Volume 635, March 2020
|Number of page(s)||8|
|Published online||28 February 2020|
A precise analytical approximation for the deprojection of the Sérsic profile
Institut d’Astrophysique de Paris (UMR 7095: CNRS & Sorbonne Université), 98 Bis Bd Arago, 75014 Paris, France
Accepted: 8 January 2020
The Sérsic model shows a close fit to the surface brightness (or surface density) profiles of elliptical galaxies and galaxy bulges, and possibly also those of dwarf spheroidal galaxies and globular clusters. The deprojected density and mass profiles are important for many astrophysical applications, in particular for mass-orbit modeling of these systems. However, the exact deprojection formula for the Sérsic model employs special functions that are not available in most computer languages. We show that all previous analytical approximations to the 3D density profile are imprecise at low Sérsic index (n ≲ 1.5). We derived a more precise analytical approximation to the deprojected Sérsic density and mass profiles by fitting two-dimensional tenth-order polynomials to the residuals of the analytical approximations by Lima Neto et al. (1999, MNRAS, 309, 481; LGM) for these profiles, relative to the numerical estimates. Our LGM-based polynomial fits have typical relative precision better than 0.2% for both density and mass profiles, for Sérsic indices 0.5 ≤ n ≤ 10 and radii 0.001 < r/Re < 1000. Our approximation is much more precise than previously published approximations (except, in some models, for a few discrete values of the index). An appendix compares the deprojected Sérsic profiles with those of other popular simple models.
Key words: methods: numerical / galaxies: elliptical and lenticular, cD / galaxies: structure / globular clusters: general / galaxies: bulges
© E. Vitral and G. A. Mamon 2020
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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