Effects of Environment on the Size Evolution of Quiescent Galaxies: Comparing Galaxies in Clusters and in the Field at Two Rest-frame Wavelengths

We investigate the impact of environment on quiescent galaxy (QG) size evolution using the CLAUDS+HSC imaging covering 18.6~deg$^2$ in five broad filters ($Ugriz$) and the effective radius of a single-S\'{e}rsic fit as a proxy for galaxy size. We estimate sizes in two rest-frame wavelengths -- 3000\r{A} (UV) and 5000\r{A} (optical) -- for $\sim86,000$ massive ($M_*>10^{9.5}$M$_\odot$) field QGs and for $1,000$ of their similarly massive counterparts from 47 clusters at $0.1<z<0.85$. We fit the size-mass relation (SMR) for field and cluster QGs in five $\Delta z=0.15$ redshift bins and use the characteristic size of $M_*=5\times10^{10}$M$_\odot$ QGs (SMR's zero point) to trace the change in galaxy size over cosmic time and in two types of environment. Sizes of QGs are larger in the rest-frame UV than in the rest-frame optical in both clusters and the field, and this difference is more prominent in the field sample. However, QGs in clusters are systematically smaller than the field QGs, and this difference is significantly more pronounced if measured in the rest-frame UV light. Modeling of the redshift evolution in the characteristic QG size as $R_e\varpropto(1+z)^{\beta}$ shows that the cluster QGs ($\beta=-1.02$ in UV and $\beta= -1.00$ in optical) grow in size as fast as the field QGs ($\beta=-0.95$ in UV and $-1.22$ in optical). This fast growth of cluster QGs is consistent with size increase driven by the accretion of two subpopulations onto clusters: a) field QGs that are larger than their quiescent counterparts in clusters, and b) environmentally quenched galaxies (newcomers) that are larger than the rest of the quiescent population.