Inferring the Intermediate Mass Black Hole Number Density from Gravitational Wave Lensing Statistics

TL;DR

This paper introduces a new gravitational wave lensing-based method to estimate the number density of intermediate mass black holes, potentially revealing their distribution and role in cosmic evolution.

Contribution

It presents a hierarchical Bayesian inference approach to determine black hole densities from gravitational wave lensing data, a novel application in astrophysics.

Findings

Existing detectors can identify or constrain black hole densities around 10^4 to 10^6 Mpc^{-3}.

The method can be extended to probe other compact matter populations.

Demonstrates feasibility of using gravitational wave lensing statistics for astrophysical inference.

Abstract

The population properties of intermediate mass black holes remain largely unknown, and understanding their distribution could provide a missing link in the formation of supermassive black holes and galaxies. Gravitational wave observations can help fill in the gap from stellar mass black holes to supermassive black holes. In our work, we propose a new method for probing lens populations through lensing statistics of gravitational waves, here focusing on inferring the number density of intermediate mass black holes. Using hierarchical Bayesian inference of injected lensed gravitational waves, we find that existing gravitational wave observatories at design sensitivity could either identify an injected number density of $10^6 \mathrm{Mpc}^{-3}$ or place an upper bound of $\lesssim 10^4 \mathrm{Mpc}^{-3}$ for an injected $10^3 \mathrm{Mpc}^{-3}$. More broadly, our method could be applied to probe other forms of compact matter as well.