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Register a new userAngular Power Spectrum Estimation of Cosmic Ray Anisotropies with Full or Partial Sky Coverage
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We study the angular power spectrum estimate in order to search for large scale anisotropies in the arrival directions distribution of the highest-energy cosmic rays. We show that this estimate can be performed even in the case of partial sky coverage and validated over the full sky under the assumption that the observed fluctuations are statistically spatial stationary. If this hypothesis - which can be tested directly on the data - is not satisfied, it would prove, of course, that the cosmic ray sky is non isotropic but also that the power spectrum is not an appropriate tool to represent its anisotropies, whatever the sky coverage available. We apply the method to simulations of the Pierre Auger Observatory, reconstructing an input power spectrum with the Southern site only and with both Northern and Southern ones. Finally, we show the improvement that a full-sky observatory brings to test an isotropic distribution, and we discuss the sensitivity of the Pierre Auger Observatory to large scale anisotropies.
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We study the possibility to extract the multipolar moments of an underlying distribution from a set of cosmic rays observed with non-uniform or even partial sky coverage. We show that if the degree is assumed to be upper bounded by $L$, each multipolar moment can be recovered whatever the coverage, but with a variance increasing exponentially with the bound $L$ if the coverage is zero somewhere. Despite this limitation, we show the possibility to test predictions of a model without any assumption on $L$ by building an estimate of the covariance matrix seen through the exposure function.
We discuss the derivation of the analytic properties of the cross-power spectrum estimator from multi-detector CMB anisotropy maps. The method is computationally convenient and it provides unbiased estimates under very broad assumptions. We also propose a new procedure for testing for the presence of residual bias due to inappropriate noise subtraction in pseudo-$C_{ell}$ estimates. We derive the analytic behavior of this procedure under the null hypothesis, and use Monte Carlo simulations to investigate its efficiency properties, which appear very promising. For instance, for full sky maps with isotropic white noise, the test is able to identify an error of 1% on the noise amplitude estimate.
Angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies is one of the most important on characteristics of the Universe such as its geometry and total density. Using flat sky approximation and Fourier analysis, we estimate the angular power spectrum from an ensemble of least foreground-contaminated square patches from WMAP W and V frequency band map. This method circumvents the issue of foreground cleaning and that of breaking orthogonality in spherical harmonic analysis due to masking out the bright Galactic plane region, thereby rendering a direct measurement of the angular power spectrum. We test and confirm Gaussian statistical characteristic of the selected patches, from which the first and second acoustic peak of the power spectrum are reproduced, and the third peak is clearly visible albeit with some noise residual at the tail.
In our recent paper (Yadav et al. 2007) we described a fast cubic (bispectrum) estimator of the amplitude of primordial non-Gaussianity of local type, f_{NL}, from a combined analysis of the Cosmic Microwave Background (CMB) temperature and E-polarization observations. In this paper we generalize the estimator to deal with a partial sky coverage as well as inhomogeneous noise. Our generalized estimator is still computationally efficient, scaling as O(N^3/2) compared to the O(N^5/2) scaling of the brute force bispectrum calculation for sky maps with N pixels. Upcoming CMB experiments are expected to yield high-sensitivity temperature and E-polarization data. Our generalized estimator will allow us to optimally utilize the combined CMB temperature and E-polarization information from these realistic experiments, and to constrain primordial non-Gaussianity.
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