Are LIGO's Black Holes Made From Smaller Black Holes?

A channel for the formation of stellar mass black holes (BHs) is through hierarchical mergers of smaller BHs. Repeated mergers between BHs leave an imprint on the spin of the resulting black hole, since the final BH spin is largely determined by the orbital angular momentum of the merging binary system. It has been shown that a population of supermassive BHs that forms through repeated mergers will have a distribution of spin magnitudes centered around a dimensionless spin magnitude of a ~ 0.7. We show that for stellar mass BHs forming from hierarchical mergers, the distribution of spin magnitudes is universal, with a peak at a ~ 0.7 and little support below a ~ 0.4. This is largely insensitive to details of the hierarchichal merger model: within realistic astrophysical scenarios, the spin distribution is robust against changes to the mass ratio of the merging binaries, the initial spin distribution of the first generation of BHs, and the number of merger generations. While we assume an isotropic distribution of spin directions in deriving the universal hierarchical merger spin distribution, we find that spins that are preferentially aligned or antialigned with the orbital angular momentum during merger lead to narrower, more constraining distributions without affecting the upper and lower limit of the universal distribution. Using the universal distribution, we explore the ability of spin measurements from ground-based gravitational wave detectors to constrain hierarchical merger scenarios. We apply a hierarchical Bayesian mixture model to mock gravitational wave data and argue that the fraction of BHs that formed through hierarchical mergers will be constrained with O(100) LIGO BBH detections. We also argue that a BH with spin magnitude a < 0.4 is unlikely to have formed hierarchically, and with O(10) detections we could falsify a model in which all component BHs form hierarchically.


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