Supermassive Black Hole Demographics: Evading $M - {\sigma}$

We consider black hole - galaxy coevolution using simple analytic arguments. We focus on the fact that several supermassive black holes are known with masses significantly larger than suggested by the $M - {\sigma}$ relation, sometimes also with rather small stellar masses. We show that these are likely to have descended from extremely compact `blue nugget' galaxies born at high redshift, whose very high velocity dispersions allowed the black holes to reach unusually large masses. Subsequent interactions reduce the velocity dispersion, so the black holes lie above the usual $M - {\sigma}$ relation and expel a large fraction of the bulge gas (as in WISE J104222.11+164115.3) that would otherwise make stars, before ending at low redshift as very massive holes in galaxies with relatively low stellar masses, such as NGC 4889 and NGC 1600. We further suggest the possible existence of two new types of galaxy: low-mass dwarfs whose central black holes lie below the $M - {\sigma}$ relation at low redshift, and galaxies consisting of very massive ($\gtrsim 10^{11}$M$_{\odot}$) black holes with extremely small stellar masses. This second group would be very difficult to detect electromagnetically, but potentially offer targets of considerable interest for LISA.