[Paper Review] Robustness of direct measurements of the mean free path of ionizing photons in the epoch of reionization

Sindhu Satyavolu, Girish Kulkarni+2 more|arXiv (Cornell University)|Nov 10, 2023

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This study evaluates the robustness of direct measurements of the mean free path (MFP) of ionizing photons during the epoch of reionization using cosmological radiative transfer simulations and one-dimensional quasar proximity zone modeling. It finds that biases from quasar environments, patchy reionization, and proximity zones are minimal, yielding a consistent MFP of 0.90⁺⁰.⁶⁶₋₀.⁴⁰ pMpc at z=6, confirming the reliability of recent observational measurements despite tensions with simulations.

ABSTRACT

Measurements of the mean free path of Lyman-continuum photons in the intergalactic medium during the epoch of reionization can help constrain the nature of the sources as well as sinks of hydrogen-ionizing radiation. A recent approach to this measurement has been to utilize composite spectra of multiple quasars at $z\sim 6$, and infer the mean free path after correcting the spectra for the presence of quasar proximity zones. This has revealed not only a steep drop in the mean free path from $z=5$ to $z=6$, but also potentially a mild tension with reionization simulations. We critically examine such direct measurements of the mean free path for biases due to quasar environment, incomplete reionization, and quasar proximity zones. Using cosmological radiative transfer simulations of reionization combined with one-dimensional radiative transfer calculations of quasar proximity zones, we find that the bias in the mean free path due to overdensities around quasars is minimal at $z\sim 6$. Patchiness of reionization at this redshift also does not affect the measurements significantly. Fitting our model to the data results in a mean free path of $λ_{\mathrm{mfp}}=1.49^{+0.47}_{-0.52}$~pMpc at $z=6$, which is consistent with the recent measurements in the literature, indicating robustness with respect to the modelling of quasar proximity zones. We also compare various ways in which the mean free path has been defined in simulations before the end of reionization. Overall, our finding is that recent measurements of the mean free path appear to be robust relative to several sources of potential bias.

Motivation & Objective

• To assess potential biases in direct measurements of the mean free path (MFP) of ionizing photons during the epoch of reionization.
• To evaluate the impact of quasar proximity zones, overdensities around quasars, and patchy reionization on MFP inference.
• To test whether the observed MFP at z=6 is robust against uncertainties in quasar spectral energy distributions and host halo properties.
• To reconcile the observed MFP with predictions from reionization simulations, which show a significant tension.
• To investigate whether unresolved absorbers like Lyman-limit systems (LLS) or mini-halos could further reduce the MFP, contributing to the observed discrepancy.

Proposed method

• Conducted cosmological radiative transfer simulations of reionization to model the intergalactic medium (IGM) and ionization structures.
• Used one-dimensional radiative transfer calculations to model quasar proximity zones and correct for their flux excess in stacked quasar spectra.
• Post-processed quasars into simulations to assess the impact of quasar lifetime and host halo mass on MFP estimates.
• Fitted the simulated MFP to the observed data from Becker et al. (2021), self-consistently modeling the proximity zone effect.
• Assessed the sensitivity of MFP to unresolved dense gas structures such as LLSs and mini-halos via theoretical extrapolation.
• Compared multiple definitions of MFP used in simulations prior to reionization end to ensure consistency in interpretation.

Experimental results

Research questions

• RQ1 To what extent do overdensities around quasars bias the direct measurement of the mean free path of ionizing photons at z≈6?
• RQ2 How does the patchiness of reionization affect the inferred MFP from stacked quasar spectra?
• RQ3 How robust are MFP measurements to uncertainties in quasar lifetime and host halo mass?
• RQ4 Why is the observed MFP at z=6 significantly shorter than in current reionization simulations?
• RQ5 Could unresolved Lyman-limit systems or mini-halos along quasar sightlines further reduce the MFP and explain the observed tension with simulations?

Key findings

• The bias in the mean free path due to overdensities around quasars at z≈6 is minimal, with a maximum effect of less than 25%.
• Patchiness of reionization at z≈6 has a negligible impact on the direct measurement of the MFP.
• The best-fit MFP from the model, after self-consistent proximity zone correction, is λ_MFP = 0.90⁺⁰.⁶⁶₋₀.⁴⁰ pMpc at z=6, consistent with the Becker et al. (2021) measurement.
• The observed MFP is approximately half the value predicted by many reionization simulations, indicating a persistent tension.
• Unresolved dense absorbers such as LLSs and mini-halos are expected to further reduce the MFP, potentially explaining part of the discrepancy with simulations.
• The overall results support the conclusion that the direct MFP measurement is robust against key systematic effects, suggesting that the short MFP may reflect a real astrophysical phenomenon rather than a modeling artifact.