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Capturing Small-Scale Reionization Physics: A Sub-Grid Model for Photon Sinks with SCRIPT

Tirthankar Roy Choudhury, Anirban Chakraborty

TL;DR

This paper tackles the challenge of capturing small-scale reionization physics by embedding a self-consistent sub-grid model for photon sinks within SCRIPT, linking emissivity, clumping, mean free path, and photoionization rate to the underlying density field. The authors validate the approach against multiple observational probes (UVLFs, Planck $ au_e$, Lyα forest temperatures, mean free paths, and opacity fluctuations) and demonstrate that key interdependencies, such as the correlation between clumping and mean free path, shape the timing and morphology of reionization. The fiducial model reproduces a broad suite of observables, including Lyα opacity fluctuations, and reveals parameter degeneracies that complicate unique constraints but reflect the interconnected physics of photon sinks and feedback. This framework provides a computationally efficient bridge between fast semi-numerical methods and radiative-transfer simulations, with practical relevance for interpreting 21 cm and Lyα observations and informing future parameter-inference efforts.

Abstract

The epoch of reionization represents a major phase transition in cosmic history, during which the first luminous sources ionized the intergalactic medium (IGM). However, the small-scale physics governing ionizing photon sinks - particularly the interplay between recombinations, photon propagation, and self-shielded regions - remains poorly understood. Accurately modeling these processes requires a framework that self-consistently links ionizing emissivity, the clumping factor, mean free path, and photoionization rate. In this work, we extend the photon-conserving semi-numerical framework, SCRIPT, by introducing a self-consistent sub-grid model that dynamically connects these quantities to the underlying density field, enabling a more realistic treatment of inhomogeneous recombinations and photon sinks. We validate our model against a comprehensive set of observational constraints, including the UV luminosity function from HST and JWST, CMB optical depth from Planck, and Lyman-$α$ forest measurements of the IGM temperature, photoionization rate, and mean free path. Our fiducial model also successfully reproduces Lyman-$α$ opacity fluctuations, reinforcing its ability to capture large-scale inhomogeneities in the reionization process. Notably, we demonstrate that traditionally independent parameters, such as the clumping factor and mean free path, are strongly correlated, with implications for the timing, morphology, and thermal evolution of reionization. Looking ahead, we will extend this framework to include machine learning-based parameter inference. With upcoming 21cm experiments poised to provide unprecedented insights, SCRIPT offers a powerful computational tool for interpreting high-redshift observations and refining our understanding of the last major phase transition in the universe.

Capturing Small-Scale Reionization Physics: A Sub-Grid Model for Photon Sinks with SCRIPT

TL;DR

This paper tackles the challenge of capturing small-scale reionization physics by embedding a self-consistent sub-grid model for photon sinks within SCRIPT, linking emissivity, clumping, mean free path, and photoionization rate to the underlying density field. The authors validate the approach against multiple observational probes (UVLFs, Planck , Lyα forest temperatures, mean free paths, and opacity fluctuations) and demonstrate that key interdependencies, such as the correlation between clumping and mean free path, shape the timing and morphology of reionization. The fiducial model reproduces a broad suite of observables, including Lyα opacity fluctuations, and reveals parameter degeneracies that complicate unique constraints but reflect the interconnected physics of photon sinks and feedback. This framework provides a computationally efficient bridge between fast semi-numerical methods and radiative-transfer simulations, with practical relevance for interpreting 21 cm and Lyα observations and informing future parameter-inference efforts.

Abstract

The epoch of reionization represents a major phase transition in cosmic history, during which the first luminous sources ionized the intergalactic medium (IGM). However, the small-scale physics governing ionizing photon sinks - particularly the interplay between recombinations, photon propagation, and self-shielded regions - remains poorly understood. Accurately modeling these processes requires a framework that self-consistently links ionizing emissivity, the clumping factor, mean free path, and photoionization rate. In this work, we extend the photon-conserving semi-numerical framework, SCRIPT, by introducing a self-consistent sub-grid model that dynamically connects these quantities to the underlying density field, enabling a more realistic treatment of inhomogeneous recombinations and photon sinks. We validate our model against a comprehensive set of observational constraints, including the UV luminosity function from HST and JWST, CMB optical depth from Planck, and Lyman- forest measurements of the IGM temperature, photoionization rate, and mean free path. Our fiducial model also successfully reproduces Lyman- opacity fluctuations, reinforcing its ability to capture large-scale inhomogeneities in the reionization process. Notably, we demonstrate that traditionally independent parameters, such as the clumping factor and mean free path, are strongly correlated, with implications for the timing, morphology, and thermal evolution of reionization. Looking ahead, we will extend this framework to include machine learning-based parameter inference. With upcoming 21cm experiments poised to provide unprecedented insights, SCRIPT offers a powerful computational tool for interpreting high-redshift observations and refining our understanding of the last major phase transition in the universe.

