Reionization revisited: Secondary cosmic microwave background anisotropies and polarization

Secondary cosmic microwave background (CMB) anisotropies and polarization provide a laboratory for studying structure formation in the reionized epoch. We consider the kinetic Sunyaev-Zeldovich effect from mildly nonlinear large-scale structure and show that it is a natural extension of the perturbative Vishniac effect. If the gas traces the dark matter to overdensities of order 10, as expected from simulations, this effect is at least comparable to the Vishniac effect at arcminute scales. On smaller scales, it can be used to study the thermal history-dependent clustering of the gas. Polarization is generated through Thomson scattering of primordial quadrupole anisotropies, kinetic (second-order Doppler) quadrupole anisotropies, and intrinsic-scattering quadrupole anisotropies. Small-scale polarization results from the density and ionization modulation of these sources. These effects generically produce comparable E- and B-parity polarization, but of negligible amplitude (10(-3)-10(-2) mu K) in adiabatic cold dark matter (CDM) models. However, the primordial and kinetic quadrupoles are observationally comparable at present, so that a null detection of B-polarization would set constraints on the evolution and coherence of the velocity field. Conversely, the detection of a cosmological B-polarization even at large angles does not necessarily imply the presence of gravity waves or vorticity. For these calculations, we develop an all-sky generalization of the Limber equation that allows for an arbitrary local angular dependence of the source for both scalar and symmetric trace-free tensor fields on the sky.