Effects of destriping errors on cosmic microwave background polarization power spectra and pixel noise covariances

Low-frequency detector noise in cosmic microwave background experiments must be corrected to produce faithful maps of the temperature and polarization anisotropies. For a Planck-type experiment the low-frequency noise corrections lead to residual stripes in the maps. Here I show that for a ring torus and idealized detector geometry it is possible to calculate analytically the effects of destriping errors on the temperature and polarization power spectra. It is also possible to compute the pixel-pixel noise covariances for maps of arbitrary resolution. The analytic model is compared to numerical simulations using realistic detector and scanning geometries. We show that Planck polarization maps at 143 GHz should be signal dominated on large scales. Destriping errors are the dominant source of detector noise for the temperature and polarization power spectra at multipoles l less than or similar to 10. A fast Monte Carlo method for characterizing noise, including destriping errors, is described that can be applied to Planck. This Monte Carlo method can be used to quantify pixel-pixel noise covariances and to remove noise biases in power spectrum estimates.