Keeping the Universe ionised: photoheating and the high-redshift clumping factor of the intergalactic gas

The critical star formation rate density required to keep the intergalactic hydrogen ionised depends crucially on the average rate of recombinations in the intergalactic medium (IGM). This rate is proportional to the clumping factor C = <rho_b^2> / avg(rho_b)^2, where rho_b and avg(rho_b) are the local and cosmic mean baryon density, respectively, and the brackets < > indicate spatial averaging over the recombining gas in the IGM. We perform a suite of cosmological smoothed particle hydrodynamics simulations that include radiative cooling to calculate the volume-weighted clumping factor of the IGM at redshifts z >= 6. We investigate the effect of photoionisation heating by a uniform ultraviolet background and find that photoheating strongly reduces the clumping factor as the increased pressure support smoothes out small-scale density fluctuations. Even our most conservative estimate for the clumping factor, C = 6, is five times smaller than the clumping factor that is usually employed to determine the capacity of star-forming galaxies to keep the z=6 IGM ionised. Our results imply that the observed population of star-forming galaxies at z = 6 may be sufficient to keep the IGM ionised, provided that the IGM was reheated at z >~ 9 and that the fraction of ionising photons that escape star-forming regions to ionise the IGM is larger than 0.25.