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 SDSS 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 Sersic profile. In agreement with previous studies, quasars are preferentially hosted by massive star-forming galaxies with disk-like light profiles. Furthermore, we find that 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 inactive star-forming galaxies on average, but not as compact as quiescent galaxies of similar stellar masses. This is true irrespective of quasar properties including bolometric luminosity, Eddington ratio, and black hole mass. These results are consistent with a scenario in which galaxies are concurrently fueling a 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 towards face-on, suggesting that galactic-scale dust can contribute to obscuring the broad-line region.
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