From a sample of 72 galaxies with reliable supermassive black hole masses M _ { bh } , we derive the M _ { bh } – ( host spheroid luminosity , L ) relation for i ) the subsample of 24 core-Sérsic galaxies with partially depleted cores , and ii ) the remaining subsample of 48 Sérsic galaxies .
Using K _ { s } -band Two Micron All Sky Survey data , we find the near-linear relation M _ { bh } \propto L _ { K _ { s } } ^ { 1.10 \pm 0.20 } for the core-Sérsic spheroids thought to be built in additive dry merger events , while M _ { bh } \propto L _ { K _ { s } } ^ { 2.73 \pm 0.55 } for the Sérsic spheroids built from gas-rich processes .
After converting literature B -band disk galaxy magnitudes into inclination- and dust-corrected bulge magnitudes , via a useful new equation presented herein , we obtain a similar result .
Unlike with the M _ { bh } – ( velocity dispersion ) diagram , which is also updated here using the same galaxy sample , it remains unknown whether barred and non-barred Sérsic galaxies are offset from each other in the M _ { bh } – L diagram .

While black hole feedback has typically been invoked to explain what was previously thought to be a nearly constant M _ { bh } / M _ { Spheroid } mass ratio of \sim 0.2 % , we advocate that the near-linear M _ { bh } – L and M _ { bh } – M _ { Spheroid } relations observed at high masses may have instead largely arisen from the additive dry merging of galaxies .
We argue that feedback results in a dramatically different scaling relation , such that black hole mass scales roughly quadratically with the spheroid mass in Sérsic galaxies .
We therefore introduce a revised cold-gas ’ quasar ’ mode feeding equation for semi-analytical models to reflect what we dub the quadratic growth of black holes in Sérsic galaxies built amidst gas-rich processes .
Finally , we use our new Sérsic M _ { bh } – L equations to predict the masses of candidate intermediate mass black holes in almost 50 low luminosity spheroids containing active galactic nuclei , finding many masses between that of stellar mass black holes and supermassive black holes .