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

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 cos = (10 −2 − 10 −1 ) and composed of BHs of (10 − 20) 𝑀 could masquerade as a BBH at a redshift of 𝑧 cos ∼ 1 and containing BHs as large as (44 − 110) 𝑀 . In the case of extreme demagnification, we also find that the same BBH could appear to be at 𝑧 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.