  We present a series of simulations of the self--regulated growth of
supermassive black holes (SMBHs) in galaxies via three different fueling
mechanisms: major mergers, minor mergers, and disk instabilities. The SMBHs in
all three scenarios follow the same black hole fundamental plane (BHFP) and
correlation with bulge binding energy seen in simulations of major mergers, and
observed locally. Furthermore, provided that the total gas supply is
significantly larger than the mass of the SMBH, its limiting mass is not
influenced by the amount of gas available or the efficiency of black hole
growth. This supports the assertion that SMBHs accrete until they reach a
critical mass at which feedback is sufficient to unbind the gas locally,
terminating the inflow and stalling further growth. At the same time, while
minor and major mergers follow the same projected correlations (e.g., the
$M_{BH}-\sigma$ and Magorrian relations), SMBHs grown via disk instabilities do
not, owing to structural differences between the host bulges. This finding is
supported by recent observations of SMBHs in pseudobulges and bulges in barred
systems, as compared to those hosted by classical bulges. Taken together, this
provides support for the BHFP and binding energy correlations as being more
"fundamental" than other proposed correlations in that they reflect the
physical mechanism driving the co-evolution of SMBHs and spheroids.

Astrophysics