DAVOS: Dwarf Active Galactic Nuclei from Variability for the Origins of Seeds: Properties of Variability-Selected Active Galactic Nuclei in the COSMOS Field and Expectations for the Rubin Observatory

We study the black hole mass $-$ host galaxy stellar mass relation, $M_{\rm{BH}}-M_{\ast}$, of a sample of $z<4$ optically-variable AGNs in the COSMOS field. The parent sample of 491 COSMOS AGNs were identified by optical variability from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) program. Using publicly-available catalogs and spectra, we consolidate their spectroscopic redshifts and estimate virial black hole masses using broad line widths and luminosities. We show that variability searches with deep, high precision photometry like the HSC-SSP can identity AGNs in low mass galaxies up to $z\sim1$. However, their black holes are more massive given their host galaxy stellar masses than predicted by the local relation for active galaxies. We report that $z\sim 0.5-4$ variability-selected AGNs are meanwhile more consistent with the $M_{\rm{BH}}-M_{\ast}$ relation for local inactive early-type galaxies. This result is consistent with most previous studies of the $M_{\rm{BH}}-M_{\ast}$ relation at similar redshifts and indicates that AGNs selected from variability are not intrinsically different from the broad-line Type 1 AGN population at similar luminosities. Our results demonstrate the need for robust black hole and stellar mass estimates for intermediate-mass black hole candidates in low-mass galaxies at similar redshifts. Assuming that these results do not reflect a selection bias, they appear to be consistent with self-regulated feedback models wherein the central black hole and stars in galaxies grow in tandem.