The Sérsic model is known to fit well the surface brightness ( or surface density ) profiles of elliptical galaxies and galaxy bulges , and possibly for 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 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 \lesssim 1.5 ) .
We have derived a more precise analytical approximation to the deprojected Sérsic density profile by fitting two-dimensional 10th-order polynomials to the differences of the logarithms of the numerical deprojection and of the analytical approximation by ( , LGM ) of the density profile on one hand and of the mass profile on the other .
Our LGM-based polynomial fits have typical relative precision better than 0.2 % for both density and mass profiles , for Sérsic indices 0.5 \leq n \leq 10 and radii 0.001 < r / R _ { e } < 1000 .
Our approximation is much more precise than those of LGM , , for non-half-integer values of the index , and of for non-one-tenth-integer values with n \lesssim 3 , and are nevertheless more than 0.2 % precise for larger Sérsic indices , for both density and mass profiles .
An appendix compares the deprojected Sérsic profiles with those of the popular simple models from , , , , and .