HST observations show that the surface brightness profiles of early-type galaxies have central cusps , I \propto r ^ { - \gamma } .
Two characteristic profile types are observed : ‘ core ’ profiles have a break at a resolved radius and \gamma \leq 0.3 inside that radius ; ‘ power-law ’ profiles have no clear break and \gamma > 0.3 .
With few exceptions , galaxies with M _ { V } < -22 have core profiles , and galaxies with M _ { V } > -20.5 have power-law profiles .
Both profile types occur in galaxies with -22 < M _ { V } < -20.5 .
We show here that these results are consistent with the hypothesis that : ( i ) all early-type galaxies have central BHs that grew adiabatically in homogeneous isothermal cores ; and ( ii ) these ‘ progenitor ’ cores followed scaling relations similar to those of the fundamental plane .

The models studied here are the ones first proposed by Young .
They predict I \propto r ^ { -1 / 2 } at asymptotically small radii , but I \propto r ^ { - \gamma } at the radii observable with HST .
The slope \gamma can take all observed values ; it increases monotonically with \mu = M _ { \bullet } / M _ { core } .
The scaling relations for early-type galaxies imply that the progenitor core mass scales with luminosity as M _ { core } \propto L ^ { 1.5 } .
If , as suggested by various arguments , the black hole ( BH ) mass M _ { \bullet } scales roughly linearly with luminosity , M _ { \bullet } \propto L , then \mu \propto L ^ { -0.5 } .
This yields larger cusp slopes in lower-luminosity galaxies .
Models with BH masses and progenitor cores that obey established scaling relations predict ( at the distance of the Virgo cluster ) that galaxies with M _ { V } < -21.2 have core profiles and galaxies with M _ { V } > -21.2 have power-law profiles .
This reproduces both the sense and the absolute magnitude of the observed transition .
Intrinsic scatter in BH and galaxy properties can explain why both types of galaxies are observed around the transition magnitude .
The observed bimodality in cusp slopes may be due to a bimodality in M _ { \bullet } / L , with rapidly rotating disky galaxies having larger M _ { \bullet } / L than slowly rotating boxy galaxies .

We apply the models to 46 galaxies with published HST photometry .
Both core and power-law galaxies are well fitted .
The models suggest a roughly linear correlation between BH mass and V -band galaxy luminosity , \log M _ { \bullet } \approx - 1.83 + \log L in solar units ( RMS scatter 0.33 dex ) .
This agrees with the average relation for nearby galaxies with kinematically determined BH masses .
Photometrically and kinematically determined BH masses agree to within \sim 0.25 dex RMS for galaxies that have both .
These results provide additional support to the hypothesis that every galaxy ( spheroid ) has a central BH .
The BH mass distribution inferred here is consistent with quasar statistics for a BH accretion efficiency of 4 % .

The proposed scenario is not a unique way to interpret the observed surface brightness cusps of galaxies , but it explains observational correlations that are otherwise unexplained , and it yields BH masses that agree with those determined kinematically .