Photo-heating and the fate of hard photons during the reionisation of He II by quasars

We use a combination of analytic and numerical arguments to consider the impact of quasar photo-heating during He II reionisation on the thermal evolution of the intergalactic medium (IGM). We demonstrate that rapid (∆z < 0.1–0.2), strong (∆T > 10 K) photo-heating is difficult to achieve across the entire IGM unless quasar spectra are significantly harder than implied by current observational constraints. Although filtering of intrinsic quasar radiation through dense regions in the IGM does increase the mean excess energy per He II photo-ionisation, it also weakens the radiation intensity and lowers the photo-ionisation rate, preventing rapid heating over time intervals shorter than the local photo-ionisation timescale. Moreover, the hard photons responsible for the strongest heating are more likely to deposit their energy inside dense clumps, which cool rapidly and are furthermore invisible to most observational probes of the IGM temperature. The abundance of such clumps is, however, uncertain and model-dependent, leading to a fairly large uncertainty in the photoheating rates. Nevertheless, although some of the IGM may be exposed to a hardened and weakened ionising background for long periods, most of the IGM must instead be reionised by the more abundant, softer photons and with accordingly modest heating rates (∆T < ∼ 10 K), although localised patches of much higher temperature are still possible. The repeated ionisation of fossil quasar He III regions does not increase the net heating because the recombination times in these regions typically exceed the IGM cooling times and the average time lag between successive rounds of quasar activity. Detailed line-of-sight radiative transfer simulations confirm these expectations and predict a rich thermal structure in the IGM during He II reionisation. The resulting complex relationship between temperature and density may help resolve discrepancies between optically thin simulations of the Lyα forest and recent observations.