  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.
