3 years ago

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

Xian Chen, Zhoujian Cao, Shuo Li

Retrieving the mass of a gravitational-wave (GW) source is a fundamental but difficult problem because the mass is degenerate with redshift. In astronomy, three types of redshift exist, namely cosmological, Doppler, and gravitational redshift, but normally the latter two are too weak to affect GWs. In this Letter, we explore the possibility that a binary of stellar black holes merges within $10$ Schwarzschild radii of a supermassive black hole (SMBH) so that both the Doppler and gravitational redshift are significant. We find that such a merger requires the SMBH to be more massive than about $5\times10^8\,M_\odot$, or at least $6\times10^6\,M_\odot$ if the SMBH has an accretion disk. In both cases, the redshift in total can be as large as $1.9\lesssim(1+z_{\rm tot})\lesssim3.4$ if the merger happens between the innermost stable circular orbit and the innermost bound one around the SMBH. Neglecting this effect will result in an overestimation of the mass of a BBH, and also the luminosity distance, by the same factor of $1+z_{\rm tot}$.

Publisher URL: http://arxiv.org/abs/1703.10543

DOI: arXiv:1703.10543v3

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