A precise analytical approximation for the deprojection of the Sersic profile

The Sersic 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 Sersic 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 Sersic index (n less than or similar to 1.5). We derived a more precise analytical approximation to the deprojected Sersic 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 Sersic 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 Sersic profiles with those of other popular simple models.