Reionization on Large Scales. Ii. Detecting Patchy Reionization Through Cross-correlation of the Cosmic Microwave Background

Abstract

We investigate the effect of patchy reionization on the cosmic microwave background (CMB) temperature. An anisotropic optical depth tau((n) over cap) alters the TT power spectrum on small scales l > 2000. We make use of the correlation between the matter density and the reionization redshift fields to construct full sky maps of tau((n) over cap). Patchy reionization transfers CMB power from large scales to small scales, resulting in a non-zero cross correlation between large and small angular scales. We show that the patchy tau correlator is sensitive to small root mean square (rms) values tau(rms) similar to 0.003 seen in our maps. We include frequency-independent secondaries such as CMB lensing and kinetic Sunyaev-Zel'dovich (kSZ) terms, and show that patchy t may still be detected at high significance. Reionization models that predict different values of tau(rms) may be distinguished even for the same mean value <tau >. It is more difficult to detect patchy tau in the presence of larger secondaries such as the thermal Sunyaev-Zel'dovich, radio background, and the cosmic infrared background. In this case, we show that patchy t may be detected if these frequency-dependent secondaries are minimized to less than or similar to 5 mu K (rms) by means of a multi-frequency analysis. We show that the patchy tau correlator provides information that is complementary to what may be obtained from the polarization and the kSZ power spectra.