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

Abstract

Prior to the detection of black holes (BHs) via the gravitational waves (GWs) they generate at merger, the presence of BHs was inferred in X-ray binaries, mostly via dynamical measurements, with masses in the range between $\sim 5-20M_{\odot }$. The 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 O1/O2 runs, the distribution of masses remains generally higher than the X-ray inferred one, while the effective spins are generally lower, suggesting 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 cut-offs, and study the resulting binary mass spectrum resulting from the dynamical interactions. Our clusters have properties similar to those of the massive remnants in an OB association $\sim 10\mathrm{Myr}$ 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 $M_{\mathrm{BH}}\propto M^{-2.35}$ with an upper mass cutoff $M_{\max }\sim 50M_{\odot }$ is favored by the data, together with a slight preference for a merger rate that increases with redshift.

Accepted to ApJL. Major updates

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• Close Encounters of Stars with Stellar-mass Black Hole Binaries
• Gravitational waves from the remnants of the first stars in nuclear star clusters
• Implications of recoil kicks for black hole mergers from LIGO/Virgo catalogs
• Population Synthesis of Black Hole Binaries with Compact Star Companions
• Host galaxies and electromagnetic counterparts to binary neutron star mergers across the cosmic time: Detectability of GW170817-like events