## Constraints on Binary Black Hole Populations from LIGO-Virgo Detections

We reanalyze the LIGO-Virgo strain data of the 6 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 lightest 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 disfavors large spins. Even if the underlying black hole population had randomly oriented spins, the typical spins are constrained to $\overline a \lesssim 0.6$. For aligned spins the constraints are tighter with typical spins required to be around $\overline a\sim 0.1$ and comparable dispersion. We detect no statistically significant tendency of the data 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) $f \lesssim 0.3$. The three lightest binary black hole events are consistent with having a maximally spinning secondary but only for small mass ratios ($q\lesssim 0.4$) as a result of the spin-mass ratio degeneracy. The three heavier black hole binaries, that have no degeneracy involving $q$, have larger mass ratios. We confirm previous findings that there is a hint of a cut-off at high mass. The distribution of mass ratios is not so well constrained, in part due to the degeneracy with the spin, but even after taking into account selection effects the data favors an average mass ratio $\overline q \gtrsim 0.5$. read more

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