  We study the population of supermassive black holes (SMBHs) and their effects
on massive central galaxies in the IllustrisTNG cosmological hydrodynamical
simulations of galaxy formation. The employed model for SMBH growth and
feedback assumes a two-mode scenario in which the feedback from active galactic
nuclei occurs through a kinetic, comparatively efficient mode at low accretion
rates relative to the Eddington limit, and in the form of a thermal, less
efficient mode at high accretion rates. We show that the quenching of massive
central galaxies happens coincidently with kinetic-mode feedback, consistent
with the notion that active supermassive black cause the low specific star
formation rates observed in massive galaxies. However, major galaxy mergers are
not responsible for initiating most of the quenching events in our model. Up to
black hole masses of about $10^{8.5}\,{\rm M}_\odot$, the dominant growth
channel for SMBHs is in the thermal mode. Higher mass black holes stay mainly
in the kinetic mode and gas accretion is self-regulated via their feedback,
which causes their Eddington ratios to drop, with SMBH mergers becoming the
main channel for residual mass growth. As a consequence, the quasar luminosity
function is dominated by rapidly accreting, moderately massive black holes in
the thermal mode. We show that the associated growth history of SMBHs produces
a low-redshift quasar luminosity function and a redshift zero black hole
mass-stellar bulge mass relation in good agreement with observations, whereas
the simulation tends to over-predict the high-redshift quasar luminosity
function.
