# A consistent and robust measurement of the thermal state of the IGM at $2 \leq z \leq 4$ from a large sample of Ly$α$ forest spectra: Evidence for late and rapid HeII reionization

**Authors:** Prakash Gaikwad, Raghunathan Srianand, Martin G. Haehnelt, Tirthankar Roy Choudhury  
**arXiv:** [2009.00016](https://arxiv.org/abs/2009.00016)  
**Date:** 2020-08-31  
**Summary page:** https://www.summarizepaper.com/en/paper/2009.00016v1/

## Key points

- The study analyzes the thermal state of the intergalactic medium (IGM) in the redshift range $2 \leq z \leq 4$ using a sample of 103 high resolution, high signal-to-noise ratio Ly$\alpha$ forest spectra.
- Four different flux distribution statistics are used to characterize the IGM's thermal state in ten redshift bins and calibrate their measurements with mock spectra from hydrodynamical simulations post-processed with their thermal IGM evolution code.
- The results show that all four flux statistics agree well within their respective errors and clearly demonstrate the peak in temperature and minimum in slope of the temperature density relation expected from HeII reionization.
- Combining their measurements from different flux statistics gives $T_0=(14750 \pm 1322)$K for the peak temperature at mean density and a corresponding minimum slope $\gamma = 1.225 \pm 0.120$.
- The authors also calculate the predicted thermal state of the IGM using five widely used UV-background models and find that two models reproduce their rather rapid thermal evolution if they assume non-equilibrium evolution with photo-heating rates reduced by a moderate factor ($\sim0.7-0.8$).
- Three other models predict HeII reionization to be more extended with an earlier as well as higher temperature peak than their measurements suggest.
- This study provides a consistent and robust measurement of the thermal state of the IGM at $2 \leq z \leq 4$, supporting late and rapid HeII reionization.
- The authors' approach and results have important implications for understanding physical processes governing IGM's thermal evolution.

## Summary

This study presents a comprehensive analysis of the thermal state of the intergalactic medium (IGM) in the redshift range $2 \leq z \leq 4$ using a sample of 103 high resolution, high signal-to-noise ratio Ly$\alpha$ forest spectra. The authors use four different flux distribution statistics to characterize the IGM's thermal state in ten redshift bins and calibrate their measurements with mock spectra from hydrodynamical simulations post-processed with their thermal IGM evolution code. They finely sample amplitude and slope of the expected temperature-density relation to infer the thermal parameters from their measurements of the flux power spectrum, Doppler parameter distribution, wavelet, and curvature statistics. The results show that all four flux statistics agree well within their respective errors and clearly demonstrate the peak in temperature and minimum in slope of the temperature density relation expected from HeII reionization. Combining their measurements from different flux statistics gives $T_0=(14750 \pm 1322)$K for the peak temperature at mean density and a corresponding minimum slope $\gamma = 1.225 \pm 0.120$. The peak in temperature evolution occurs at $z\approx3$, consistent with previous measurements that suggested its presence but with reduced scatter. The authors also calculate the predicted thermal state of the IGM using five widely used UV-background models and find that two models reproduce their rather rapid thermal evolution if they assume non-equilibrium evolution with photo-heating rates reduced by a moderate factor ($\sim0.7-0.8$). However, three other models predict HeII reionization to be more extended with an earlier as well as higher temperature peak than their measurements suggest. In addition to presenting these results, this paper also includes detailed comparisons between their observed flux statistics and those from previous studies in literature, demonstrating good agreement overall. The authors validate their approach by comparing it with previous work and show that their method of calculating the flux power spectrum using FFT is consistent with other methods. Overall, this study provides a consistent and robust measurement of the thermal state of the IGM at $2 \leq z \leq 4$, supporting late and rapid HeII reionization. The authors' approach and results have important implications for understanding physical processes governing IGM's thermal evolution.