  Recent Hubble Space Telescope (HST) observations have revealed that a
majority of active galactic nuclei (AGN) at z ~ 1-3 are resident in isolated
disk galaxies, contrary to the usual expectation that AGN are triggered by
mergers. Here we develop a new test of the cosmic evolution of supermassive
black holes (SMBHs) in disk galaxies by considering the local population of
SMBHs. We show that substantial SMBH growth in spiral galaxies is required as
disks assemble. SMBHs exhibit a tight relation between their mass and the
velocity dispersion of the spheroid within which they reside, the M_BH-sigma
relation. In disk galaxies the bulge is the spheroid of interest. We explore
the evolution of the M_BH-sigma relation when bulges form together with SMBHs
on the M_BH-sigma relation and then slowly reform a disk around them. The
formation of the disk compresses the bulge raising its sigma. We present
evidence for such compression in the form of larger velocity dispersion of
classical bulges compared with elliptical galaxies at the same mass. This
compression leads to an offset in the M_BH-sigma relation if it is not
accompanied by an increased M_BH. We quantify the expected offset based on
photometric data and show that, on average, SMBHs must grow by ~ 50-65% just to
remain on the M_BH-sigma relation. We find no significant offset in the
M_BH-sigma relations of classical bulges and of ellipticals, implying that
SMBHs have been growing along with disks. Our simulations demonstrate that SMBH
growth is necessary for the local population of disk galaxies to have remained
on the M_BH-sigma relation.
