Impact of gravitational lensing on black hole mass function inference with third-generation gravitational wave detectors

TL;DR

This study assesses how gravitational lensing affects black hole mass function inference using third-generation gravitational wave detectors, finding that lensing has minimal impact on main parameters even at high redshifts.

Contribution

It demonstrates through simulations that gravitational lensing does not significantly bias black hole mass function estimates with the Einstein Telescope, especially for the main distribution parameters.

Findings

Parameters are accurately recovered within 1σ.

BHMF models are reconstructed within 68% credible interval.

Lensing impact is negligible for main structure at high redshifts.

Abstract

The recent rapid growth of the black hole (BH) catalog from gravitational waves (GWs), has allowed us to study the substructure of black hole mass function (BHMF) beyond the simplest Power-Law distribution. However, the BH masses inferred from binary BH merger events, may be systematically 'brightened' or 'dimmed' by the gravitational lensing effect. In this work, we investigate the impact of gravitational lensing on the BHMF inference considering the detection of the third-generation GW detector -- the Einstein Telescope (ET). We focus on high redshift, $z=10$, in order to obtain the upper limits of this effect. We use Monte Carlo (MC) method to simulate the data adopting 3 original BHMFs under Un-Lensed and Lensed scenarios, then recover the parameters of BHMFs from the mock data, and compare the difference of results, respectively. We found that all the parameters are well recovered within one standard deviation(std., 1$\sigma$), and all 3 BHMF models are reconstructed within 68\% credible interval, suggesting that lensing would not change the main structure drastically, even at very high redshifts and with high precision of ET. And the modest influence beyond $50M_{\odot}$, depends on the modeling of the high mass tail or substructure of BHMF. We conclude that the impact of lensing on BHMF inference with ET can be safely ignored in the foreseeable future. Careful handling of lensing effects is required only when focusing on an accurate estimation of the high mass end of BHMF at high redshifts.