Detectability of Microwave Background Polarization

Abstract

[NOTE: Previous versions of this paper (both on astro-ph and published in Phys. Rev. D) contain results that are in error. The power spectra C_l were normalized incorrectly by a factor of 2 pi. All observing times in detector-years in those versions are too large by a factor of 2 pi. The main place these numbers appear is on the vertical axes of Figures 4 and 5. Note that because all calculations were based on the same power spectra, all conclusions pertaining to comparisons of different techniques remain unchanged. This error has been corrected in the present version of the paper. An erratum is being sent to Phys. Rev. D. I apologize for the error.] Using a Fisher-matrix formalism, we calculate the required sensitivities and observing times for an experiment to measure the amplitudes of both E and B components as a function of sky coverage, taking full account of the fact that the two components cannot be perfectly separated in an incomplete sky map. We also present a simple approximation scheme that accounts for mixing of E and B components in computing predicted errors in the E-component power spectrum amplitude. In an experiment with small sky coverage, mixing of the two components increases the difficulty of detecting the subdominant B component by a factor of two or more in observing time; however, for larger survey sizes the effect of mixing is less pronounced. Surprisingly, mixing of E and B components can enhance the detectability of the E component by increasing the effective number of independent modes that probe this component