Probing the $z\gtrsim6$ quasars in a universe with IllustrisTNG physics:
  Impact of gas-based black hole seeding models
  We explore implications of a range of black hole (BH) seeding prescriptions
on the formation of the brightest $z\gtrsim6$ quasars in cosmological
hydrodynamic simulations. The underlying galaxy formation model is the same as
in IllustrisTNG. Using constrained initial conditions, we study the growth of
BHs in rare overdense regions (forming $\gtrsim10^{12}M_{\odot}/h$ halos by
$z=7$) using a $(9~\mathrm{Mpc}/h)^3$ simulated volume. BH growth is maximal
within halos that are compact and have a low tidal field. For these halos, we
consider an array of gas-based seeding prescriptions wherein
$M_{\mathrm{seed}}=10^4-10^6~M_{\odot}/h$ seeds are inserted in halos above
critical thresholds for halo mass and dense, metal-poor gas mass (defined as
$\tilde{M}_{\mathrm{h}}$ and $\tilde{M}_{\mathrm{sf,mp}}$, respectively, in
units of $M_{\mathrm{seed}}$). We find that a seed model with
$\tilde{M}_{\mathrm{sf,mp}}=5$ and $\tilde{M}_{\mathrm{h}}=3000$ successfully
produces a $z\sim6$ quasar with $\sim10^9~M_{\odot}$ mass and
$\sim10^{47}~\mathrm{ergs~s^ {-1}}$ luminosity. BH mergers play a crucial role
at $z\gtrsim9$, causing an early boost in BH mass at a time when
accretion-driven BH growth is negligible. When more stringent seeding
conditions are applied (for e.g., $\tilde{M}_{\mathrm{sf,mp}}=1000$), the
relative paucity of BH seeds results in a much lower merger rate. In this case,
$z\gtrsim6$ quasars can only be formed if we enhance the maximum allowed BH
accretion rates (by factors $\gtrsim10$) compared to the accretion model used
in IllustrisTNG. This can be achieved either by allowing for super-Eddington
accretion, or by reducing the radiative efficiency. Our results show that
progenitors of $z\sim6$ quasars have distinct BH merger histories for different
seeding models, which will be distinguishable with LISA observations.
