Gas accretion versus black-hole-merger-driven growth modes of supermassive black holes and implications for the little red dots

We investigated the growth of central supermassive black holes (SMBHs) in galaxies, with the aim of distinguishing between gas accretion and black-hole (BH) merger-driven growth modes. We performed cosmological hydrodynamical simulations of $(50 Mpc )^3$ comoving volumes, and analyzed how the BH feedback parameters affect the coevolution between SMBHs and their host galaxies. Starting as 10^5 M_⊙ seeds, we find that the BHs initially grow via BH mergers to ∼ 10^7 M_⊙. Gas accretion onto the BHs is low soon after seeding, and then the accretion rate increases with time and reaches the Eddington rate after 7-9 Gyr. The BHs then undergo very fast growth via efficient gas accretion over a time period of 600 - 700 Myr; during this period the BH mass increases 10^2 - 10^3 times, causing their predominant growth from 10^7 M_⊙ to $(10^9 - 10^ 10 ) M_⊙$. Taking into account the cosmological gas inflows and outflows, SMBHs do not grow to more than 10^ 10 M_⊙ by z=0, which is because of gas depletion from galaxy centers driven by BH feedback. In terms of the coevolution of SMBHs and their host galaxies along the M_ ̊m BH - M_⋆ relation, we find that they initially lie below the relation at earlier epochs and thereby move upward toward the relation. We made some physical implications about the growth of high-z little red dots recently observed by the JWST: the normal-mass SMBHs had predominantly undergone BH-merger-driven evolution, whereas the overmassive BHs underwent periods of Eddington-limited or super-Eddington bursts of gas accretion.