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I read a preprint last week (Palmese & Conselice 2020) that suggested that the recent gravitational wave detection GW190521 could be the end result of a merger of two extremely low-mass galaxies. Each black hole would have originally been at the center of one of the two galaxies, and the two would have coalesced $\sim4$ Gyr after the galactic merger.

The scenario requires two ultra-dwarf galaxies of masses $M\sim10^5\text{-}10^6M_{\odot}$. The authors calculate this by using a power-law relation between the galactic stellar mass $M_*$ and black hole mass $M_{\text{BH}}$ empirically found by Reines & Volonteri 2015: $$\log(M_{\text{BH}})=\alpha+\beta\log(M_*/10^{11}M_{\odot})$$ However - as with some other assumptions Palmese & Conselice make - this power-law was derived by looking at much more massive galaxies, with the great majority falling in the range $10^{9.5}M_{\odot}<M_*<10^{11.5}M_{\odot}$. Even the lowest mass galaxy in that sample lies just under $\sim10^{9.5}M_{\odot}$.

My question, then, is this: Can we extrapolate this sort of purely empirical result to the extremely low-mass galaxies that would have been involved in the merger? My guess is not necessarily, and the authors only used this form because of the sheer lack of data involving low-mass galaxies with extremely low-mass central black holes - it seems difficult, if not impossible, to detect black holes of $60\text{-}90M_{\odot}$ in low-mass and presumably very dim galaxies outside the local universe.

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I am doing a research on central SMBH-galaxy mass relation. Through my research, I came across many papers on observations of this relation. Almost all of them had a mass range of $~10^{10}M_\odot to ~10^{13}M_\odot$ as the DM halo mass. Whereas the SMBH mass was in range of $~10^{6}M_\odot to ~10^{11}M_\odot$ in the local universe.

Here are some points to be noted:

  1. There are observational constraints even in the local universe. In the local universe, we do not have a lot of data on low-mass SMBH-DM halo. (This does not mean there are not many low-mass SMBH-DM halos to study. I'm only talking about local universe.)
  2. This mass relation has a redshift dependence, which can be seen when we observe SMBH's at high redshifts.

So, because of these two constraints, we cannot observationally prove the mass relation between low-mass galaxies and extremely low-mass central BHs. If we try to study high redshifts, we have both observational constraints (low mass BH's are extremely difficult to spot) and redshift dependence on the local relation.

It is possible that the power-law relation can be extrapolated even for low-mass system but there is also a chance that low-mass systems follow a completely different trend. There is no way to observationally prove it (atleast for now). Maybe improvement in gravitational waves technology in the future might help.

Ferrarese L. 2002 Shimasaku K. 2019 Kormendy and Ho 2013 Bassem M. Sabra 2015

There are many other papers referenced by the authors of these papers. Some of these papers are quite acclaimed and have 2000 citations.

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