Secondary Cosmic Microwave Background Anisotropies in a Universe Reionized in Patches

In a universe reionized in patches, the Doppler effect from Thomsonscattering off free electrons generates secondary cosmic microwave background(CMB) anisotropies. For a simple model with small patches and latereionization, we analytically calculate the anisotropy power spectrum. Patchyreionization can, in principle, be the main source of anisotropies on arcminutescales. On larger angular scales, its contribution to the CMB power spectrum isa small fraction of the primary signal and is only barely detectable in thepower spectrum with even an ideal, i.e. cosmic variance limited, experiment andan extreme model of reionization. Consequently patchy reionization is unlikelyto affect cosmological parameter estimation from the acoustic peaks in the CMB.Its detection on small angles would help determine the ionization history ofthe universe, in particular the typical size of the ionized region and theduration of the reionization process.Comment: 7 pages, 2 figures, submitted to Ap