The relationship of SMBHs and host galaxies at z<4 in the deep optical variability-selected AGN sample in the COSMOS field

We present the study on the relationship between SMBHs and their host galaxies using our variability-selected AGN sample (iAB 25. 9, \ z 4. 5) constructed from the HSC-SSP Ultra-deep survey in the COSMOS field. We estimated the BH mass (MBH=10^5. 5-10\ M_) based on the single-epoch virial method and the total stellar mass (Mₛtar=10^10-12\ M_) by separating the AGN component with SED fitting. We found that the redshift evolution of the BH-stellar mass ratio (MBH/Mₛtar) depends on the MBH which is caused by the no significant correlation between MBH and Mₛtar. Variable AGNs with massive SMBHs (MBH>10^9\ M_) at 1. 51\%) than the BH-bulge ratios (MBH/Mbulge) observed in the local universe for the same BH range. This implies that there is a typical growth path of massive SMBHs which is faster than the formation of the bulge component as final products seen in the present day. For the low-mass SMBHs (MBH 4. We interpret that host galaxies harboring less massive SMBHs at intermediate redshift have already acquired sufficient stellar mass, although high-z galaxies are still in the early stage of galaxy formation relative to those at the intermediate/local universe.