Gas Accretion versus BH Merger driven Growth Modes of Central Supermassive Black Holes and Implications for the Little Red Dots

We investigate the growth of central supermassive black holes in galaxies, aiming to distinguish between gas accretion versus BH merger-driven growth modes. By performing and analysing cosmological hydrodynamical simulations of $(50 ~ {\rm Mpc})^3$ comoving boxes, we also study how the BH feedback physical parameters affect the coevolution between SMBHs and their host galaxies. Starting as $10^5 M_{\odot}$ seeds, we find that the BHs grow initially via BH mergers to $\sim 10^7 M_{\odot}$. Gas accretion onto the BHs is initially low, then increases with time, and reaches the Eddington rate after $7-9$ Gyrs. The BHs then undergo very fast growth via efficient gas accretion over a period of $600 - 700$ Myr, when the BH mass increases $10^2 - 10^3$ times, causing their predominant growth from $10^7 M_{\odot}$ to $(10^9 - 10^{10}) M_{\odot}$. Taking into account the cosmological gas inflows and outflows, SMBHs do not grow to more than $10^{10} M_{\odot}$ by $z=0$, because of gas depletion from galaxy centers driven by AGN feedback. In terms of SMBH - host galaxy coevolution along the $M_{\rm BH} - M_{\star}$ relation, we find that they initially lie below and thereby move upward toward the relation. We make some physical implications of the growth of high-$z$ Little Red Dots recently observed by 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.