Polarization of the cosmic microwave background from nonuniform reionization

We study the polarization anisotropy in the cosmic microwave background (CM B) resulting from patchy reionization of the intergalactic medium by stars in galaxies. It is well known that the polarization of the CMB is very sens itive to the details of reionization, including the reionization epoch and the density fluctuations in the ionized gas. We calculate the effects of re ionization by combining a semianalytic model of galaxy formation, which pre dicts the redshifts and luminosities of the ionizing sources, with a high-r esolution N-body simulation, to predict the spatial distribution of the ion ized gas. The models predict reionization at redshifts z similar to 5-10, w ith electron scattering optical depths due to reionization of similar to0.0 14-0.05. We find that reionization generates a peak in the polarization spe ctrum with amplitude similar to0.05-0.15 muK at large angular scales (l sim ilar to 3). The position of this peak reveals the size of the horizon at re ionization, whilst its amplitude is a measure of the optical depth to reion ization. On small scales (l greater than or similar to 6000), reionization produces a second-order polarization signal due to the coupling of fluctuat ions in the free electron density with the quadrupole moment of the tempera ture anisotropy. Careful study reveals that this coupling generates equal s econd-order polarization power spectra for the electric and magnetic modes, with amplitude similar to 10 nK. This amplitude depends strongly on the to tal baryon density Omega (b) and on the spatial correlations of the free el ectron density, and weakly on the fraction f(esc) of ionizing photons able to escape their source galaxy. The first- and second-order signals are ther efore sensitive to different details of how the reionization occurred. Dete ction of these signals will place important constraints on the reionization history of the universe.