Constraints on binary black hole populations from LIGO-Virgo detections

We re-analyse the Laser Interferometer Gravitational-Wave Observatory (LIGO)-Virgo strain data of the 10 binary black hole mergers reported to date and compute the likelihood function in terms of chirp mass, mass ratio, and effective spin. We discuss the strong degeneracy between mass ratio and spin for the three lighter events. We use this likelihood and an estimate of the horizon volume as a function of intrinsic parameters to constrain the properties of the population of merging binary black holes. The data disfavour large spins. Typical spins are constrained to (a) over bar less than or similar to 0.4, even if the underlying population has randomly oriented spins. For aligned spins, the constraints are tighter, with typical spins required to be around (a) over bar similar to 0.1 and have comparable dispersion. We detect no statistically significant tendency towards a positive average spin in the direction of the orbital angular momentum. We put an upper limit on the fraction of systems where the secondary could have been tidally locked prior to the formation of the black holes (corresponding to merger times shorter than 10(8) yr) f less than or similar to 0.3. Four events are consistent with having a maximally spinning secondary, although one only marginally. We confirm previous findings that there is a hint of a cut-off at high mass. The data favour distributions of mass ratios with an average (q) over bar greater than or similar to 0.7.