Residual noise covariance for Planck low-resolution data analysis

<BR /> Aims We develop and validate tools for estimating residual noise covariance in Planck frequency maps, we also quantify signal error effects and compare different techniques to produce low-resolution maps. <BR /> Methods We derived analytical estimates of covariance of the residual noise contained in low-resolution maps produced using a number of mapmaking approaches. We tested these analytical predictions using both Monte Carlo simulations and by applying them to angular power spectrum estimation. We used simulations to quantify the level of signal errors incurred in the different resolution downgrading schemes considered in this work. <BR /> Results We find excellent agreement between the optimal residual noise covariance matrices and Monte Carlo noise maps. For destriping mapmakers, the extent of agreement is dictated by the knee frequency of the correlated noise component and the chosen baseline offset length. Signal striping is shown to be insignificant when properly dealt with. In map resolution downgrading, we find that a carefully selected window function is required to reduce aliasing to the subpercent level at multipoles, l > 2N<SUB>side</SUB>, where N<SUB>side</SUB> is the HEALPix resolution parameter. We show that, for a polarization measurement, reliable characterization of the residual noise is required to draw reliable constraints on large-scale anisotropy. <BR /> Conclusions Methods presented and tested in this paper allow for production of low-resolution maps with both controlled sky signal error level and a reliable estimate of covariance of the residual noise. We have also presented a method for smoothing the residual noise covariance matrices to describe the noise correlations in smoothed, bandwidth-limited maps.