Analytical properties of Einasto dark matter haloes

Details Analytical properties of Einasto dark matter haloes Analytical properties of Einasto dark matter haloes

2012-02-23

arxiv.org/abs/1202.5242v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

10 pages, 2 figures. Accepted for publication in Astronomy and Astrophysics

Scientific paper

10.1051/0004-6361/201118543

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.

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