Constraints on Binary Black Hole Populations from LIGO-Virgo Detections

Abstract

We reanalyse the 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 $\overline{a}\lesssim 0.4$, even if the underlying population has randomly-oriented spins. For aligned spins the constraints are tighter, with typical spins required to be around $\overline{a}\sim 0.1$ 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 $10^8$ years) $f\lesssim 0.3$. 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 cutoff at high mass. The data favour distributions of mass ratios with an average $\overline{q}\gtrsim 0.7$.

15 pages, 11 figures. v2: Includes 4 more events, announced Dec 1 2018 by the LIGO and Virgo Collaborations. Matches version accepted for publication in MNRAS. Added appendix A clarifying our approach to selection bias

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