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

## TL;DR

This study uses N-body simulations to analyze the initial mass distribution of black holes and compares the results with LIGO/Virgo gravitational wave data, suggesting a specific power-law spectrum with an upper mass cutoff.

## Contribution

It introduces high-resolution dynamical simulations of black hole clusters to constrain the initial mass function using gravitational wave observations.

## Key findings

- A power-law initial mass spectrum with index -2.35 is favored.
- An upper mass cutoff around 50 solar masses fits the data.
- The merger rate likely increases with redshift.

## 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 $\sim 5-20~M_\odot$. The LIGO discovery of the first BHs via GWs was surprising in that the two BHs that merged had masses of $35.6^{+4.8}_{-3.0}$ and $30.6^{+3.0}_{-4.4}\,M_\odot$, 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 $M_{\rm BH}\propto M^{-2.35}$ with an upper mass cutoff $M_{\rm max}\sim 50M_\odot$ is favored by the data, together with a slight preference for a merger rate that increases with redshift.