The Lumina Project: Intergalactic Clumping and Recombination Sinks

Recombinations during the Epoch of Reionization are intrinsically inhomogeneous, with different regions of the intergalactic medium contributing unevenly depending on their density, temperature, ionization state, and spatial patchiness. We combine the high- and medium-resolution 95.5 cMpc Thesan-1 and Thesan-2 runs with the significantly larger 500 cMpc Lumina simulation to measure clumping factors and recombination rates consistently across different resolutions and box sizes. We consider the standard \(\Delta<100\) ionized hydrogen clumping factor, \(C_{\rm HII} \equiv \langle n_{\rm HII}^2\rangle_{<100}/\langle n_{\rm HII}\rangle^2\), and a recombination-weighted clumping factor, \(C_{\rm rec}\). Despite differences in resolution, volume, and reionization history, the simulations show an approximately universal clumping evolution at the 10–20% level when parametrized by the global ionized fraction \(x_{\rm HII}\) rather than by redshift. Across all simulations, \(C_{\rm rec}\) remains systematically below \(C_{\rm HII}\), with the discrepancy increasing toward lower redshift as photoheating suppresses recombinations. In Lumina, the density-only prescription overpredicts the instantaneous recombination rate by factors of 1.34 at \(z\approx8\) and 2.02 at \(z\approx5\), and the cumulative recombination count by a factor of 1.53 by \(z\approx5\). Mapping the recombination budget in the joint overdensity–temperature plane reveals that the dominant recombination ridges closely follow simple analytic thermal equilibrium bands derived from the Hui–Gnedin equation of state. Finally, we introduce a phase-space recombination integral and define a phase-space clumping factor, \(C_{\rm ps}(\Delta,T)\), which isolates the intrinsic recombination enhancement associated with ionization structure and thermal state at fixed overdensity and temperature while closely reproducing the globally measured recombination rate obtained from direct cell-by-cell calculations. This formulation naturally decomposes the total recombination budget as a function of overdensity, temperature, and ionization state.