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The critical star formation rate density required to keep the intergalactichydrogen ionised depends crucially on the average rate of recombinations in theintergalactic 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 cosmicmean baryon density, respectively, and the brackets < > indicate spatialaveraging over the recombining gas in the IGM. We perform a suite ofcosmological smoothed particle hydrodynamics simulations that include radiativecooling to calculate the volume-weighted clumping factor of the IGM atredshifts z >= 6. We investigate the effect of photoionisation heating by auniform ultraviolet background and find that photoheating strongly reduces theclumping factor as the increased pressure support smoothes out small-scaledensity fluctuations. Even our most conservative estimate for the clumpingfactor, C = 6, is five times smaller than the clumping factor that is usuallyemployed to determine the capacity of star-forming galaxies to keep the z=6 IGMionised. Our results imply that the observed population of star-forminggalaxies at z = 6 may be sufficient to keep the IGM ionised, provided that theIGM was reheated at z >~ 9 and that the fraction of ionising photons thatescape star-forming regions to ionise the IGM is larger than 0.25.

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