Analytical properties of the R^(1/m) luminosity law

TL;DR

This paper explores the analytical properties of the R^{1/m} law used for galaxy profiles, providing a comprehensive asymptotic expansion for the scale factor that applies across a wide range of galaxy types.

Contribution

It presents a full asymptotic expansion for the scale factor in the R^{1/m} law, applicable even for low m values, unifying analysis for various galaxy profiles.

Findings

Asymptotic expansion for b(m) derived

Applicable for m as low as 1

Useful for both observational and theoretical studies

Abstract

In this paper we describe some analytical properties of the R^{1/m} law proposed by Sersic (1968) to categorize the photometric profiles of elliptical galaxies. In particular, we present the full asymptotic expansion for the dimensionless scale factor b(m) that is introduced when referring the profile to the standard effective radius. Surprisingly, our asymptotic analysis turns out to be useful even for values of m as low as unity, thus providing a unified analytical tool for observational and theoretical investigations based on the R^{1/m} law for the entire range of interesting photometric profiles, from spiral to elliptical galaxies.