Synchronized Co-evolution between Supermassive Black Holes and Galaxies Over the Last Seven Billion Years as Revealed by the Hyper Suprime-Cam

We measure the evolution of the $M_{\rm BH}-M_*$ 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 $7.0<{\rm log}\,M_{\rm BH}/M_\odot<9.5$. The host-galaxy stellar masses ($M_*$), which cover the interval $10.0<{\rm log}\,M_* / M_\odot <11.5$, 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 $M_{\rm BH}-M_*$ 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, $M_{\rm BH}/M_*$ 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 $M_{\rm BH}-M_*$ relation, which has a best inference of $0.25_{-0.04}^{+0.03}$ dex, consistent with the local value. The redshift evolution of the $M_{\rm BH}-M_*$ 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 $M_{\rm BH}-M_{\rm bulge}$ relation may evolve as previously seen at higher redshifts.