IUCAA Preprints

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Author: search.filters.author.Sengupta, AnandSubject: search.filters.subject.CMB

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    CMB power spectrum estimation using non-circular beam
    (2011-07-06) Mitra, Sanjit; Sengupta, Anand; Souradeep, Tarun
    The measurements of the angular power spectrum of the Cosmic Microwave Background (CMB) anisotropy has 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 the inability to account for finer systematic effects in data analysis. The non-circularity 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 non- circular beam on the CMB power spectrum estimation. We consider a non-circular beam of fixed shape but variable orientation. We compute the bias in the pseudo-Cl power spectrum estimator and then construct an unbiased estimator using the bias matrix. The covariance matrix of the unbiased estimator is computed for smooth, non-circular beams. Quantitative results are shown for CMB maps made by a hypothetical experiment with a non-circular beam comparable to our fits to the 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 non-circular beam on multipoles comparable to, and beyond, the inverse average beam-width where the pseudo-Cl approach may be the method of choice due to computational limitations of analyzing the large datasets from current and near future CMB experiments.
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    CMB power spectrum estimation with non-circular beam and incomplete sky coverage
    (2007-02-05) Mitra, Sanjit; Sengupta, Anand; Souradeep, Tarun; et al.
    Over the last decade, measurements of the CMB anisotropy has spearheaded the remarkable transition of cosmology into a precision science. However, addressing the systematic effects in the increasingly sensitive, high resolution, ‘full’ sky measurements from different CMB experiments pose a stiff challenge. The analysis techniques must not only be computationally fast to contend with the huge size of the data, but, the higher sensitivity also limits the simplifying assumptions which can then be invoked to achieve the desired speed without compromising the final precision goals. While maximum likelihood is desirable, the enormous computational cost makes the suboptimal method of power spectrum estimation using Pseudo-Cl unavoidable for high resolution data. The debiasing of the Pseudo-Cl needs account for non-circular beams, together with non-uniform sky coverage. We provide an analytic framework for correcting the power spectrum for the effect of beam noncircularity and non-uniform sky coverage (including incomplete/masked sky maps). The approach is perturbative in the distortion of the beam from non-circularity allowing for rapid computations when the beam is mildly non-circular. When non-circular beam effect is important, we advocate that it is computationally advantageous to employ ‘soft’ azimuthally apodized masks whose spherical harmonic transform die down fast with m.