Inferring the IGM thermal history during reionisation with the Lyman-$\alpha$ forest power spectrum at redshift $z \simeq 5$

TL;DR

This study demonstrates that the thermal history of the intergalactic medium during reionisation can be constrained using the Lyα forest power spectrum at redshift around 5, with an expected uncertainty of about 20-30%.

Contribution

It introduces a method to infer the IGM's thermal history during reionisation by analyzing the Lyα forest power spectrum and using a parameterization linked to the energy deposited into gas.

Findings

Potential to distinguish reionisation scenarios differing by 2-3 eV per proton.

Achieves ~20% statistical uncertainty in measuring the thermal energy parameter.

Existing data can constrain the thermal history within ~30% accuracy.

Abstract

We use cosmological hydrodynamical simulations to assess the feasibility of constraining the thermal history of the intergalactic medium during reionisation with the Ly$\alpha$ forest at $z\simeq5$. The integrated thermal history has a measureable impact on the transmitted flux power spectrum that can be isolated from Doppler broadening at this redshift. We parameterise this using the cumulative energy per proton, $u_0$, deposited into a gas parcel at the mean background density, a quantity that is tightly linked with the gas density power spectrum in the simulations. We construct mock observations of the line of sight Ly$\alpha$ forest power spectrum and use a Markov Chain Monte Carlo approach to recover $u_{0}$ at redshifts $5 \leq z \leq 12$. A statistical uncertainty of $\sim 20$ per cent is expected (at 68 per cent confidence) at $z\simeq 5$ using high resolution spectra with a total redshift path length of $\Delta z=4$ and a typical signal-to-noise ratio of $\rm S/N=15$ per pixel. Estimates for the expected systematic uncertainties are comparable, such that existing data should enable a measurement of $u_0$ to within $\sim 30$ per cent. This translates to distinguishing between reionisation scenarios with similar instantaneous temperatures at $z\simeq 5$, but with an energy deposited per proton that differs by $2$-$3\, \rm eV$ over the redshift interval $5\leq z \leq 12$. For an initial temperature of $T\sim 10^{4}\rm\,K$ following reionisation, this corresponds to the difference between early ($z_{\rm re}=12$) and late ($z_{\rm re}=7$) reionisation in our models.