A New Empirical Model for the Structural Analysis of Early-Type Galaxies, and A Critical Review of the Nuker Model

By Alister W. Graham, P. Erwin, Ignacio Trujillo, A. A. Ramos. 2003

205 citations recorded by the source corpus.

The Nuker law was designed to match the inner few (∼3–10) arcseconds of predominantly nearby (≲30 Mpc) early-type galaxy light profiles; it was never intended to describe an entire profile. The Sérsic model, on the other hand, was developed to fit the entire profile; however, because of the presence of partially depleted galaxy cores, the Sérsic model cannot always describe the very inner region. We have therefore developed a new empirical model consisting of an inner power law, a transition region, and an outer Sérsic model to connect the inner and outer structure of elliptical galaxies. We have additionally explored the stability of the Nuker model parameters. Surprisingly, none are found to be stable quantities; all are shown to vary systematically with a profile's fitted radial extent, and often by more than 100%. Considering elliptical galaxies spanning a range of 7.5 mag, we reveal that the central stellar densities of the underlying host galaxies increase with galaxy luminosity until the onset of core formation, detected only in the brightest elliptical galaxies. We suggest that the so-called power-law galaxies may actually be described by the Sérsic model over their entire radial range.

Subfields: Astronomy and Astrophysics, Electrical and Electronic Engineering, Instrumentation

View Paper: https://www.semanticscholar.org/paper/d5c4afddebf58661505ee51d2fdc49ae59b9f59f

