A Concise Reference to (Projected) Sérsic R 1/n Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes

By Alister W. Graham, S. Driver. Publications Astronomical Society of Australia, 2005

403 citations recorded by the source corpus.

Abstract Given the growing use of Sérsic's (1963, 1968) R 1/n model for describing the stellar distributions in galaxies, and the lack of any single reference that provides the various associated mathematical expressions, we have endeavoured to compile such a resource here. We present the standard intensity profile, and its various guises such as the luminosity, surface-brightness, and aperture–magnitude profile. Expressions to transform the effective surface brightness into the mean effective and central surface brightness are also given, as is the expression to transform between effective radii and exponential scale-lengths. We additionally provide expressions for deriving the ‘concentration’ of an R 1/n profile, and two useful equations for the logarithmic slope of the light-profile are given. Petrosian radii and fluxes are also derived for a range of Sérsic profiles and compared with the effective radii and total flux. Similarly, expressions to obtain Kron radii and fluxes are presented as a function of the Sérsic index n and the number of effective radii sampled. Illustrative figures are provided throughout. Finally, the core–Sérsic model, consisting of an inner power-law and an outer Sérsic function, is presented.

Subfields: Astronomy and Astrophysics, Instrumentation

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Citations in the corpus

Inclination- and dust-corrected galaxy parameters: bulge-to-disc ratios and size–luminosity relations (2008, methodology): “Using equations 7, 9 and 12 from Graham & Driver (2005), one has an expression involving M, Re, µ0 and n for any Sérsic profile.”
GAMA: towards a physical understanding of galaxy formation (2009, methodology): “For those systems with z > 0.1, a single elliptical Sérsic profile will be measured (Graham and Driver 2005), enough to separate concentrated and diffuse systems and measure ellipticities and inclinations.”
FEEDBACK FROM CENTRAL BLACK HOLES IN ELLIPTICAL GALAXIES. III. MODELS WITH BOTH RADIATIVE AND MECHANICAL FEEDBACK (2010, background): “Such “cuspy” ellipticals provide one of the two important branches of the elliptical galaxy sequence (e.g., see Graham 2004, Graham & Driver 2005, Lauer et al. 2005, Kormendy et al. 2009; see also Ciotti 2009b).”
The Millennium Galaxy Catalogue: bulge–disc decomposition of 10 095 nearby galaxies (2006, background): “The intensity profile of the spheroidal (bulge) components, Ib(R), can be described using a Sérsic function (Sérsic 1968; Graham & Driver 2005): Ib(R) = Ie exp {−bn[(R/Re)1/n − 1]}, (1) where the effective radius, Re, encloses half the total bulge luminosity, and Ie is the intensity at the…”
Total Galaxy Magnitudes and Effective Radii from Petrosian Magnitudes and Radii (2005, background): “3 A useful compilation of various Sérsic expressions can be found in Graham & Driver (2005).”
Families of dynamically hot stellar systems over 10 orders of magnitude in mass (2011, methodology): “For calculating these limits, we used equations (9) and (12) from Graham & Driver (2005), approximating 〈µ〉e,abs ≈ 〈µ〉e.”
THE LUMINOSITY PROFILE AND STRUCTURAL PARAMETERS OF THE ANDROMEDA GALAXY (2011, background): “See Graham & Driver (2005) for more details about the Sérsic function.”
Empirical Models for Dark Matter Halos. II. Inner Profile Slopes, Dynamical Profiles, and ρ/σ3 (2006, methodology): “Although we use the exact solution for bn, coming from Γ(2n) = 2×γ(2n, bn) (see Graham & Driver 2005), bn can be approximated by 2n−1/3 + 0.009876/n for values of n & 0.5 (Prugniel & Simien 1997).”
Radiative Feedback from Massive Black Holes in Elliptical Galaxies: AGN Flaring and Central Starburst Fueled by Recycled Gas (2007, neutral): “…observed in ellipticals: however, in the final model we note the presence of a central ( 30 pc) nucleus originated by star formation that stays above the best-fit profile, similar to the light spikes characterizing ‘‘nucleated’’ galaxies (see, e.g., Graham & Driver 2005; Coté et al. 2006).”
A Log-Quadratic Relation for Predicting Supermassive Black Hole Masses from the Host Bulge Sérsic Index (2006, methodology): “The quantity n is the inverse exponent from the best-fitting Sérsic (1963) R1/n light profile (see Graham & Driver 2005 for a review of thismodel).”
BULGES OF NEARBY GALAXIES WITH SPITZER: SCALING RELATIONS IN PSEUDOBULGES AND CLASSICAL BULGES (2010, background): “(Also, see Graham & Driver 2005 for a review of the properties of the Sérsic function.)”
The Millennium Galaxy Catalogue : morphological classification and bimodality in the colour-concentration plane (2006, methodology): “The software uses the standard Sérsic profile (Sérsic 1963; Graham & Driver 2005) returning the total flux, Sérsic index (n), half-light radius (Re), ellipticity, position angle and positional and background offsets.”
COSMOS Morphological Classification with the Zurich Estimator of Structural Types (ZEST) and the Evolution Since z = 1 of the Luminosity Function of Early, Disk, and Irregular Galaxies (2006, background): “For a surface brightness distribution described by a de Vaucouleurs or an exponential profile, a value of η = 0.2 is reached at RP ∼ 1.8R1/2 and RP ∼ 2.2R1/2, respectively (with R1/2 the half–light or “effective” radius of the galaxy, Graham & Driver (2005)).”
Nuclear star clusters (2009, methodology): “…that describe the observed NSC shape as a convolution of the instrumental point spread function (PSF) with an analytical function used to describe Galactic GCs or galaxy light profiles, e.g. the widely used King models (King 1962) or Sérsic profiles (Sérsic 1968; Graham and Driver 2005).”
The black hole mass – spheroid luminosity relation (2007, background): “3 A modern review of the Sérsic model can be found in Graham & Driver (2005).”
MegaMorph - multiwavelength measurement of galaxy structure: complete Sersic profile information from modern surveys (2012, background): “…uncertainties as returned byGALFIT, 8 For a more detailed discussion of this effect of Sérsic profiles, please see external literature, e.g. Graham & Driver (2005) c© 2012 RAS, MNRAS000, 1–41 which have been shown to underestimate the true values (H07)and should be interpreted as a lower…”