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

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 $z\simeq 5$. 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 $5\le z\le 12$. 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 $S/N=15$ 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 $2$-$3\mathrm{eV}$ over the redshift interval $5\le z\le 12$. For an initial temperature of $T\sim 10^4\mathrm{K}$ following reionisation, this corresponds to the difference between early ($z_{\mathrm{re}}=12$) and late ($z_{\mathrm{re}}=7$) reionisation in our models.

14 pages, 8 figures, 2 Tables, Accepted for publication in MNRAS

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