Publications of the Astronomical Society of Australia

Research Article

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

Alister W. Grahama1 c1 and Simon P. Drivera1

a1 Mount Stromlo and Siding Spring Observatories, Australian National University, Weston Creek ACT 2611, Australia


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.

(Received January 07 2005)

(Accepted February 25 2005)


  • galaxies: structure;
  • galaxies: fundamental parameters;
  • methods: analytical;
  • methods: data analysis


c1 Corresponding author. Email: