Studying dark gaps in Ly-$α$ forest transmission with large reionization simulation

TL;DR

The study investigates the final stages of cosmic reionization by analyzing dark gaps in the Ly-$\alpha$ forest using gigaparsec-scale semi-numerical simulations. It develops a large-volume pipeline to generate Ly-$\alpha$ transmission lightcones across $z=4.9$–$6.2$, and compares eight model variants against 42 high-redshift E-XQR-30 quasar spectra using dark-gap CDFs, long-gap fractions, and flux correlation matrices. The fiducial model best matches the data, with a slightly later reionization end around $z\sim5.4$ providing an even closer fit; models with fixed short mean free paths are disfavored at lower redshift, and none reproduce the strongest observed large-scale correlations, indicating missing physics or the need for larger, more detailed simulations. Overall, the results support a late end to reionization ($z\lesssim5.7$) and demonstrate the value of dark-gap statistics as a diagnostic tool, while highlighting open questions about the origin of extreme large-scale Ly-$\alpha$ transmission correlations.

Abstract

The physical conditions of the intergalactic medium (IGM) during the final stages of cosmic reionization ($z\sim5.0-6.0$) are not yet fully understood. Recent reports of unexpectedly large-scale ($\ge 150 h^{-1}\mathrm{cMpc}$) correlation in Ly-$α$ transmission flux using extended XQR-30 quasar spectra pose interesting consequences on the reionization end stages. In this work, we investigate the Ly-$α$ forest dark-gap distribution (defined as regions with transmitted flux below 0.05) as another sensitive tracer of the IGM, using an efficient, large-volume ($\sim 1 ~\mathrm{Gpc}$) simulation framework. By constructing a suite of physically motivated model variants (i.e, varying the reionization redshift, IGM temperature, and ionizing-photon mean free path), we generate synthetic sightlines and compare their predicted cumulative distribution of dark gaps with that of observed spectra (at redshift intervals of $Δz=0.2$). We find that most of the models achieve qualitatively consistent agreement with the data. Specifically, the scenario involving a slightly later reionization completion ($z\sim 5.4$) provides the closest match, while a short constant mean free path model disfavors the data at lower redshifts. These findings give further support for the emerging scenario of reionization end extending to $z\le5.7$, although they can not rule out a slightly early reionization with enhanced post-ionization ultraviolet (UV) background fluctuations. A similar conclusion arises from the redshift distribution of long dark gap ($L\ge 30 ~h^{-1}\mathrm{cMpc}$) fraction. However, the model variants are still not able to reproduce the observed strong flux correlations at unusually large scales, which remains open for further investigations.

Figures (7)

• Figure 1: Different observables for the various model scenarios assumed in this study. From left to right, the panels show redshift evolution of global neutral fraction ($Q_{\mathrm{HI}}^V$), mean IGM temperature ($T_0$), index of temperature-density relation ($\gamma$) and the effective photon mean free path ($\lambda_0$). We also show various constraints on these quantities, as suggested by recent studies, i.e, constraints on neutral fraction Davies182022MNRAS.512.5390G2023ApJ...942...59J2024AA...688L..26SZhu2024_damping, IGM temperature estimates 2020MNRAS.494.5091G, mean free path estimates 2021MNRAS.508.1853BGaikwad232023ApJ...955..115ZDavies24.
• Figure 2: Lightcone snapshots for three different cases in (top: fiducial, middle: cons mfp / wo neutral, and bottom: low temp) in three rows. The columns correspond to density ($\Delta$), neutral fractions ($x_{\mathrm{HI}}$), UVB fluctuations ($\Gamma_{\mathrm{HI}}/\langle \Gamma_{\mathrm{HI}}\rangle$), temperature ($T$), and flux ($F$). The colorbars have been shown in logarithmic scales. The rest of the scenarios has been shown in Appendix \ref{['app:appendix1']}.
• Figure 3: The cumulative probability distribution functions (CDFs) of dark gap lengths at different redshift ranges (within an interval of $\Delta z=0.2$), corresponding to the set of different model variants, discussed in section \ref{['sec:model_suite']}. The solid lines denote the derived distribution from the observed data, while the dashed lines are the corresponding predictions using model skewers. The shaded region signifies 68% uncertainties on the model distributions.
• Figure 4: Fraction of skewers with dark gap length, $L\ge 30 ~h^{-1}\mathrm{cMpc}$ ($F_{30}$) as a function of redshift ($z$) for the different model variants, discussed in section \ref{['sec:model_suite']}. The red lines are derived distributions from the observed spectra. The blue dashed lines denote the mean distribution after averaging over skewer realizations from the model suites. The shaded regions show the corresponding 68% and 95% uncertainties. In black dashed, we show similar estimates from an earlier study Zhu_2021, with different skewer resolution and samples.
• Figure 5: Correlation coefficients of the transmission flux between redshift ranges considered in this study ($z=5.0-6.1$). The panels show the different scenarios, as discussed in section \ref{['sec:model_suite']}. The correlation matrix derived from 67 quasar sigtlines (including E-XQR-30 samples) has been reported in Spina25.