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 (i_AB≤ 25.9,z ≤ 4.5) constructed from the HSC-SSP Ultra-deep survey in the COSMOS field. We estimated the BH mass (M_BH=10^5.5-10 M_⊙) based on the single-epoch virial method and the total stellar mass (M_star=10^10-12 M_⊙) by separating the AGN component with SED fitting. We found that the redshift evolution of the BH-stellar mass ratio (M_BH/M_star) depends on the M_BH which is caused by the no significant correlation between M_BH and M_star. Variable AGNs with massive SMBHs (M_BH>10^9M_⊙) at 1.5∼1%) than the BH-bulge ratios (M_BH/M_bulge) 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 (M_BH<10^8 M_⊙) at 0.5 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.