A New Analytic Galactic Luminosity Profile Function

TL;DR

This paper evaluates Spergel's modified Bessel function-based galactic luminosity profile, demonstrating it often fits galaxy data better than the traditional Sersic profile and simplifies integral calculations.

Contribution

It provides a quantitative comparison showing Spergel's profile can outperform Sersic's in fitting galaxy luminosity data and offers computational advantages.

Findings

Spergel profile fits 16 galaxy samples better than Sersic.

Spergel profile simplifies integral calculations in galactic modeling.

Spergel's profile is as accurate as Sersic's in general.

Abstract

In 2010 Spergel introduced an alternative to the traditional Sersic form for galactic luminosity profiles based on modified Bessel functions of the second kind. His motivation was the desire for an accurate one-parameter profile form with a simple Fourier transform (in contrast to the Fourier transform of the Sersic profile which can't be written in closed form), but we have found that the Spergel profile almost universally makes integrals easier when it replaces the Sersic profile in the integrand. In the original paper on the subject Spergel noted that his profile seems to fit galaxies on average just as well as Sersic's. Here we make this observation quantitative by comparing the residuals from fitting Sersic and Spergel forms to data. We find that the Spergel profile actually fits better than the Sersic for a random sample of 16 galaxies.