NumCosmoHaloDensityProfileEinasto

Density profile of Einasto type.

This object implements the NcHaloDensityProfile class for the Einasto density profile.

As described NcHaloDensityProfile, we just need to implement the dimensionless 3D density $\hat{\rho}(x)$ [which refers to the virtual function nc_halo_density_profile_eval_dl_density()]. In particular, the Einasto profile is given by \begin{equation} \hat{\rho}(x) = \exp \left[ - \frac{2}{\alpha} \left( x^\alpha - 1 \right) \right], \end{equation} where $x = r/r_s$ and $r_s$ is the scale radius and $\alpha$ is a parameter that defines how the profile steepens with slope.

Both the mass $M_\Delta$ and the scale profile $\rho_s$ are written in terms of the integral $I_{x^2\hat\rho}(c_\Delta)$ [virtual function nc_halo_density_profile_eval_dl_spher_mass()]. The respective Einasto implementation provides \begin{equation} I_{x^2\hat\rho}(x) = \left(\frac{\alpha}{2}\right)^{3/\alpha} \frac{e^{2/\alpha}}{\alpha} \Gamma \left( \frac{3}{\alpha} \right) \left[1 - \frac{\Gamma \left( 3/\alpha, 2c_{\Delta}^\alpha / \alpha\right)}{\Gamma \left( 3/\alpha \right)} \right], \end{equation} where $c_{\Delta}$ is the concentration parameter.

References: Einasto (1965), arXiv:1712.04512. $\alpha$ parameter range values: Gao et al. (2008) https://ui.adsabs.harvard.edu/abs/2008MNRAS.387..536G/abstract, Dutton \& Maccio (2014) https://academic.oup.com/mnras/article/441/4/3359/1209689.