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We explore implications of a range of black hole (BH) seeding prescriptionson the formation of the brightest $z\gtrsim6$ quasars in cosmologicalhydrodynamic simulations. The underlying galaxy formation model is the same asin IllustrisTNG. Using constrained initial conditions, we study the growth ofBHs 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 maximalwithin halos that are compact and have a low tidal field. For these halos, weconsider an array of gas-based seeding prescriptions wherein$M_{\mathrm{seed}}=10^4-10^6~M_{\odot}/h$ seeds are inserted in halos abovecritical thresholds for halo mass and dense, metal-poor gas mass (defined as$\tilde{M}_{\mathrm{h}}$ and $\tilde{M}_{\mathrm{sf,mp}}$, respectively, inunits of $M_{\mathrm{seed}}$). We find that a seed model with$\tilde{M}_{\mathrm{sf,mp}}=5$ and $\tilde{M}_{\mathrm{h}}=3000$ successfullyproduces a $z\sim6$ quasar with $\sim10^9~M_{\odot}$ mass and$\sim10^{47}~\mathrm{ergs~s^ {-1}}$ luminosity. BH mergers play a crucial roleat $z\gtrsim9$, causing an early boost in BH mass at a time whenaccretion-driven BH growth is negligible. When more stringent seedingconditions are applied (for e.g., $\tilde{M}_{\mathrm{sf,mp}}=1000$), therelative 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 BHaccretion rates (by factors $\gtrsim10$) compared to the accretion model usedin IllustrisTNG. This can be achieved either by allowing for super-Eddingtonaccretion, or by reducing the radiative efficiency. Our results show thatprogenitors of $z\sim6$ quasars have distinct BH merger histories for differentseeding models, which will be distinguishable with LISA observations.

Probing the $z\gtrsim6$ quasars in a universe with IllustrisTNG physics: Impact of gas-based black hole seeding models