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

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

2007-03-08

arxiv.org/abs/astro-ph/0703168v1

2006 JKPS, 48, L331

Astronomy and Astrophysics

Astrophysics

4 pages, 2 figures, preprint version of the paper published in JKPS on March 15, 2006

Scientific paper

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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