Constraints on warm dark matter from cosmological reionization

We study the constraints that high-redshift structure formation in the univ erse places on warm dark matter (WDM) dominated cosmological models. We mod ify the extended Press-Schechter formalism to derive the halo mass function in WDM models. We show that our predictions agree with recent numerical si mulations at low redshift over the halo masses of interest. Applying our mo del 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, resu lts in strong limits on the root-mean-square velocity dispersion v(rms,o) o f the WDM particles at redshift zero. For fermions decoupling while relativ istic, these limits are equivalent to constraints on the mass m(x) of the p articles. The presence of a approximate to4 x 10(9) M-. supermassive black hole at redshift 5.8, believed to power the quasar SDSS 1044-1215, implies m(x) greater than or similar to 0.5 keV (or v(rms,o) less than or similar t o 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 limi t on If high-redshift galaxies produce ionizing photons with an m X. effici ency similar to their redshift-three counterparts, we find m(x) greater tha n or similar to 1.2 keV (or v(rms,o) less than or similar to 0.03 s(-1)). H owever, given the uncertainties in current measurements from the proximity effect of the ionizing background at redshift three, values of m(x) as low as 0.75 keV (or v(rms,o) = 0.06 s(-1)) are not ruled out. The limit weakens further to m(x) greater than or similar to 0.4 keV (or v(rms,o) less than or similar to 0.14 s(-1)), if, instead, the ionizing-photon production effi ciency is 10 times greater at high redshift, but this limit will tighten co nsiderably if reionization is shown in the future to have occurred at highe r redshifts. WDM models with m(x) less than or similar to 1 keV (or v(rms,o ) greater than or similar to 0.04 s(-1)) produce a low-luminosity cutoff in the high-redshift galaxy luminosity function that is directly 0.04 detecta ble with the Next Generation Space Telescope, and which serves as a direct constraint on m(x).