Analytical expressions for the deprojected Sérsic model - II. General expressions in terms of the Fox H function

Abstract

The Sérsic model is the de facto standard to describe the surface brightness distribution of hot stellar systems. An important inconvenience of this analytical model is that the corresponding luminosity density and associated properties cannot be expressed using elementary functions or even standard special functions. We present a set of compact and elegant analytical expressions for the luminosity density, cumulative luminosity and potential for the Sérsic model in terms of the Fox H function for general values of the Sérsic index. Furthermore, we present explicit series expansions of these quantities and discuss the asymptotic behaviour. Our analysis completes the work of Mazure & Capelato (2002) and Baes & Gentile (2011) and demonstrates the power of the underestimated Fox H function as a tool for analytical work.

8 pages, accepted for publication in A&A

References in corpus (4)

• Structural Properties of Pseudo-Bulges, Classical Bulges and Elliptical Galaxies: an SDSS Perspective
• Dynamical models with a general anisotropy profile
• Analytical expressions for the deprojected Sersic model
• A comparison of the strong lensing properties of the Sersic and the NFW profiles

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