# Measuring the photo-ionization rate, neutral fraction and mean free path of HI ionizing photons at $4.9 \leq z \leq 6.0$ from a large sample of XShooter and ESI spectra

**Authors:** Prakash Gaikwad, Martin G. Haehnelt, Frederick B. Davies, Sarah E. I. Bosman, Margherita Molaro, Girish Kulkarni, Valentina D'Odorico, George D. Becker, Rebecca L. Davies, Fahad Nasir, James S. Bolton, Laura C. Keating, Vid Iršič, Ewald Puchwein, Yongda Zhu, Shikhar Asthana, Jinyi Yang, Samuel Lai, Anna-Christina Eilers  
**arXiv:** [2304.02038](https://arxiv.org/abs/2304.02038)  
**Date:** 2023-04-04  
**Summary page:** https://www.summarizepaper.com/en/paper/2304.02038v1/

## Key points

- Gaikwad et al. present a comprehensive study of the Lyα forest at redshifts $4.85<z<6.05$
- They use a large sample of moderate resolution XShooter and ESI QSO absorption spectra to measure:
- mean free path ($\lambda_{\rm mfp,HI}$)
- photo-ionization rate ($\langle \Gamma_{\rm HI} \rangle$)
- neutral fraction ($\langle f_{\rm HI} \rangle$) of hydrogen in 12 redshift bins
- They introduce a new code called EXtended reionization based on the Code for Ionization and Temperature Evolution (EX-CITE) to model fluctuations in ionizing radiation field
- The authors compare their simulations with unprecedented quality QSO absorption spectra taken with XShooter and ESI instruments to measure the three parameters by forward-modeling the Ly$\alpha$ forest and comparing the effective optical depth ($\tau_{\rm eff, HI}$) distribution in simulations and observations
- They use three statistics of the Lyα forest to further check consistency of their best-fit models with observations:
- cumulative distribution function of effective optical depth (τeff,HI CDF)
- cumulative distribution function of dark gap lengths (dark gap statistics)
- pseudo-Column Density Distribution Function (pCDDF)
- Their best-fit parameters show significant evolution with redshift such that $\lambda_{\rm mfp,HI}$ and $\langle f_{\rm HI} \rangle$ decrease and increase by a factor of approximately 6 and $10^4$, respectively, from $z \sim 5$ to $z \sim 6$
- By comparing their parameter evolution with state-of-the-art Aton radiative transfer simulations and Thesan/CoDa-III simulations, they find that their best-fit parameter evolution is consistent with a model in which reionization completes by $z \sim 5.2$
- Gaikwad et al.'s work provides valuable insights into the properties of hydrogen at high redshifts while demonstrating the effectiveness of their new code EX-CITE for modeling fluctuations in ionizing radiation field

## Summary

In their recent work, Gaikwad et al. present a comprehensive study of the Lyα forest at redshifts $4.85<z<6.05$, using a large sample of moderate resolution XShooter and ESI QSO absorption spectra to measure the mean free path ($\lambda_{\rm mfp,HI}$), photo-ionization rate ($\langle \Gamma_{\rm HI} \rangle$) and neutral fraction ($\langle f_{\rm HI} \rangle$) of hydrogen in 12 redshift bins. To model the fluctuations in ionizing radiation field, they introduce a new code called EXtended reionization based on the Code for Ionization and Temperature Evolution (EX-CITE), which uses efficient Octree summation for computing intergalactic medium attenuation and can generate a large number of high-resolution $\Gamma_{\rm HI}$ fluctuation models. The authors compare their simulations with unprecedented quality QSO absorption spectra taken with XShooter and ESI instruments to measure the three parameters by forward-modeling the Ly$\alpha$ forest and comparing the effective optical depth ($\tau_{\rm eff, HI}$) distribution in simulations and observations. They use three statistics of the Lyα forest - cumulative distribution function of effective optical depth (τeff,HI CDF), cumulative distribution function of dark gap lengths (dark gap statistics), and pseudo-Column Density Distribution Function (pCDDF) - to further check the consistency of their best-fit models with observations. The accuracy of their measurements is usually limited by noise properties of spectra; however, they calculate effective optical depth for each sightline as τeff,HI = −ln(F/Fcont), where F is normalized flux. The uncertainties are calculated by considering uncertainties in mean flux that also account for uncertainty in continuum placement. Their best-fit parameters show significant evolution with redshift such that $\lambda_{\rm mfp,HI}$ and $\langle f_{\rm HI} \rangle$ decrease and increase by a factor of approximately 6 and $10^4$, respectively, from $z \sim 5$ to $z \sim 6$. By comparing their $\lambda_{\rm mfp,HI}$, $\langle \Gamma_{\rm HI} \rangle$, and $\langle f_{\rm HI} \rangle$ evolution with that in state-of-the-art Aton radiative transfer simulations and the Thesan and CoDa-III simulations, they find that their best-fit parameter evolution is consistent with a model in which reionization completes by $z \sim 5.2$. Overall, Gaikwad et al. 's work provides valuable insights into the properties of hydrogen at high redshifts while demonstrating the effectiveness of their new code EX-CITE for modeling fluctuations in ionizing radiation field. Their results suggest that reionization may have completed by $z=5.2$.