Analytical expressions for the deprojected Sérsic model

II. General expressions in terms of the Fox H function

Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent, Belgium
e-mail: maarten.baes@ugent.be

Received: 15 July 2011
Accepted: 8 August 2011

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 earlier work and demonstrates the power of the underestimated Fox H function as a tool for analytical work.