Analytical properties of the R^{1/m} law

TL;DR

This paper analyzes the mathematical properties of the R^{1/m} law used in galaxy photometry, providing an asymptotic expansion for the scale factor that applies across a wide range of galaxy types.

Contribution

It presents a comprehensive 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

Derived a full asymptotic expansion for b(m)

The analysis is valid for m as low as 1

Provides a unified analytical tool for galaxy profile studies

Abstract

In this paper we describe some analytical properties of the R^{1/m} law proposed by Sersic 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.