Constraining the Black Hole Initial Mass Function with LIGO/Virgo Observations

Prior to the detection of black holes (BHs) via the gravitational waves (GWs) that they generate at merger, the presence of BHs was inferred in X-ray binaries, mostly via dynamical measurements, with masses in the range between ∼5 and 20 M⊙. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovery of the first BHs via GWs was surprising in that the two BHs that merged had masses of ${35.6}_{-3.0}^{+4.8}$ and ${30.6}_{-4.4}^{+3.0}\,{M}_{\odot }$, which are both above the range inferred from X-ray binaries. With 20 BH detections from the first/second observing (O1/O2) runs, the distribution of masses remains generally higher than the X-ray inferred one, while the effective spins are generally lower. This suggests that, at least in part, the GW-detected population might be of dynamical origin rather than produced by the common evolution of field binaries. Here we perform high-resolution N-body simulations of a cluster of isolated BHs with a range of initial mass spectra and upper mass cutoffs, and study the resulting binary mass spectrum resulting from the dynamical interactions. Our clusters have properties that are similar to those of the massive remnants in an OB association ∼10 Myr after formation. We perform a likelihood analysis for each of our dynamically formed binary population against the data from the O1 and O2 LIGO/Virgo runs. We find that an initial mass spectrum MBH ∝ M−2.35 with an upper mass cutoff Mmax ∼ 50M⊙ is favored by the data, together with a slight preference for a merger rate that increases with redshift.