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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 $\lambda _{\rm mfp,H\, \small {I}}$more »and $\langle f_{\rm H\, \small {I}} \rangle$ decreases and increases by a factor ∼6 and ∼104, 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.

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Abstract Becker et al. measured the mean free path of Lyman-limit photons in the intergalactic medium (IGM) at z = 6. The short value suggests that absorptions may have played a prominent role in reionization. Here we study physical properties of ionizing photon sinks in the wake of ionization fronts (I-fronts) using radiative hydrodynamic simulations. We quantify the contributions of gaseous structures to the Lyman-limit opacity by tracking the column-density distributions in our simulations. Within Δ t = 10 Myr of I-front passage, we find that self-shielding systems ( N H I > 10 17.2 cm −2 ) are comprised of two distinct populations: (1) overdensity Δ ∼ 50 structures in photoionization equilibrium with the ionizing background, and (2) Δ ≳ 100 density peaks with fully neutral cores. The self-shielding systems contribute more than half of the opacity at these times, but the IGM evolves considerably in Δ t ∼ 100 Myr as structures are flattened by pressure smoothing and photoevaporation. By Δ t = 300 Myr, they contribute ≲10% to the opacity in an average 1 Mpc 3 patch of the universe. The percentage can be a factor of a few larger in overdense patches, where more self-shielding systemsmore »survive. We quantify the characteristic masses and sizes of self-shielding structures. Shortly after I-front passage, we find M = 10 4 –10 8 M ⊙ and effective diameters d eff = 1–20 ckpc h −1 . These scales increase as the gas relaxes. The picture herein presented may be different in dark matter models with suppressed small-scale power.« less

ABSTRACT A number of independent observations suggest that the intergalactic medium was significantly neutral at z = 7 and that reionization was, perhaps, still in progress at z = 5.7. The narrowband survey, SILVERRUSH, has mapped over 2000 Lyman-α emitters (LAEs) at these redshifts ( G58). Previous analyses have assumed that reionization was over by z = 5.7, but this data may actually sample the final stages of reionization when the last neutral islands were relegated to the cosmic voids. Motivated by these developments, we re-examine LAE void and peak statistics and their ability to constrain reionization. We construct models of the LAE distribution in (1 Gpc h−1)3 volumes, spanning a range of neutral fractions at z = 5.7 and 6.6. Models with a higher neutral fraction show an enhanced probability of finding holes in the LAE distribution. When comparing models at fixed mean surface density, however, LAEs obscured by neutral gas in the voids must be compensated by visible LAEs elsewhere. Hence, in these models, the likelihood of finding an overdense peak is also enhanced in the latter half of reionization. Compared to the widely used angular two-point correlation function (2PCF), we find that the void probability function (VPF) provides a more sensitive testmore »of models during the latter half of reionization. By comparison, at neutral fractions $\sim 50{{\ \rm per\ cent}}$, the VPF and a simple peak thresholding statistic are both similar to the 2PCF in constraining power. Lastly, we find that the cosmic variance and large-scale asymmetries observed in the SILVERRUSH fields are consistent with large-scale structure in a ΛCDM universe.« less