A Concise Reference to (Projected) Sersic R¹Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes

Given the growing use of Sersic's (1963, 1968) Rⁿmodel 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^liⁿprofile, 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 Sersic 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 Sersic index n and the number of effective radii sampled. Illustrative figures are provided throughout. Finally, the core–Sersic model, consisting of an inner power-law and an outer Sersic function, is presented.