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A Concise Reference to (Projected) Sérsic R1/n Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes

Published online by Cambridge University Press:  05 March 2013

Alister W. Graham  and
Simon P. Driver
Alister W. Graham*
Affiliation:
Mount Stromlo and Siding Spring Observatories, Australian National University, Weston Creek ACT 2611, Australia
Simon P. Driver
Affiliation:
Mount Stromlo and Siding Spring Observatories, Australian National University, Weston Creek ACT 2611, Australia
*
BCorresponding author. Email: Graham@mso.anu.edu.au
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Abstract

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Given the growing use of Sérsic'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–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 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 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.

Keywords

galaxies: structuregalaxies: fundamental parametersmethods: analyticalmethods: data analysis
Type
Research Article
Information
Publications of the Astronomical Society of Australia , Volume 22 , Issue 2 , 2005 , pp. 118 - 127
Copyright
Copyright © Astronomical Society of Australia 2005

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