The appearance of a merging binary black hole very close to a spinning supermassive black hole

TL;DR

This paper investigates how gravitational lensing by a nearby supermassive black hole can significantly alter the observed properties of merging binary black holes, potentially leading to misinterpretations of their true mass and redshift.

Contribution

It introduces a detailed analysis of lensing effects near a Kerr SMBH on GW signals, revealing how these effects can bias mass and redshift measurements in gravitational-wave astronomy.

Findings

Lensing causes a positive correlation between redshift and demagnification.

Signals are more likely to appear redshifted and demagnified than blueshifted and magnified.

A nearby BBH can mimic a distant, more massive system due to lensing effects.

Abstract

The mass and distance of a binary black hole (BBH) are fundamental parameters to measure in gravitational-wave (GW) astronomy. It is well-known that the measurement is affected by cosmological redshift, and recent works also showed that Doppler and gravitational redshifts could further affect the result if the BBH coalesces close to a supermassive black hole (SMBH). Here we consider the additional lensing effect induced by the nearby SMBH on the measurement. We compute the null geodesics originating within $10$ gravitational radii of a Kerr SMBH to determine the redshift and magnification of the GWs emitted by the BBH. We find a positive correlation between redshift and demagnification, which results in a positive correlation between the mass and distance of the BBH in the detector frame. More importantly, we find a higher probability for the signal to appear redshifted and demagnified to a distant observer, rather than blueshifted and magnified. Based on these results, we show that a binary at a cosmological redshift of $z_{\rm cos}=(10^{-2}-10^{-1})$ and composed of BHs of $(10-20)M_\odot$ could masquerade as a BBH at a redshift of $z_{\rm cos}\sim1$ and containing BHs as large as $(44-110)M_\odot$. In the case of extreme demagnification, we also find that the same BBH could appear to be at $z_{\rm cos}>10$ and contain subsolar-mass BHs. Such an effect, if not accounted for, could bias our understanding of the origin of the BHs detected via GWs.