Inferring the Intermediate-mass Black Hole Number Density from Gravitational-wave Lensing Statistics

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 with masses between ∼100–104 M ⊙. In our work, we propose a new method for examining lens populations through lensing statistics of gravitational waves, here focusing on inferring the number density of intermediate-mass black holes through hierarchical Bayesian inference. Simulating ∼200 lensed gravitational-wave signals, we find that existing gravitational-wave observatories at their design sensitivity could either constrain the number density of 106 Mpc−3 within a factor of 10, or place an upper bound of ≲104 Mpc−3 if the true number density is 103 Mpc−3. More broadly, our method leaves room for incorporation of additional lens populations, providing a general framework for probing the population properties of lenses in the universe.