Efficient Modelling of Lyman-α opacity fluctuations during late reionization epoch

TL;DR

Efficient semi-numerical modelling of Ly-$\alpha$ opacity fluctuations during late reionization is developed by calibrating a modified FGPA against Nyx hydrodynamics and incorporating density, temperature, and UVB fluctuations. The model is validated against high-redshift Ly-$\alpha$ data (z ~ 5–6) and used in an MCMC framework to constrain the mean photoionization rate $\langle\Gamma_{12}^{\mathrm{HI}}\rangle$ and the effective mean free path $\lambda_0$. The analysis indicates a slightly higher $\langle\Gamma_{12}^{\mathrm{HI}}\rangle$ and a shorter $\lambda_0$ than some prior works, driven by temperature fluctuations and the timing of reionization. This framework offers a computationally efficient path to extract physical information about the EoR from current and forthcoming datasets and complements full hydrodynamic simulations for parameter-space exploration.

Abstract

The Lyman-$α$ forest opacity fluctuations observed from high-redshift quasar spectra have been proven to be extremely successful in order to probe the late phase of the reionization epoch. For ideal modeling of these opacity fluctuations, one of the main challenges is to satisfy the extremely high dynamic range requirements of the simulation box, resolving the Lyman-$α$ forest while probing the large cosmological scales. In this study, we adopt an efficient approach to model Lyman-$α$ opacity fluctuations in a coarse simulation volume, utilizing the semi-numerical reionization model SCRIPT (including inhomogeneous recombination and radiative feedback) integrated with a realistic photoionization background fluctuation generating model. Our model crucially incorporates ionization and temperature fluctuations, which are consistent with the reionization model. After calibrating our method with respect to high-resolution full hydrodynamic simulation, Nyx, we compared the models with available observational data at the redshift range, $z=5.0-6.1$. With a fiducial reionization model (reionization end at $z=5.8$), we demonstrated that the observed scatter in the effective optical depth can be matched reasonably well by tuning the free parameters of our model, i.e., the effective ionizing photon mean free path and mean photoionization rate. We further pursued an MCMC-based parameter space exploration, utilizing the available data to put constraints on the above free parameters. Our estimation prefers a slightly higher photoionization rate and slightly lower mean free path than the previous studies, which is also a consequence of temperature fluctuations. This study holds significant promise for efficiently extracting important physical information about the Epoch of Reionization, utilizing the wealth of available and upcoming observational data.

Figures (15)

• Figure 1: The figure shows the 2D density plot of optical depth ($\tau_{\mathrm{hyd},i}$) vs density ($\Delta_i$) averaged at the pixel scale ($4~h^{-1}\mathrm{cMpc}$) from NyX hydro simulation suite at redshift $z=5.0$. The slope of the correlation matches with $\alpha=0.56$, which is used to calibrate our semi-analytic model.
• Figure 2: Global variation of optical depth ($\Delta \log\tau$) at the resolution scale ($4 h^{-1}\mathrm{cMpc}$) for variations in mean photoionization rates ($\Delta\log\langle \Gamma_{\mathrm{HI}}\rangle$, in left panel) and for variations in temperatures ($\Delta \log \langle T\rangle$, in right panel).
• Figure 3: The comparison of optical depths from hydro simulation ($\tau_{\mathrm{hyd}}$) and calibrated empirical model ($\tau_{\mathrm{model}}$) for three different redshifts ($z=5.0,5.5$ & $6.0$) used for calibration. The different colors indicate the set of different values of mean photoionization rates.
• Figure 4: Left Panel: The distribution of densities ($\log \Delta$) from the hydro simulation (blue) and the semi-numerical setup (dashed orange). Middle Panel: The distribution of optical depths averaged at $4h^{-1}\mathrm{cMpc}$ scale ($\tau_i$) for hydro simulation (blue), calibrated empirical relation (green), and calibrated semi-numerical setup (dashed orange). Right Panel: The distributions of effective optical depth skewers ($\tau_{\mathrm{eff}}$) for the previous three cases.
• Figure 5: The figure shows the neutral fraction ($Q_{\mathrm{HI}}^V$), mean IGM temperature ($T_0$), and $T-\Delta$ power law index ($\gamma$) evolution with redshift for our fiducial reionization model (blue solid lines) along with other two variants using different reionization temperature increment, $T_{\mathrm{re}}$ (high: green dashed; low: red dashed). We also show the recent observational constraints on the neutral fractions 2018ApJ...864..142D2022MNRAS.512.5390G2024MNRAS.533L..49Z2024AA...688L..26S and IGM temperatures 2020MNRAS.494.5091G.