Keeping the Universe ionised: Photo-heating and the clumping factor of   the high-redshift intergalactic medium
  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 focus on the effect of photo-ionisation heating by a uniform ultra-violet background and find that photo-heating strongly reduces the clumping factor because the increased pressure support smoothes out small-scale density fluctuations. Photo-ionisation heating is often said to provide a negative feedback on the reionisation of the IGM because it suppresses the cosmic star formation rate by boiling the gas out of low-mass halos. However, because of the reduction of the clumping factor it also makes it easier to keep the IGM ionised. Photo-heating therefore also provides a positive feedback which, while known to exist, has received much less attention. We demonstrate that this positive feedback is in fact very strong. Using conservative assumptions, we find that if the IGM was reheated at z >~ 9, the observed population of star-forming galaxies at z = 6 may be sufficient to keep the IGM ionised, provided that the fraction of ionising photons that escape the star-forming regions to ionise the IGM is larger than 0.2. 
Andreas H. Pawlik, Joop Schaye, Eveline van Scherpenzeel