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Citations in the corpus

Structure and Kinematics of Early-Type Galaxies from Integral Field Spectroscopy (2016, methodology): “Alternative ways of quantifying inner profiles is by measuring either“extra light” or a “deficit” with respect to a global Sersic fit to the outer profile (e.g. Ferrarese et al. 2006; Kormendy et al. 2009), or using the “Core-Sersic” parametrization (Graham et al. 2003; Trujillo et al. 2004b).”
SIZES AND SURFACE BRIGHTNESS PROFILES OF QUIESCENT GALAXIES AT z ∼ 2 (2011, methodology): “Sérsic (1968) profiles are commonly used, since these have been shown to closely match the surface brightness profiles of nearby early-type galax- ies (e.g., Caon et al. 1993; Graham et al. 2003; Trujillo et al. 2004; Ferrarese et al. 2006; Côté et al. 2007; Kormendy et al. 2009).”
A Log-Quadratic Relation for Predicting Supermassive Black Hole Masses from the Host Bulge Sérsic Index (2006, methodology): “…agrees well with the slope obtained using the bisector linear regression routine BCES from Akritas & Bershady (1996), which gives logMbh ¼ 2:85 0:40ð Þ log n=3ð Þ þ 7:80 0:07ð Þ: ð5Þ This relation is in good agreement with the intrinsic astrophysical relation presented in Graham et al. (2003a).”
Evidence for a New Elliptical-Galaxy Paradigm: Sérsic and Core Galaxies (2004, methodology): “In our first paper (Graham et al. 2003a, hereafter Paper I), we discussed some of the systematic problems and ambiguities that can arise when using a double power-law model to fit galaxy light profiles and suggested a new hypothesis and a new model that might resolve some of these problems.”
A Fundamental Relation between Compact Stellar Nuclei, Supermassive Black Holes, and Their Host Galaxies (2006, methodology): “The 11 ACSVCS galaxies brighter than MB ≈ −20 mag are found to have surface brightness profiles that are accurately represented by a “core-Sérsic” model (Graham et al. 2003; Trujillo et al. 2004), described by a Sérsic (1968) model outside a “break radius”, rb, of a few arcseconds, and a…”
STRUCTURE AND FORMATION OF ELLIPTICAL AND SPHEROIDAL GALAXIES (2008, methodology): “The dichotomy has been challenged by Jerjen & Binggeli (1997); Graham & Guzmán (2003); Graham et al. (2003); Trujillo et al. (2004), and Gavazzi et al. (2005).”
DISSIPATION AND EXTRA LIGHT IN GALACTIC NUCLEI. II. “CUSP” ELLIPTICALS (2008, background): “The differences grow if we add a degree of freedom and fit a “core-Sérsic” profile, of the form I ∝ [1 + (rb/r)α]γ /α exp {−bn [(rα + rαb )/rαe ]1/αn} (e.g., Graham et al. 2003), which behaves as a single Sérsic profile outside of rb and breaks to a power law of slope γ within rb.”
THE NEXT GENERATION VIRGO CLUSTER SURVEY (NGVS). I. INTRODUCTION TO THE SURVEY (2012, methodology): “The solid curve in Figure 18 shows a coreSérsic model (Graham et al. 2003) fitted to this NGVS composite profile, allowing both the core and global properties to be derived with high precision.”
THE MBH–LSPHEROID RELATION AT HIGH AND LOW MASSES, THE QUADRATIC GROWTH OF BLACK HOLES, AND INTERMEDIATE-MASS BLACK HOLE CANDIDATES (2012, background): “…coincides with the division between core-Sérsic galaxies (which have a central deficit of light relative to the inward extrapolation of their outer Sérsic light profile) and Sérsic galaxies3 which do not (Graham & Guzmán 2003; Graham et al. 2003; Trujillo et al. 2004; Matković & Guzmán 2005).”
Ejection of Supermassive Black Holes from Galaxy Cores (2007, methodology): “As approximate representations of galaxies with binarydepleted cores, we adopt core-Sérsic models (Graham et al. 2003) for our initial conditions.”
A Concise Reference to (Projected) Sérsic R 1/n Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes (2005, background): “Thus, at constant (R/Re), γ is a monotonically increasing function of the Sérsic index n (Graham et al. 2003b).”
The Masses of Nuclear Black Holes in Luminous Elliptical Galaxies and Implications for the Space Density of the Most Massive Black Holes (2006, methodology): “Graham et al. (2003) have criticized the Nuker rb as being highly sensitive to the domain over which the Nuker law was fitted, LAUER ET AL.830 Vol. 662 but their concerns can be refuted by comparing the fitted rb values with those derived from nonparametric methods.”
Dissipation and Extra Light in Galactic Nuclei. I. Gas-Rich Merger Remnants (2008, background): “=( n)" # ð3Þ (e.g., Graham et al. 2003), where rb is the core break radius within which the profile breaks to a power law of slope , re is the effective radius, n is the Sersic index of the outer light profile, and is a parameter describing how rapidly the break occurs.”
The black hole mass – spheroid luminosity relation (2007, background): “Specifically, the central density (prior to core-depletion10 in massive spheroids – requiring the use of the core-Sérsic model, Graham et al. 2003), or the central density of less massive spheroids after modelling and excluding the flux from their additional nuclear components (e.g. Graham &…”
A MegaCam Survey of Outer Halo Satellites. III. Photometric and Structural Parameters (2018, background): “(see, e.g., Jerjen & Binggeli 1997; Graham & Guzmán 2003; Graham et al. 2003; Ferrarese et al. 2006a; Côté et al. 2007).”
Rates of stellar tidal disruption as probes of the supermassive black hole mass function (2014, unknown): “A more complex variant of this is the core-Sersic model (Graham et al. 2003), given by ICS(R) = ĨCS(1+(Rb/R) α)Γ/α exp(−b((Rα+Rαb )/Rαe )1/(nα)).”
A Universal Density Profile for Dark and Luminous Matter? (2005, unknown): “In a recent series of papers, A. Graham and co-workers have shown that the Sérsic law provides a remarkably good fit to the luminosity profiles of stellar spheroids, from dE galaxies to the most luminous ellipticals (Graham 2001, 2002; Graham & Guzman 2003; Graham et al. 2003; Trujillo et al. 2004).”
The Centers of Early-Type Galaxies with Hubble Space Telescope. VI. Bimodal Central Surface Brightness Profiles (2006, methodology): “…Comparisons of smoothed models to smoothed data always look better than unsmoothed 4 It should be noted that rb in the core Sérsic form advanced by Graham et al. (2003) does not correspond to the maximal curvature of the brightness profile and thus is not mathematically equivalent to the Nuker…”