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

We measure the mean free path (), photoionization rate (), and neutral fraction () 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 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 () 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 and decreases and increases by a factor ∼6 and ∼104, respectively from z ∼5 to z ∼6. By comparing our, and 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 distribution also reproduces the dark gap length distribution and transmission spike height distribution suggesting robustness and accuracy of our measured parameters.