The Nuker model for galactic nuclei

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.

15 pages, 5 figures, accepted for publication in A&A

References in corpus (28)

• The Centers of Early-Type Galaxies with HST. IV. Central Parameter Relations
• Analytical Models For Galactic Nuclei
• A concise reference to (projected) Sersic R^{1/n} quantities, including Concentration, Profile Slopes, Petrosian indices, and Kron Magnitudes
• The ACS Virgo Cluster Survey. VI. Isophotal Analysis and the Structure of Early-Type Galaxies
• The Centers of Early-Type Galaxies with HST. V. New WFPC2 Photometry
• A Family of Models for Spherical Stellar Systems
• A New Empirical Model for the Structural Analysis of Early-type Galaxies and a Critical Review of the Nuker Model
• Evidence for a New Elliptical-Galaxy Paradigm: Sersic and Core Galaxies
• The Centers of Early-Type Galaxies with HST. VI. Bimodal Central Surface Brightness Profiles
• WFPC2 Images of the Central Regions of Early-Type Galaxies - I. The Data
• Weak homology of elliptical galaxies
• Hubble Space Telescope Imaging of Brightest Cluster Galaxies
• The Centers of Early-Type Galaxies with HST II: Empirical Models and Structural Parameters
• Analytical properties of Einasto dark matter haloes
• Fractional reaction-diffusion equations
• Depleted cores, multi-component fits, and structural parameter relations for luminous early-type galaxies
• A NICMOS Survey of Early-Type Galaxy Centers: The Relation Between Core Properties, Gas and Dust Content and Environment
• Analytical Dynamical Models for Double-Power-Law Galactic Nuclei
• Analytical expressions for the deprojected Sersic model
• Hypervirial Models of Stellar Systems
• Are radio galaxies and quiescent galaxies different? Results from the analysis of HST brightness profiles
• Analytical expressions for the deprojected Sérsic model - II. General expressions in terms of the Fox H function
• Analytical shear and flexion of Einasto dark matter haloes
• The dynamical structure of dark matter halos with universal properties
• The link between brightest cluster galaxy properties and large scale extensions of 38 DAFT/FADA and CLASH clusters in the redshift range 0.2<z<0.9
• Stellar systems following the $R^{1/m}$ luminosity law. IV. The total energy and the central concentration of galaxies
• Stellar systems following the $R^{1/m}$ luminosity law. III. Photometric, intrinsic, and dynamical properties for all Sérsic indices
• Exact potential-density pairs for flattened dark haloes

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