Mass-redshift Degeneracy for Gravitational-wave Sources in the Vicinity of a Supermassive Black Hole. (arXiv:1703.10543v4 [astro-ph.HE] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Chen_X/0/1/0/all/0/1">Xian Chen</a> (PKU), <a href="http://arxiv.org/find/astro-ph/1/au:+Li_S/0/1/0/all/0/1">Shuo Li</a> (NAOC), <a href="http://arxiv.org/find/astro-ph/1/au:+Cao_Z/0/1/0/all/0/1">Zhoujian Cao</a> (AMSS-CAS)

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 the latter two are normally too weak to affect the observation.

In this Letter, we show that the current astrophysical models allow binary

black holes (BBHs) to merge within $10$ Schwarzschild radii of a supermassive

black hole (SMBH). We find that in this case both the Doppler and gravitational

redshift are significant, and in the most extreme condition they could increase

the “apparent” black-hole mass and distance by a factor of $1.9-3.4$. We show

that such a factor is consistent with the distribution in the distance-mass

diagram of the ten BBHs detected so far by LIGO/Virgo. We also discuss the

difficulties of this redshift scenario caused by the low event rate predicted

by the current models, as well the potential solutions.

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 the latter two are normally too weak to affect the observation.

In this Letter, we show that the current astrophysical models allow binary

black holes (BBHs) to merge within $10$ Schwarzschild radii of a supermassive

black hole (SMBH). We find that in this case both the Doppler and gravitational

redshift are significant, and in the most extreme condition they could increase

the “apparent” black-hole mass and distance by a factor of $1.9-3.4$. We show

that such a factor is consistent with the distribution in the distance-mass

diagram of the ten BBHs detected so far by LIGO/Virgo. We also discuss the

difficulties of this redshift scenario caused by the low event rate predicted

by the current models, as well the potential solutions.

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