Characterisation of lensing selection effects for LISA massive black hole binary mergers

TL;DR

This paper develops a method to account for lensing selection effects in gravitational wave observations by LISA, revealing biases in luminosity distance estimates for high-redshift black hole mergers, crucial for accurate cosmological analysis.

Contribution

It introduces a novel approach to include lensing selection effects in gravitational wave data analysis, quantifying their impact on distance measurements for high-redshift sources.

Findings

Lensing biases increase with redshift, affecting distance estimates.

Selection effects shift the mean magnification distribution to higher values.

Lensing is the dominant error source in high-redshift GW distance measurements.

Abstract

We present a method to include lensing selection effects due to the finite horizon of a given detector when studying lensing of gravitational wave (GW) sources. When selection effects are included, the mean of the magnification distribution is shifted from one to higher values for sufficiently high-redshift sources. This introduces an irreducible (multiplicative) bias on the luminosity distance reconstruction, in addition to the typical source of uncertainty in the distance determination. We apply this method to study lensing of GWs emitted by massive black hole binary mergers at high redshift detectable by LISA. We estimate the expected bias induced by selection effects on the luminosity distance reconstruction as function of cosmological redshift, and discuss its implications for cosmological and astrophysical analyses with LISA. We also reconstruct the distribution of lensing magnification as a function of the observed luminosity distance to a source, that is the observable quantity in the absence of an electromagnetic counterpart. Lensing provides the dominant source of errors in distance measurements of high-redshift GW sources. Its full characterisation, including the impact of selection effects, is of paramount importance to correctly determine the astrophysical properties of the underlying source population and to be able to use gravitational wave sources as a new cosmological probe.