Mass-redshift Degeneracy for Gravitational-wave Sources in the Vicinity of a Supermassive Black Hole

Xian Chen, Shuo Li, Zhoujian Cao

Published 2017-03-30Version 1

Retrieving the mass of a gravitational-wave (GW) source is a difficult problem because it is degenerate with redshift. In astronomy three types of redshift exist, namely cosmological, Doppler, and gravitational redshift, but the latter two are often neglected in the analysis of GW data. Motivated by recent proposals that the binary black hole (BH) mergers detected by the Laser Interferometer GW Observatory (LIGO) could have happened in the vicinity of supermassive BHs (SMBHs), we study the effects of Doppler and gravitational redshifts on GWs. We find that they together can contribute an effective redshift as large as $1.9\lesssim(1+z)\lesssim3.4$ if a merger happens between the innermost stable circular orbit and the innermost bound one of a SMBH. Consequently, the "redshift mass" extracted from GW data is greater than the intrinsic, rest mass of the source by the same factor. Neglecting these effects would result in an overestimation of the distance of the source. Our results imply that BHs of $10~M_\odot$ could masquerade as much bigger ones if they merge close to SMBHs. Distinguishing them requires simultaneous observation of GWs in both $(10-10^2)$ Hertz and milli-Hertz bands.