Trinity I: Self-Consistently Modeling the Dark Matter
  Halo-Galaxy-Supermassive Black Hole Connection from $z=0-10$
  We present Trinity, a flexible empirical model that self-consistently infers
the statistical connection between dark matter haloes, galaxies, and
supermassive black holes (SMBHs). Trinity is constrained by galaxy observables
from $0 < z < 10$ (galaxies' stellar mass functions, specific and cosmic SFRs,
quenched fractions, and UV luminosity functions) and SMBH observables from $0 <
z < 6.5$ (quasar luminosity functions, quasar probability distribution
functions, active black hole mass functions, local SMBH mass-bulge mass
relations, and the observed SMBH mass distributions of high redshift bright
quasars). The model includes full treatment of observational systematics (e.g.,
AGN obscuration and errors in stellar masses). From these data, Trinity infers
the average SMBH mass, SMBH accretion rate, merger rate, and Eddington ratio
distribution as functions of halo mass, galaxy stellar mass, and redshift. Key
findings include: 1) the normalization of the SMBH mass-bulge mass relation
increases only mildly from $z=0$ to $z=3$, but decreases more strongly from
$z=3$ to $z=10$; 2) The AGN radiative$+$kinetic efficiency is $\sim$0.04-0.07,
and does not show significant redshift dependence given the existing data
constraints; 3) AGNs show downsizing, i.e., the Eddington ratios of more
massive SMBHs start to decrease earlier than those of lower-mass objects; 4)
The average ratio between average SMBH accretion rate and SFR is $\sim10^{-3}$
for low-mass galaxies, which are primarily star-forming. This ratio increases
to $\sim10^{-1}$ for the most massive haloes below $z\sim1$, where star
formation is quenched but SMBHs continue to accrete.
