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Analytical expressions for the deprojected Sérsic model

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Abstract
The Sersic model has become the standard for parametrizing the surface brightness distribution of early-type galaxies and bulges of spiral galaxies. A major problem is that the deprojection of the Sersic surface brightness profile to a luminosity density cannot be executed analytically for general values of the Sersic index. We use Mellin integral transforms to derive an analytical expressions for the luminosity density in terms of the Fox H function for all values of the Sersic index. We derive simplified expressions for the luminosity density, cumulative luminosity, and gravitational potential in terms of the Meijer G function for all rational values of the Sersic index, and we investigate their asymptotic behaviour at small and large radii. As implementations of the Meijer G function are currently available both in symbolic computer algebra packages and as high-performance computing code, our results open up the possibility to calculate the density of the Sersic models to arbitrary precision.
Keywords
methods: analytical, galaxies: photometry, MULTI-GAUSSIAN EXPANSION, EARLY-TYPE GALAXIES, SURFACE BRIGHTNESS GALAXIES, UNIVERSAL DENSITY PROFILE, DARK-MATTER HALOES, STELLAR-SYSTEMS, ELLIPTIC GALAXIES, LUMINOSITY LAW, STRUCTURAL PARAMETERS, KINEMATICAL MODELS

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Citation

Please use this url to cite or link to this publication:

Chicago
Baes, Maarten, and Gianfranco Gentile. 2011. “Analytical Expressions for the Deprojected Sérsic Model.” Astronomy & Astrophysics 525.
APA
Baes, M., & Gentile, G. (2011). Analytical expressions for the deprojected Sérsic model. ASTRONOMY & ASTROPHYSICS, 525.
Vancouver
1.
Baes M, Gentile G. Analytical expressions for the deprojected Sérsic model. ASTRONOMY & ASTROPHYSICS. 2011;525.
MLA
Baes, Maarten, and Gianfranco Gentile. “Analytical Expressions for the Deprojected Sérsic Model.” ASTRONOMY & ASTROPHYSICS 525 (2011): n. pag. Print.
@article{1241064,
  abstract     = {The Sersic model has become the standard for parametrizing the surface brightness distribution of early-type galaxies and bulges of spiral galaxies. A major problem is that the deprojection of the Sersic surface brightness profile to a luminosity density cannot be executed analytically for general values of the Sersic index. We use Mellin integral transforms to derive an analytical expressions for the luminosity density in terms of the Fox H function for all values of the Sersic index. We derive simplified expressions for the luminosity density, cumulative luminosity, and gravitational potential in terms of the Meijer G function for all rational values of the Sersic index, and we investigate their asymptotic behaviour at small and large radii. As implementations of the Meijer G function are currently available both in symbolic computer algebra packages and as high-performance computing code, our results open up the possibility to calculate the density of the Sersic models to arbitrary precision.},
  articleno    = {A136},
  author       = {Baes, Maarten and Gentile, Gianfranco},
  issn         = {0004-6361},
  journal      = {ASTRONOMY \& ASTROPHYSICS},
  keyword      = {methods: analytical,galaxies: photometry,MULTI-GAUSSIAN EXPANSION,EARLY-TYPE GALAXIES,SURFACE BRIGHTNESS GALAXIES,UNIVERSAL DENSITY PROFILE,DARK-MATTER HALOES,STELLAR-SYSTEMS,ELLIPTIC GALAXIES,LUMINOSITY LAW,STRUCTURAL PARAMETERS,KINEMATICAL MODELS},
  language     = {eng},
  pages        = {7},
  title        = {Analytical expressions for the deprojected S{\'e}rsic model},
  url          = {http://dx.doi.org/10.1051/0004-6361/201015716},
  volume       = {525},
  year         = {2011},
}

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