The Relationship of Supermassive Black Holes and Host Galaxies at z < 4 in the Deep Optical Variability-selected Active Galactic Nuclei Sample in the COSMOS Field

We present the study on the relationship between supermassive black holes (SMBHs) and their host galaxies using our variability-selected active galactic nuclei (AGNs) sample ( i AB ≤ 25.9 and z ≤ 4.5) constructed from the Hyper Suprime-Cam Subaru Strategic Program Ultradeep survey in the COSMOS field. We estimated the black hole (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 spectral energy distribution 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 no significant correlation between M BH and M star . Variable AGNs with massive SMBHs ( M BH > 10 9 M ⊙ ) at 1.5 < z < 3 show considerably higher BH–stellar mass ratios (> ∼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 < z < 3, on the other hand, variable AGNs show similar BH–stellar mass ratios with the local objects (∼0.1%), but smaller than those observed at z > 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.