A precise analytical approximation for the deprojection of the Sérsic profile
Abstract
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 massorbit 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 twodimensional tenthorder 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 LGMbased 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/R_{e} < 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.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 March 2020
 DOI:
 10.1051/00046361/201937202
 arXiv:
 arXiv:2001.03121
 Bibcode:
 2020A&A...635A..20V
 Keywords:

 methods: numerical;
 galaxies: elliptical and lenticular;
 cD;
 galaxies: structure;
 globular clusters: general;
 galaxies: bulges;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 8 pages, 6 figures, 1 table, accepted by Astronomy &