Analytical properties of Einasto dark matter haloes

TL;DR

This paper derives analytical formulas for the surface density and lensing properties of Einasto dark matter haloes using advanced mathematical functions, improving precision in modeling and comparing them to Sersic profiles.

Contribution

It provides the first closed-form expressions for the Einasto surface density using Mellin transforms and special functions, enhancing analytical understanding of dark matter halo lensing.

Findings

Derived a closed-form formula for Einasto surface density.

Compared lensing properties of Einasto and Sersic profiles.

Enabled high-precision calculations for dark matter halo models.

Abstract

Recent high-resolution N-body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matter haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the S\'ersic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.