
%0 Journal Article
%A Graham, Alister W. 
%A Driver, Simon P. 
%T A Concise Reference to (Projected) S&#233;rsic <emph type="3">R</emph><emph type="7">1/</emph><emph type="7">n</emph> Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes
%J Publications of the Astronomical Society of Australia
%D 2005/04/28
%V 22
%N 2
%P 118-127
%K galaxies: structure &#8212; galaxies: fundamental parameters &#8212; methods: analytical &#8212; methods: data analysis
%R https://doi.org/10.1071/AS05001
%U https://www.publish.csiro.au/paper/AS05001 
%X Given the growing use of S&#233;rsic&#39;s (1963, 1968) R1/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&#8211;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 &#39;concentration&#39; of an R1/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 S&#233;rsic 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 S&#233;rsic index n and the number of effective radii sampled. Illustrative figures are provided throughout. Finally, the core&#8211;S&#233;rsic model, consisting of an inner power-law and an outer S&#233;rsic function, is presented. 
