The early growth of supermassive black holes in cosmological hydrodynamic simulations with constrained Gaussian realizations.

We examine the early growth of supermassive black holes (SMBHs) using constrained realization cosmological simulations. We reconstruct the initial conditions (ICs) in the large volume BlueTides (BT) hydrodynamic simulation and run them to $z=6$. We compare the constrained simulations with BT to test the accuracy of this method for reproducing the first quasars and their environments. At the high redshifts of interest, non-linear mode coupling on the scale of even small simulation box sizes is not present. This allows our re-simulations in a volume of $(15h^{-1}{\rm Mpc})^3$ to correctly recover the evolution of large-scale structure, and the stellar and BH mass functions in the vicinity of a $\sim10^{12}M_{\odot}$ halo which we identified in BT at $z\sim7$ to be hosting a $\sim10^9M_{\odot}$ SMBH. Our re-simulations confirm that only with the lowest tidal field, high-density peaks in the ICs can induce the fastest BH growth required to explain the $z>6$ quasars. We carry out three simulations with the same ICs but different BH seed masses of $5\times10^3$, $5\times10^4$, and $5\times10^5h^{-1}M_{\odot}$ (the one used in BT) while keeping the halo to BH mass ratio fixed. We find that the BH mass converges to $\sim10^9M_{\odot}$ by $z=6$ regardless of the seeding procedure while their early growth histories at $z>10$ differ. The simulations with small BH seeds lead to the emergence of a large population of BHs which merge frequently at early times (four BH mergers, with masses $10^4\sim10^6M_{\odot}$ at $z\gtrsim12$). This is also accompanied by a few major BH mergers at $z\lesssim8$ for intermediate and small BH seeds while there are no mergers in the large BH seed simulation. The increased BH merger rate for low mass BH seeds provides an exciting prospect for discriminating BH formation mechanisms with the advent of multi-messenger astrophysics and next-generation GW facilities.