Was Star-Formation Suppressed in High-Redshift Minihalos?

The primordial gas in the earliest dark matter halos, collapsing at redshifts around z=20, with masses M_halo=10^6 M_sun, and virial temperatures T_vir<10^4K, relied on the presence of molecules for cooling. Several theoretical studies have suggested that gas contraction and star-formation in these minihalos was suppressed by radiative, chemical, thermal, and dynamical feedback processes. The recent measurement by the Wilkinson Microwave Anisotropy Probe (WMAP) of the optical depth to electron scattering, tau=0.09+/-0.03, provides the first empirical evidence for this suppression. The new WMAP result is consistent with vanilla models of reionization, in which ionizing sources populate cold dark matter (CDM) halos down to a virial temperature of T_vir=10^4K. On the other hand, we show that in order to avoid overproducing the optical depth, the efficiency for the production of ionizing photons in minihalos must have been about an order of magnitude lower than expected and lower than the efficiency in large halos that can cool via atomic hydrogen (T_vir > 10^4K). This conclusion is insensitive to assumptions about the efficiency of ionizing photon production in the large halos, as long as reionization ends by z=6, as required by the spectra of bright quasars at z<6. Our conclusion is strengthened if the clumping of the ionized gas evolves with redshift, as suggested by semi-analytical predictions and three-dimensional numerical simulations.