# Does this black hole mass/galaxy stellar mass relation hold for extremely low-mass galaxies?

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 $$10^{9.5}M_{\odot}. Even the lowest mass galaxy in that sample lies just under $$\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.

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.