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

Abstract

Given the growing use of Sérsic's (1963Sérsic's ( , 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.

Analytical expressions for the deprojected Sérsic model

“…We derived simplified expressions for ν(r) in terms of the Meijer G function for all rational values of m, and for integer values of m our results are equivalent to the expressions found by Mazure & Capelato (2002). Our analytical calculations complement other theoretical studies of the Sérsic model (Ciotti 1991;Ciotti & Lanzoni 1997;Ciotti & Bertin 1999;Trujillo et al 2001;Cardone 2004;Graham & Driver 2005;Elíasdóttir & Möller 2007) and, given the extended literature on the analytical properties of the Meijer G function, can be used to further examine the properties of this model analytically. We have investigated the asymptotic behaviour of the luminosity density at small and large radii, and find a rich variety in behviour depending on the value of m. We also derived analytical expression for derived quantities, in particular the cumulative luminosity and the gravitational potential.…”

“…Ciotti & Bertin (1999) provide a full asymptotic expansion of the dimensionless scale factor b of the Sérsic model. Graham & Driver (2005) present a compendium of mathematical formulae on photometric parameters such as Kron magnitues and Petrosian indices, and Cardone (2004) and Elíasdóttir & Möller (2007) investigate the lensing properties. A major problem with the Sérsic models is that the deprojection of the surface brightness profile to a luminosity density is in general nonanalytical.…”

Depleted cores, multicomponent fits, and structural parameter relations for luminous early-type galaxies

“…The review by Graham & Driver (2005) describes the Sérsic model in greater detail. The Sérsic model fits the surface brightness profiles of the low-and intermediate-luminosity (MV > ∼ − 21.5 mag) spheroids all the way to the very inner region.…”

What will blue compact dwarf galaxies evolve into?

“…The exponentially fitted LSB-component was integrated up to R tail and was then continued with the observed data points of the tail. From this LSB+tail profile -also taking the possible inner flattening into account -we derive the Petrosian radius (Petrosian 1976;Graham & Driver 2005), where the intensity drops to a fifth of the mean intensity within that radius (Blanton et al 2001;Yasuda et al 2001). (g-r) (g-i)…”