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GEnum ╰── NcHaloDensityProfileEinastoParams GObject ╰── NcmModel ╰── NcHaloDensityProfile ╰── NcHaloDensityProfileEinasto
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.
NcHaloDensityProfileEinasto * nc_halo_density_profile_einasto_new (const NcHaloDensityProfileMassDef mdef,const gdouble Delta);
This function returns the NcHaloDensityProfileEinasto implementation of
NcHaloDensityProfile setting “mass-def” to mdef
and “Delta” to Delta
.
#define NC_HALO_DENSITY_PROFILE_EINASTO_LOCAL_SPARAM_LEN (NC_HALO_DENSITY_PROFILE_EINASTO_SPARAM_LEN - NC_HALO_DENSITY_PROFILE_SPARAM_LEN)
#define NC_HALO_DENSITY_PROFILE_EINASTO_DEFAULT_ALPHA (0.25)