Constraints on warm dark matter from cosmological reionization

We study the constraints that high-redshift structure formation in the universe places on warm dark matter (WDM) dominated cosmological models. We modify the extended Press-Schechter formalism to derive the halo mass function in WDM models. We show that our predictions agree with recent numerical simulations at low redshift over the halo masses of interest. Applying our model to galaxy formation at high redshift, we find that the loss of power on small scales, together with the delayed collapse of low-mass objects, results in strong limits on the root-mean-square velocity dispersion vrms,0 of the WDM particles at redshift zero. For fermions decoupling while relativistic, these limits are equivalent to constraints on the mass mX of the particles. The presence of a ≈4 × 109 M☉ supermassive black hole at redshift 5.8, believed to power the quasar SDSS 1044-1215, implies mX ≳ 0.5 keV (or vrms,0 ≲ 0.10 km s-1), assuming that the quasar is unlensed and radiating at or below the Eddington limit. Reionization by redshift 5.8 also implies a limit on mX. If high-redshift galaxies produce ionizing photons with an efficiency similar to their redshift-three counterparts, we find mX ≳ 1.2 keV (or vrms,0 ≲ 0.03 s-1). However, given the uncertainties in current measurements from the proximity effect of the ionizing background at redshift three, values of mX as low as 0.75 keV (or vrms,0 = 0.06 s-1) are not ruled out. The limit weakens further to mX ≳ 0.4 keV (or vrms,0 ≲ 0.14 s-1), if, instead, the ionizing-photon production efficiency is 10 times greater at high redshift, but this limit will tighten considerably if reionization is shown in the future to have occurred at higher redshifts. WDM models with mX ≲ 1 keV (or vrms,0 ≳ 0.04 s-1) produce a low-luminosity cutoff in the high-redshift galaxy luminosity function that is directly detectable with the Next Generation Space Telescope, and which serves as a direct constraint on mX.