Non-uniform reionization by galaxies and its effect on the cosmic microwave backgroun

We present predictions for the reionization of the intergalactic medium by stars in high-redshift galaxies. We calculate ionizing luminosities of galaxies, including the effects of absorption by interstellar gas and dust on the escape fraction, in order to calculate the filling factor of ionized hydrogen in the IGM. For a $\Lambda{\rm CDM}$ cosmology and a physical calculation of the escape fraction, we find that the hydrogen in the IGM will be reionized at redshift z=6.1 if the IGM has uniform density, but only by z=4.5 if the IGM is clumped. We combine our model with an N-body simulation of the distribution of dark matter in the universe in order to calculate the secondary temperature anisotropies induced in the cosmic microwave background (CMB) by scattering off free electrons. The models predict a spectrum of secondary anisotropies covering a broad range of angular scales, with fractional temperature fluctuations $\sim 10^{-7}-10^{-6}$ on arcminute scales. The amplitude depends somewhat on the geometry of reionization, with models in which the regions of highest gas density are reionized first giving larger CMB fluctuations than the case where galaxies ionize surrounding spherical regions, and models where low density regions reionize first giving the smallest fluctuations. Measurement of these anisotropies can therefore put important constraints on the reionization process, in particular, the redshift evolution of the filling factor, and should be a primary objective of a next generation submillimeter telescope such as the Atacama Large Millimeter Array. (abrdiged)