Abstract
We measure the evolution of the $M_BH-M_*$ relation using 584
uniformly-selected SDSS quasars at $0.2<z<0.8$. The black-hole masses ($M_\rm
BH$) are derived from the single-epoch virial mass estimator using the
H$\beta$ emission line, and span the range $7.0<log\,M_\rm
BH/M_ødot<9.5$. The host-galaxy stellar masses ($M_*$), which cover the
interval $10.0<log\,M_* / M_<11.5$, are determined by performing
two-dimensional quasar-host decomposition of the Hyper Suprime-Cam images and
spectral energy distribution fitting. To quantify sample-selection biases and
measurement uncertainties on the mass terms, a mock quasar sample is
constructed to jointly constrain the redshift evolution of the $M_BH-M_*$
relation and its intrinsic scatter ($\sigma_\mu$) through forward modeling. We
find that the level of evolution is degenerate with $\sigma_\mu$, such that
both positive mild evolution (i.e, $M_BH/M_*$ increases with redshift)
with a small $\sigma_\mu$, and negative mild evolution with a larger
$\sigma_\mu$ are consistent with our data. The posterior distribution of
$\sigma_\mu$ enables us to put a strong constraint on the intrinsic scatter of
the $M_BH-M_*$ relation, which has a best inference of
$0.25_-0.04^+0.03$ dex, consistent with the local value. The redshift
evolution of the $M_BH-M_*$ relation relative to the local relation is
constrained to be $(1+z)^0.12_-0.27^+0.28$, in agreement with no
significant evolution since $z\sim0.8$. The tight and non-evolving $M_\rm
BH-M_*$ relation is suggestive of a coupling through AGN feedback or/and a
common gas supply at work, thus restricting the mass ratio of galaxies and
their black holes to a limited range. Given the considerable stellar disk
component, the $M_BH-M_bulge$ relation may evolve as previously
seen at higher redshifts.
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