  [ABRIDGED] Inhomogeneous reionization acts as a source of arcminute-scale
anisotropies in the cosmic microwave background (CMB), the most important of
which is the kinetic Sunyaev-Zel'dovich (kSZ) effect. Observational efforts
with the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT)
are poised to detect this signal for the first time. Indeed, recent SPT
measurements place a bound on the dimensionless kSZ power spectrum around a
multipole of l=3000 of P_tot < 2.8 (6) micro K^2 at 95% C.L., by ignoring
(allowing) correlations between the thermal Sunyaev-Zel'dovich (tSZ) effect and
the cosmic infrared background (CIB). To interpret these and upcoming
observations, we compute the kSZ signal from a suite of ~ 100 reionization
models using the publicly available code 21cmFAST. Our physically motivated
reionization models are parameterized by the ionizing efficiency of
high-redshift galaxies, the minimum virial temperature of halos capable of
hosting stars, and the ionizing photon mean free path. We predict the
contribution of patchy reionization to be P_patchy = 1.5-3.5 micro K^2.
Therefore, even when conservatively adopting a low estimate of the
post-reionization signal, P_OV ~ 2 micro K^2, none of our models are consistent
with the aggressive 2sigma SPT bound that does not include correlations. This
implies that either: (i) the early stages of reionization occurred in a much
more homogeneous manner than suggested by the stellar-driven scenarios we
explore, such as would be the case if, e.g., very high energy X-rays or exotic
particles contributed significantly; and/or (ii) that there is a significant
correlation between the CIB and the tSZ. On the other hand, the conservative
SPT bound is compatible with all of our models, and is on the boarder of
constraining reionization.
