An emulator for the ionizing photon mean free path in ultra-high resolution simulations: the implications of mean free path measurements for the reionization history

Abstract

Measurements of the mean free path of ionizing photons from high-redshift quasar spectra at $z \sim 5$-$6$ constrain the reionization history, but interpreting them requires modeling the kiloparsec-scale clumping that large-volume reionization simulations cannot resolve. We present a deep learning emulator for the mean free path (MFP) trained on high-resolution cosmological radiative transfer simulations of ionization fronts sweeping through small 2 comoving~Mpc/h volumes. Using a residual multi-layer perceptron neural network, we predict the MFP at a given redshift as a function of the reionization redshift, photoionization rate, wavelength, and box-scale density, achieving a median relative error of 1.6\% across nearly four orders of magnitude in MFP. Integrating its predictions over box-scale overdensity and an extended reionization history allows the emulator to predict the global MFP. We apply the emulator to extended reionization histories constrained by observed photoionization rates, finding that models prefer late reionization with substantial neutral fractions persisting at $z \lesssim 6$. Fitting a parametric ionization history yields a midpoint of reionization of $z_{\rm re} = 6.8\pm 1.2$ for reionization durations consistent with Planck and kinetic Sunyaev-Zeldovich constraints, and the universe being $10\%$ neutral still at $z_{\rm re} < 5.8 ~(6.3)$ at 1~(2)$\sigma$. Global ionizing emissivity inferences using measurements of the photoionization rate and MFP plus our emulator, which avoids common power-law assumptions, suggest a factor of $2-3$ decline between $z = 6$ and $4.8$, in agreement with previous studies. Our method provides an efficient (and more converged) alternative to large-volume radiative-hydrodynamic simulations of reionization for interpreting MFP measurements, and can also serve as a subgrid prescription for the ionizing opacity within such simulations.