Polarization of the microwave background in reionized models

Abstract

I discuss the physics of polarization in models with early reionization. For sufficiently high optical depth to recombination the polarization is boosted on large scales while it is suppressed on smaller scales. New peaks appear in the polarization power spectrum; their position is proportional to the square root of the redshift at which the reionization occurs while their amplitude is proportional to the optical depth. For standard scenarios the rms degree of linear polarization as measured with a $7\ifmmode^\circ\else\textdegree\fi{}$ full width at half maximum (FWHM) antenna (such as the one of the Brown University experiment) is 1.6 $\ensuremath{\mu}\mathrm{K}$, 1.2 $\ensuremath{\mu}\mathrm{K}$, $4.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ $\ensuremath{\mu}\mathrm{K}$ for an optical depth of $1$, $0.5$, or $0$, respectively. For a $1\ifmmode^\circ\else\textdegree\fi{}$ FWHM antenna these same models give 2.7 $\ensuremath{\mu}\mathrm{K}$, 1.8 $\ensuremath{\mu}\mathrm{K}$, and 0.77 $\ensuremath{\mu}\mathrm{K}$. Detailed measurement of polarization on large angular scales could provide an accurate determination of the epoch of reionization, which cannot be obtained from temperature measurements alone.