The Nuker model for galactic nuclei

TL;DR

This paper derives an analytical density expression for the Nuker model, analyzes its properties, and refines the classification of galactic nuclei based on the model's parameters, enhancing understanding of galactic core structures.

Contribution

It provides a new compact analytical formula for the Nuker density profile and extends the classification of galactic nuclei considering density and break sharpness.

Findings

Derived a compact analytical density expression for the Nuker model.

Identified unphysical density profiles in models with infinitely sharp breaks.

Refined the classification of galactic nuclei based on density slope and break sharpness.

Abstract

The Nuker profile, characterised by an inner and outer power-law profile smoothly merged around a break radius, is a very popular model to describe the surface brightness profile of galactic nuclei. A disadvantage of this model for dynamical studies is that the spatial density distribution that corresponds to this surface brightness profile cannot be written in terms of elementary or regular special functions. We derive a compact and elegant analytical expression for the density of the Nuker model, based the Mellin integral transform method. We use this expression to discuss the general behaviour and asymptotic expansion of the density. We also discuss the special subclass of Nuker models with an infinitely sharp break, and demonstrate that these models are always characterised by non-monotonous and hence unphysical density profile. We extend our study to the dynamical structure of spherical isotropic galactic nuclei with a Nuker surface brightness profile. Based on this analysis, we extend and refine the classification of spherical isotropic galactic nuclei introduced by Tremaine et al. (1994). We demonstrate that both the inner density slope and the sharpness of the break between the inner and outer profiles critically determine the consistency and stability of the Nuker models.