Analytical expressions for the deprojected Sérsic model
Abstract
The Sérsic model has become the standard for parametrizing the surface brightness distribution of earlytype galaxies and bulges of spiral galaxies. A major problem is that the deprojection of the Sérsic surface brightness profile to a luminosity density cannot be executed analytically for general values of the Sérsic index. We use Mellin integral transforms to derive an analytical expressions for the luminosity density in terms of the Fox H function for all values of the Sérsic index. We derive simplified expressions for the luminosity density, cumulative luminosity, and gravitational potential in terms of the Meijer G function for all rational values of the Sérsic index, and we investigate their asymptotic behaviour at small and large radii. As implementations of the Meijer G function are currently available both in symbolic computer algebra packages and as highperformance computing code, our results open up the possibility to calculate the density of the Sérsic models to arbitrary precision.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 January 2011
 DOI:
 10.1051/00046361/201015716
 arXiv:
 arXiv:1009.4713
 Bibcode:
 2011A&A...525A.136B
 Keywords:

 methods: analytical;
 galaxies: photometry;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 9 pages, accepted for publication in Astronomy and Astrophysics