Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...279..668b&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 279, no. 2, p. 668-673
Astronomy and Astrophysics
Astrophysics
5
Abel Function, Astronomical Models, Brightness Distribution, Density Distribution, Elliptical Galaxies, Exponential Functions, Gauss Equation, Luminosity, Series Expansion, Bessel Functions, Inversions, Mathematical Models
Scientific paper
The series expansion by gaussian or exponential functions of a brightness profile (given in numerical or analytical form), supplies an easy and accurate way to derive its spatial deprojection, also in the form of series, thus by-passing the numerical difficulties related to the direct solution of the Abel integral equation. In this paper we consider in particular the problem of the Abel inversion when the unprojected density profile is highly peaked (or divergent) in the center. Under the assumption of the exponential function as 'basis' for the expansions, the unprojected density is obtained as a sum of Bessel functions. The expressions for the most used properties of a spherical model are then derived. The capability of exponentials to reproduce peaked density distributions, with respect to a gaussian expansion, is shown by the application of the exponential expansion to the R1/4 profile. Many other basic properties of this profile are expanded in the gaussian and exponential basis, and the coefficients are given.
Bendinelli Orazio
Ciotti Luca
Parmeggiani Gianluigi
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