Paper Structure

This paper contains 21 sections, 68 equations, 16 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical Model
  3. Ionization sources
  4. Ionization field
  5. Temperature of the IGM
  6. Clumping factor
  7. Photoionization rate
  8. Mean free path of ionizing photons
  9. Conditional density distribution
  10. Observables and physical quantities
  11. Free parameters
  12. Model Comparison with the Data
  13. Data sets and the fiducial model
  14. Sensitivity to different parameters
  15. The unconditional density distribution
  16. ...and 6 more sections

Figures (16)

  • Figure 1: Comparison of the UV luminosity function at various redshifts between the predictions of the fiducial model and observational data represented by points with error-bars. The UVLF data are compiled from different studies that use surveys using HST 2021AJ....162...47B and JWST 2023MNRAS.518.6011D2023ApJS..265....5H2023MNRAS.523.1009B2024MNRAS.527.5004M2024MNRAS.533.3222D. We also show data from lensed HFF fields 2022ApJ...940...55B, yellow points, although they are not used for selecting the fiducial model parameters. The fiducial model provides a good description of the UVLF data across a wide range of redshifts.
  • Figure 2: The cumulative distribution of ionizing emissivity produced by galaxies as a function of UV magnitude, shown for different redshifts in the fiducial model. The vertical dashed line indicates $M_\mathrm{UV} = -17$. Most ionizing photons are produced by faint galaxies at all redshifts.
  • Figure 3: Evolution of globally averaged physical quantities in the fiducial model (blue solid curves), compared with relevant observational constraints. Top:Left: Mass-averaged ionized fraction $Q_\mathrm{HII}$. Reionization completes at $z \approx 5.6$ in the fiducial model. Observational constraints (not used in model selection) are shown from Ly$\alpha$ opacity measurements 2023MNRAS.525.4093G, damping wing analyses of high-$z$ quasars 2018ApJ...864..142D2022MNRAS.512.5390G2024ApJ...969..162D, and JWST observations of UV-bright galaxies 2024ApJ...971..124U. Right: CMB optical depth $\tau_e$ integrated up to redshift $z$. The red shaded band shows the $1\sigma$ Planck uncertainty 2020AA...641A...6P, with the mean marked by the red line. Second row:Left: Temperature at mean density $T_0$, compared with Ly$\alpha$ forest measurements 2020MNRAS.494.5091G. Right: Slope $\gamma$ of the temperature-density relation, also compared with Ly$\alpha$ constraints 2020MNRAS.494.5091G. Third row:Left: Ionizing emissivity $\dot{n}_\mathrm{ion}$. Right: Mean free path $\lambda_\mathrm{mfp}$ compared with Ly$\alpha$ absorption spectra measurements 2023ApJ...955..115Z. Dashed line: mean free path in ionized regions ($\lambda_\mathrm{ss}$). Inset zooms in on the redshift range with data. The divergence between $\lambda_\mathrm{mfp}$ and $\lambda_\mathrm{ss}$ at $z \gtrsim 5.6$ reflects the presence of remaining neutral regions. Fourth row:Left: Photoionization rate $\Gamma_\mathrm{HI}$ in ionized regions. Red: Ly$\alpha$ forest data 2011MNRAS.412.1926W. Dashed: global $\Gamma_\mathrm{HI}$ (including neutral regions). Dotted: estimated from emissivity and $\lambda_\mathrm{ss}$. Inset: zoom on data range, including other estimates 2011MNRAS.412.2543C2018MNRAS.473..560D2023MNRAS.525.4093G (not used in fit). Right: Global clumping factor $\mathcal{C}_\mathrm{HII}$, averaged over all grid cells. If Case B recombination is used instead of the default Case A, the clumping factor increases by a factor of $\approx 1.6$, while all other quantities remain unchanged; see appendix \ref{['app:case_B']} for details.
  • Figure 4: Two-dimensional slices through the simulation volume of the fiducial model at $z = 6$, showing the emissivity, ionized fraction, photoionization rate, mean free path, clumping factor, and temperature. Fluctuations in these quantities are clearly visible, and their inter-correlations are clearly seen.
  • Figure 5: The dependence of physical quantities mean free path $\lambda_{\mathrm{mfp}, i}$ (top row), photoionization rate $\Gamma_{\mathrm{HI}, i}$ (middle row) and clumping factor $C_{H, i}$ (bottom row) on the cell density $\Delta_i$, shown for three redshifts as mentioned in the title of the columns. Each scatter point represents a cell, color-coded by the ionized fraction. For the mean free path, we also show the self-shielded mean free path $\lambda_{\mathrm{ss}, i}$ by gray points for comparison. It is obvious that $\lambda_{\mathrm{mfp}, i} = \lambda_{\mathrm{ss}, i}$ for highly ionized cells (yellowish points). Although post-reionization $z \sim 5$, the quantities have a clear correlation with the density with susbtantially lower scatter, the pre-reionization redshifts show a more complex relationship due to the presence of neutral islands.
  • ...and 11 more figures