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 Sérsic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.

Aims. Both numerical simulations and observational evidence indicate that the outer regions of galaxies and dark matter haloes are typically mildly to significantly radially anisotropic. The inner regions can be significantly non-isotropic, depending on the dynamical formation and evolution processes. In an attempt to break the lack of simple dynamical models that can reproduce this behaviour, we explore a technique to construct dynamical models with an arbitrary density and an arbitrary anisotropy profile. Methods. We outline a general construction method and propose a more practical approach based on a parameterized anisotropy profile. This approach consists of fitting the density of the model with a set of dynamical components, each of which have the same anisotropy profile. Using this approach we avoid the delicate fine-tuning difficulties other fitting techniques typically encounter when constructing radially anisotropic models.Results. We present a model anisotropy profile that generalizes the Osipkov-Merritt profile, and that can represent any smooth monotonic anisotropy profile. Based on this model anisotropy profile, we construct a very general seven-parameter set of dynamical components for which the most important dynamical properties can be calculated analytically. We use the results to look for simple one-component dynamical models that generate simple potential-density pairs while still supporting a flexible anisotropy profile. We present families of Plummer and Hernquist models in which the anisotropy at small and large radii can be chosen as free parameters. We also generalize these two families to a three-parameter family that self-consistently generates the set of Veltmann potential-density pairs. These new analytical models are an important step forward compared to isotropic or Osipkov-Merritt models and can be used to generate the initial conditions for realistic simulations of galaxies or dark matter haloes.

The Sérsic model is the de facto standard to describe the surface brightness distribution of hot stellar systems. An important inconvenience of this analytical model is that the corresponding luminosity density and associated properties cannot be expressed using elementary functions or even standard special functions. We present a set of compact and elegant analytical expressions for the luminosity density, cumulative luminosity, and potential for the Sérsic model in terms of the Fox H function for general values of the Sérsic index. Furthermore, we present explicit series expansions of these quantities and discuss the asymptotic behaviour. Our analysis completes earlier work and demonstrates the power of the underestimated Fox H function as a tool for analytical work.

No abstract