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.
