Measuring the photoionization rate, neutral fraction, and mean free path of H I ionizing photons at 4.9 ≤ z ≤ 6.0 from a large sample of XShooter and ESI spectra

Abstract

We measure the mean free path ($\lambda _{\rm mfp,H\, \small {I}}$), photoionization rate ($\langle \Gamma _{\rm H\, \small {I}} \rangle$), and neutral fraction ($\langle f_{\rm H\, \small {I}} \rangle$) of hydrogen in 12 redshift bins at 4.85 < z < 6.05 from a large sample of moderate resolution XShooter and ESI QSO absorption spectra. The fluctuations in ionizing radiation field are modelled by post-processing simulations from the Sherwood suite using our new code 'EXtended reionization based on the Code for Ionization and Temperature Evolution' (EX-CITE). EX-CITE uses efficient Octree summation for computing intergalactic medium attenuation and can generate large number of high resolution $\Gamma _{\rm H\, \small {I}}$ fluctuation models. Our simulation with EX-CITE shows remarkable agreement with simulations performed with the radiative transfer code Aton and can recover the simulated parameters within 1σ uncertainty. We measure the three parameters by forward-modelling the Lyα forest and comparing the effective optical depth ($\tau _{\rm eff, H\, \small {I}}$) distribution in simulations and observations. The final uncertainties in our measured parameters account for the uncertainties due to thermal parameters, modelling parameters, observational systematics, and cosmic variance. Our best-fitting parameters show significant evolution with redshift such that $\lambda _{\rm mfp,H\, \small {I}}$ and $\langle f_{\rm H\, \small {I}} \rangle$ decreases and increases by a factor ~6 and ~10<SUP>4</SUP>, respectively from z ~ 5 to z ~ 6. By comparing our $\lambda _{\rm mfp,H\, \small {I}}$, $\langle \Gamma _{\rm H\, \small {I}} \rangle$ and $\langle f_{\rm H\, \small {I}} \rangle$ evolution with that in state-of-the-art Aton radiative transfer simulations and the Thesan and CoDa-III simulations, we find that our best-fitting parameter evolution is consistent with a model in which reionization completes by z ~ 5.2. Our best-fitting model that matches the $\tau _{\rm eff, H\, \small {I}}$ distribution also reproduces the dark gap length distribution and transmission spike height distribution suggesting robustness and accuracy of our measured parameters.