On the estimation of galaxy structural parameters: the Sérsic model

By Ignacio Trujillo, Alister W. Graham, Nicola Caon. 2001

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This paper addresses some questions which have arisen from the use of the Sersic r1/n law in modelling the luminosity profiles of early-type galaxies. The first issue deals with the trend between the half-light radius and the structural parameter n. We show that the correlation between these two parameters is not only real, but also a natural consequence from the previous relations found to exist between the model-independent parameters: total luminosity, effective radius and effective surface brightness. We also define a new galaxy concentration index which is largely independent of the image exposure depth, and is shown to be monotonically related with n. The second question concerns the curious coincidence between the form of the Fundamental Plane and the coupling between 〈I〉e and re when modelling a light profile. We explain, through a mathematical analysis of the Sersic law, why the quantity re〈I〉e0.7 appears almost constant for an individual galaxy, regardless of the value of n (over a large range) adopted in the fit to the light profile. Consequently, Fundamental Planes of the form re〈I〉e0.7∝σ0x (for any x, and where σ0 is the central galaxy velocity dispersion) are insensitive to galaxy structure. Finally, we address the problematic issue of the use of model-dependent galaxy light-profile parameters versus model-independent quantities for the half-light radii, mean surface brightness and total galaxy magnitude. The former implicitly assume that the light-profile model can be extrapolated to infinity, while the latter quantities, in general, are derived from a signal-to-noise ratio truncated profile. We quantify (mathematically) how these parameters change as one reduces the outer radius of an r1/n profile, and reveal how these can vary substantially when n≥4.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/29169ebd5337ec0036de9a523af7d9c2310d4573

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Citations in the corpus

A Concise Reference to (Projected) Sérsic R 1/n Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes (2005, background): “It was actually, in part, because of the unstable nature of the popular concentration indices that Trujillo et al. (2001c) introduced the notably more stable index given in Equations (20) and (21).”
A Correlation between Galaxy Light Concentration and Supermassive Black Hole Mass (2001, background): “More luminous (massive) bulges have larger values of n (Trujillo et al. 2001b, and references therein), greater central concentrations, deeper gravitational potential wells with steeper central gradients (Ciotti 1991, Trujillo et al. 2001a), and more massive SMBHs.”
Fundamental Planes and the Barless MBH-σ Relation for Supermassive Black Holes (2008, background): “…connection between Mbh and the radial structure in the stellar distribution of the host bulge (see also Graham et al. 2007, their Section 1), and hence the need to advance beyond R1/4 models and their associated luminosity/mass dependent biases (e.g., Trujillo et al. 2001; Brown et al. 2003).”
STRUCTURE AND FORMATION OF ELLIPTICAL AND SPHEROIDAL GALAXIES (2008, background): “These correlations have been confirmed by D’Onofrio et al. (1994); Graham et al. (1996); Graham & Colless (1997); Graham (2001); Trujillo et al. (2001, 2002), Ferrarese et al. (2006a), and others.”
GEMS: Galaxy Fitting Catalogs and Testing Parametric Galaxy Fitting Codes: GALFIT and GIM2D (2007, background): “…disks (n = 1) and the R1/4-law (de Vaucouleurs law) profiles typical of luminous early-type galaxy (n = 4) (e.g., deVaucouleurs 1948; Freeman 1970); fitting with this profile has been explored in detail in a number of works (e.g., Simard 1998, 2002; Graham et al. 2005; Trujillo et al. 2001).”
The massive end of the luminosity and stellar mass functions: Dependence on the fit to the light profile (2013, background): “…facts that (a) Petrosian magnitudes underestimate the total light when the light profile has extended wings, and (b) this is particularly an issue at the bright end (e.g. Binggeli & Cameron 1991; Blanton et al. 2001; Trujillo et al. 2001; Andreon 2002; Brown et al. 2003; Graham et al. 2005).”
Inclination- and dust-corrected galaxy parameters: bulge-to-disc ratios and size–luminosity relations (2008, methodology): “Underestimation also occurs when using R1/4 models to describe systems with n > 4 (see Trujillo et al. 2001, their Figure 4) which may explain why Bernardi et al. (2003) report that R ∼ L0.”
Weak homology of elliptical galaxies (2002, background): “In the discussion of the properties of the FP, it has often been noted (see Kelson et al. 2000a; Treu et al. 2001a; see also Trujillo et al. 2001) that much of our uncertainties in relation to the parameters derived by fitting the photometric profile is resolved by an unexpected circumstance, that…”
SUPERDENSE MASSIVE GALAXIES IN THE NEARBY UNIVERSE (2009, background): “…note that the total galaxy luminosity within 3re is (for a Sérsic surface brightness profile with a n=4) only a 1.6 larger than that within 1re (Trujillo et al. 2001), so if the outer regions were the clue for the strong differences in luminosity-weighted age between both galaxy…”
The ATLAS3D project XV: benchmark for early-type galaxies scaling relations from 260 dynamical models: mass-to-light ratio, dark matter, fundamental plane and mass plane (2012, background): “Column (13): Galaxy concentration conc ≡ L(Re/3)/L(Re) (Trujillo et al. 2001), where L(R) is the light of the circularized MGE model contained within the radius R. Column (14): ellipticity of the galaxy light distribution.”
The Velocity Dispersion Function of Early-Type Galaxies (2003, background): “Recent work (e.g. Trujillo et al. 2001) has revived interest in Sersic’s (1968) generalization of the deVaucouleur (1/4)-profile to (1/n)-profiles.”
Total Galaxy Magnitudes and Effective Radii from Petrosian Magnitudes and Radii (2005, background): “…corrections outlined in this study cannot be applied in such circumstances, at least until the radii are corrected for seeing (e.g., Trujillo et al. 2001b,c) We also direct readers to Blanton et al. (2001) who present a study of how the SDSS Petrosian magnitudes are affected by…”
HST Photometry of Dwarf Elliptical Galaxies in Coma, and an Explanation for the Alleged Structural Dichotomy between Dwarf and Bright Elliptical Galaxies (2003, methodology): “We model individual profiles as a combination of a PSF-convolved R1/n bulge model (Trujillo et al. 2001) and either a point-source or a PSF-convolved central Gaussian.”