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Smoothing of an All-sky Survey Map with a Fisher-von Mises Function

Kwang-Il Seon
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Abstract

A convolution of the all-sky survey data with a smoothing function is crucial in calculating the smooth surface brightness of the sky survey data. The convolution is usually performed using a spherical version of the convolution theorem. However, a Gaussian function, applicable only in the flat-sky approximation, has been usually adopted as a smoothing kernel. In this paper, we present an exact analytic solution of the spherical-harmonics transformation of a Fisher-von Mises function, the mathematical version of a Gaussian function in spherical space. We also obtain the approximate solutions exp[-l(l + 1)/2k]. The exact and the approximate solutions may be useful when an astrophysical survey map is convolved with a smoothing function of k>1.

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Kwang-Il Seon. 2007-03-08. Smoothing of an All-sky Survey Map with a Fisher-von Mises Function. https://arxiv.org/abs/astro-ph/0703168

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