| Summary: | We use cosmological hydrodynamical simulations to assess the feasibility of constraining the thermal history of the intergalactic medium during reionisation with the Lyα forest at z ≃ 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, u₀, 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 Lyα forest power spectrum and use a Markov Chain Monte Carlo approach to recover u₀ at redshifts 5≲z≲12. A statistical uncertainty of ∼ 20 per cent is expected (at 68 per cent confidence) at z ≃ 5 using high resolution spectra with a total redshift path length of Δz = 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 u₀ to within ∼ 30 per cent. This translates to distinguishing between reionisation scenarios with similar instantaneous temperatures at z ≃ 5, but with an energy deposited per proton that differs by 2–3eV over the redshift interval 5≲z≲12. For an initial temperature of T ∼ 10⁴K following reionisation, this corresponds to the difference between early (zre = 12) and late (zre = 7) reionisation in our models.
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