The lensing properties of the Einasto profile

TL;DR

This paper derives exact analytical expressions for the lensing properties of the Einasto profile using special functions, facilitating its application in strong and weak lensing studies of dark matter halos.

Contribution

It provides the first complete analytical formulas for the Einasto profile's lensing properties in terms of Fox H and Meijer G functions, enabling easier use in lensing analyses.

Findings

Derived exact surface mass density in terms of Fox H-function.

Expressed lensing quantities using Meijer G-function for rational Einasto indices.

Compared Einasto and Sersic profiles, highlighting differences in lensing behavior.

Abstract

In recent high resolution N-body CDM simulations, it has been had found that nonsingular three-parameter models, e.g. the Einasto profile has a better performance better than the singular two-parameter models, e.g. the Navarro, Frenk and White in the fitting of a wide range of dark matter halos. A problem with this profile is that the surface mass density is non-analytical for general values of the Einasto index. Therefore, its other lensing properties have the same problem. We obtain an exact analytical expression for the surface mass density of the Einasto profile in terms of the Fox H-function for all values of the Einasto index. With the idea of facilitate the use of the Einasto profile in lensing studies, we calculate the surface mass density, deflection angle, lens equation, deflection potential, magnification, shear and critical curves of the Einasto profile in terms of the Meijer G-function for all rational values of the Einasto index. The Meijer G-function have been implemented in several commercial and open-source computer algebra systems, thus the use of the lensing properties of the Einasto profile in strong and weak lensing studies is straighforward. We also compare the S\'ersic and Einasto surface mass densities profiles and found differences between them. This implies that the lensing properties are not equal for both profiles.