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The Sloan Digital Sky Survey Reverberation Mapping Project: The Black Hole Mass$-$Stellar Mass Relations at $0.2\lesssim z\lesssim 0.8$

We measure the correlation between black-hole mass $M_{\rm BH}$ and host stellar mass $M_*$ for a sample of 38 broad-line quasars at $0.2\lesssim z\lesssim 0.8$ (median redshift $z_{\rm med}=0.5$). The black-hole masses are derived from a dedicated reverberation mapping program for distant quasars, and the stellar masses are estimated from two-band optical+IR HST imaging. Most of these quasars are well centered within $\lesssim 1$kpc from the host galaxy centroid, with only a few cases in merging/disturbed systems showing larger spatial offsets. Our sample spans two orders of magnitude in stellar mass ($\sim 10^9-10^{11}\,M_\odot$) and black-hole mass ($\sim 10^7-10^9\,M_\odot$), and reveals a significant correlation between the two quantities. We find a best-fit intrinsic (i.e., selection effects corrected) $M_{\rm BH}-M_{\rm *,host}$ relation of $\log (M_{\rm BH}/M_{\rm \odot})=7.01_{-0.33}^{+0.23} + 1.74_{-0.64}^{+0.64}\log (M_{\rm *,host}/10^{10}M_{\rm \odot})$, with an intrinsic scatter of $0.47_{-0.17}^{+0.24}$dex. Decomposing our quasar hosts into bulges and disks, there is a similar $M_{\rm BH}-M_{\rm *,bulge}$ relation with a slightly larger scatter, likely caused by systematic uncertainties in the bulge-disk decomposition. The $M_{\rm BH}-M_{\rm *,host}$ relation at $z_{\rm med}=0.5$ is similar to that in local quiescent galaxies, with negligible evolution over the redshift range probed by our sample. With direct black-hole masses from reverberation mapping and a large dynamical range of the sample, selection biases do not appear to affect our conclusions significantly. Our results, along with other samples in the literature, suggest that the locally-measured black-hole mass$-$host stellar mass relation is already in place at $z\sim 1$.