are newly presented here, to find that the observed distribution of orbital periods is approximately uniform in log P for P<45 d, but it is not scale-free. Inflections in the cumulative distribution near 6 d, 14, d, and 45 d, suggest key physical scales of ~0.2, ~0.4, and ~1 A.U. where yet-to-be-identified phenomena create distinct features. No single power law provides a statistically compelling prescription, but if features are ignored, a power law with exponent beta = -0.22 provides a crude approximation over P=1.4 -- 2000 d, as does a piece-wise linear function with a break near 45 d. The cumulative period distribution flattens at P > 45 d, even after correction for completeness, indicating either a lower binary fraction or a shift toward low-mass companions. A high degree of similarity (91% likelihood) between the Cyg OB2 period distribution and that of other surveys suggests that the binary properties at P<25 d are determined by local physics of disk/clump fragmentation and are relatively insensitive to environmental and evolutionary factors. Fully 30% of the unbiased parent sample is a binary with period P < 45 d. Completeness corrections imply a binary fraction near 55% for P < 5000 d. The observed distribution of mass ratios 0.2<q<1 is consistent with uniform, while the observed distribution of eccentricities 0.1<e<0.6 is consistent with uniform plus an excess of e ~ 0 systems. We identify six stars, all supergiants, that exhibit aperiodic velocity variations of ~30 km/s attributed to atmospheric fluctuations.