Reionisation, chemical enrichment and seed black holes from the first stars: is Population III important?

We investigate the effects of a top-heavy stellar initial mass function on the reionisation history of the intergalactic medium (IGM). We use cosmological simulations that include self-consistently the feedback from ionising radiation, H_2 dissociating radiation and supernova (SN) explosions. We find that it is difficult to reionise the IGM at z_rei>10 with stellar sources even after making extreme assumptions. If star formation in 10^9 M_\odot galaxies is not suppressed by SN explosions, the optical depth to Thomson scattering is tau_e< 0.13. If we allow for the normal energy input from SNe or if pair-instability SNe are dominant, we find taue<0.09. Assuming normal yields for the first stars (popIII), the mean metallicity of the IGM is already Z/Z_\odot=2x10^-3 (10^-3<Z/Z_\odot<1 in overdense regions) when the IGM mean ionisation fraction is less than 10%. For these reasons popIII stars cannot contribute significantly to reionisation unless the mechanical energy input from SNe is greatly reduced and either the metal yield or the mixing efficiency is reduced by a factor of 1000. Both problems have a solution if popIII stars collapse to black holes. This can happen if, having masses M_*< 130 M_\odot, they are characterised by heavy element fall-back or if, having masses M_*>260 M_\odot, they collapse directly onto black holes without exploding as SNe.If metal-poor stars are initially important and collapse to black holes is the typical outcome, then the secondary emission of ionising radiation from accretion on SN induced seed black holes, might be more important than the primary emission. Surprisingly, including feedback effects, we estimate that a warm dark matter scenario (with particle mass of 1.25 keV) reduces tau_e by only approximately 10%.[abridged]