Analysis of cosmic microwave background data on an incomplete sky

Abstract

Measurement of the angular power spectrum of the cosmic microwave background is most often based on a spherical harmonic analysis of the observed temperature anisotropies. Even if all-sky maps are obtained, however, it is likely that the region around the Galactic plane will have to be removed due to its strong microwave emissions. The spherical harmonics are not orthogonal on the cut sky, but an orthonormal basis set can be constructed from a linear combination of the original functions. Previous implementations of this technique, based on Gram-Schmidt orthogonalisation, were limited to maximum Legendre multipoles of l_max < 50 as they required all the modes have appreciable support on the cut sky, whereas for large l_max the fraction of modes supported is equal to the fractional area of the region retained. This problem is solved by using a singular value decomposition to remove the poorly-supported basis functions, although the treatment of the non-cosmological monopole and dipole modes necessarily becomes more complicated. A further difficulty is posed by computational limitations -- orthogonalisation for a general cut requires O(l_max^6) operations and O(l_max^4) storage and so is impractical for l_max > 200 at present. These problems are circumvented for the special case of constant (Galactic) latitude cuts, for which the storage requirements scale as O(l_max) and the operations count scales as O(l_max^4). Less clear, however, is the stage of the data analysis at which the cut is best applied. As convolution is ill-defined on the incomplete sphere, beam-deconvolution should not be performed after the cut, and, if all-sky component separation is as successful as simulations indicate, the Galactic plane should probably be removed immediately prior to power spectrum estimation.

MNRAS, in press; 17 pages, 22 figures: significant changes; major additions

References in corpus (10)

• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• A High Spatial Resolution Analysis of the MAXIMA-1 Cosmic Microwave Background Anisotropy Data
• The Pseudo-$C_l$ method: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
• First Intrinsic Anisotropy Observations with the Cosmic Background Imager
• Fast Convolution on the Sphere
• Neural networks and separation of Cosmic Microwave Background and astrophysical signals in sky maps
• A Map-Making Algorithm for the Planck Surveyor
• MAPCUMBA : a fast iterative multi-grid map-making algorithm for CMB experiments
• The Planck-LFI instrument: analysis of the 1/f noise and implications for the scanning strategy
• The Cosmic Microwave Background: State of the Art

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