The relationship between quasars and their host galaxies provides clues on how supermassive black holes (SMBHs) and massive galaxies are jointly assembled. To elucidate this connection, we measure the structural and photometric properties of the host galaxies of ∼5000 Sloan Digital Sky Survey quasars at 0.2 < z < 1 using five-band (grizy) optical imaging from the Hyper Suprime-Cam Subaru Strategic Program. An automated analysis tool is used to forward-model the blended emission of the quasar as characterized by the point-spread function and the underlying host galaxy as a two-dimensional Sérsic profile. We find that quasars are preferentially hosted by massive star-forming galaxies with disklike light profiles. Furthermore, the size distribution of quasar hosts is broad at a given stellar mass and the average values exhibit a size–stellar mass relation as seen with inactive galaxies. In contrast, the sizes of quasar hosts are more compact than those of inactive star-forming galaxies on average, but not as compact as those of quiescent galaxies of similar stellar masses. This is true irrespective of quasar properties, including the bolometric luminosity, Eddington ratio, and black hole mass. These results are consistent with a scenario in which galaxies are concurrently fueling an SMBH and building their stellar bulge from a centrally concentrated gas reservoir. Alternatively, quasar hosts may be experiencing a compaction process in which stars from the disk and inflowing gas are responsible for growing the bulge. In addition, we confirm that the host galaxies of type 1 quasars have a bias of being closer to face-on systems, suggesting that galactic-scale dust can contribute to obscuring the broad-line region.

We measure the evolution of the  BH –  ⋆ relation using 584 uniformly selected Sloan Digital Sky Survey quasars at 0.2 < z < 0.8. The black hole masses (  BH ) are derived from the single-epoch virial mass estimator using the Hβ emission line and span the range 7.0 < log  BH / M ⊙ < 9.5 . The host-galaxy stellar masses (  ⋆ ), which cover the interval 10.0 < log  ⋆ / 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  BH –  ⋆ relation and its intrinsic scatter (σ μ ) through forward modeling. We find that the level of evolution is degenerate with σ μ , such that both a positive mild evolution (i.e.,  BH /  ⋆ increases with redshift) with a small σ μ and a negative mild evolution with a larger σ μ are consistent with our data. The posterior distribution of σ μ enables us to put a strong constraint on the intrinsic scatter of the  BH –  ⋆ relation, which has a best inference of 0.25 − 0.04 + 0.03 dex, consistent with the local value. The redshift evolution of the  BH –  ⋆ 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 ∼ 0.8. The tight and unevolving  BH –  ⋆ relation is suggestive of a coupling through active galactic nuclei 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  BH –  bulge relation may evolve as previously seen at higher redshifts.