CMB power spectrum estimation using noncircular beams

The measurements of the angular power spectrum of the Cosmic Microwave Background (CMB) anisotropy have proved crucial to the emergence of cosmology as a precision science in recent years. In this remarkable data rich period, the limitations to precision now arise from the inability to account for finer systematic effects in data analysis. The noncircularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. We present an analytic framework for studying the leading order effects of a noncircular beam on the CMB power spectrum estimation. We consider a noncircular beam of fixed shape but variable orientation. We compute the bias in the pseudo-C-l power spectrum estimator and then construct an unbiased estimator using the bias matrix. The covariance matrix of the unbiased estimator is computed for smooth, noncircular beams. Quantitative results are shown for CMB maps made by a hypothetical experiment with a noncircular beam comparable to our fits to the Wilkinson Microwave Anisotropy Probe (WMAP) beam maps described in the appendix and uses a toy scan strategy. We find that significant effects on CMB power spectrum can arise due to noncircular beam on multipoles comparable to, and beyond, the inverse average beamwidth where the pseudo-C-l approach may be the method of choice due to computational limitations of analyzing the large data sets from current and near future CMB experiments.