Warm Dark Matter, small scale crisis, and the high redshift universe

Warm Dark Matter (WDM) models have recently been resurrected to resolve apparent conflicts of Cold Dark Matter (DM) models with observations. Endowing the DM particles with non-negligible velocities causes free-streaming, which suppresses the primordial power spectrum on small scales. The choice of a root-mean-square velocity dispersion v(rms) = 0.05 km/s at redshift z=0 (corresponding to a particle mass of 1 keV if the WDM particles are fermions decoupling while relativistic) helps alleviate most, but probably not all, of the small-scale problems faced by CDM. An important side-effect of the particle velocities is the severe decrease in the number of collapsed halos at high redshift. This is caused both by the loss of small-scale power, and by the delay in the collapse of the smallest individual halos (with masses near the effective Jeans mass of the DM). The presence of early halos is required in order (1) to host either early quasars or galaxies that can reionize the universe by redshift z=5.8, and (2) to allow the growth of the supermassive black hole believed to power the recently discovered quasar SDSS 1044-1215 at this redshift. We quantify these constraints using a modified Press-Schechter formalism, and find v(rms) < 0.04 km/s (or m_X > 1 keV). If future observations uncover massive black holes at z > 10, or reveal that reionization occurred at z > 10, this could conclusively rule out WDM models as the solution to the small-scale crisis of the CDM paradigm.