91ÃÛÌÒ¸ó

Authors:ÌýJoshua J. Hibbard, Keith Tauscher, David Rapetti, Jack O. Burns

´¡²ú²õ³Ù°ù²¹³¦³Ù:ÌýIn order to characterize and model the beam-weighted foreground for global 21-cm signal experiments, we present a methodology for generating basis eigenvectors that combines analytical and observational 91ÃÛÌÒ¸ó of both the galactic spectral index and sky brightness temperature with simulations of beams having various angular and spectral dependencies and pointings. Each combination creates a unique beam-weighted foreground. By generating eigenvectors to fit each foreground model using Singular Value Decomposition (SVD), we examine the effects of varying the components of the beam-weighted foreground. We find that the eigenvectors for modelling an achromatic, isotropic beam -- the ideal case -- are nearly identical regardless of the unweighted foreground model used, and are practicably indistinguishable from polynomial-based 91ÃÛÌÒ¸ó. When anisotropic, chromatic beams weight the foreground, however, a coupling is introduced between the spatial and spectral structure of the foreground which distorts the eigenvectors away from the polynomial 91ÃÛÌÒ¸ó and induces a dependence of the basis upon the exact features of the beam (chromaticity, pattern, pointing) and foreground (spectral index, sky brightness temperature map). We find that the beam has a greater impact upon the eigenvectors than foreground 91ÃÛÌÒ¸ó. Any model which does not account for its distortion may produce RMS uncertainties on the order of ∼10 - 103 Kelvin for six-parameter, single spectrum fits. If the beam is incorporated directly using SVD and training sets, however, the resultant eigenvectors yield milli-Kelvin level uncertainties. Given a sufficiently detailed description of the sky, our methodology can be applied to any particular experiment with a suitably characterized beam for the purpose of generating accurate beam-weighted foreground 91ÃÛÌÒ¸ó.

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