Dark Matter Profile Shapes

Class providing the shape parameter \(\alpha\) of dark matter halo density profiles such as the Einasto profile, \(\rho(r) \propto \exp\{-\frac{2}{\alpha}[(r/r_\mathrm{s})^\alpha - 1]\}\). The shape parameter controls the curvature of the profile near the center and is typically fit from \(N\)-body simulations as a function of halo mass and redshift.

Default implementation: darkMatterProfileShapeGao2008

Methods

shape → double precision

Returns the dimensionless shape parameter \(\alpha\) of the Einasto dark matter density profile for the halo in node, controlling the curvature of the inner profile with typical values in the range \(0.1\)–\(0.3\) from N-body simulations.

• type(treeNode), intent(inout) :: node

darkMatterProfileShapeBrown2021

A dark matter profile shape class in which the shape parameter for Einasto density profiles is computed using a fitting function from Brown et al. (2022):

\[\begin{split}\alpha = \left\{ \begin{array}{ll} 8.52 \times 10^{-4} \nu_\alpha^4 + 0.166 & \hbox{ if } \nu_\alpha < 3.541 \\ 0.3 & \hbox{ if } \nu_\alpha \ge 3.541, \end{array} \right.\end{split}\]

where \(\nu_\alpha=\delta_\mathrm{c}(t)/\sigma_\alpha(M)\) is the peak height of the halo. The truncation at \(\alpha = 0.3\) is included since Brown et al. (2022)’s fits do not probe this region and extremely large values of \(\alpha\) are numerically troublesome.

This implementation accepts any cosmologicalMassVarianceClass object for use in computing for computing \(\sigma_\mathrm{c}(M)\). However, Brown et al. (2022) recommend using \(\sigma_\mathrm{c}(M)\) computed using a generalized top-hat window function (powerSpectrumWindowFunctionTopHatGeneralized) with \(\mu_\mathrm{g}=0.01\).

darkMatterProfileShapeGao2008

A dark matter profile shape class in which the shape parameter for Einasto density profiles is computed using a fitting function from Gao et al. (2008):

\[\begin{split}\alpha = \left\{ \begin{array}{ll} 0.155 + 0.0095\nu^2 & \hbox{ if } \nu < 3.907 \\ 0.3 & \hbox{ if } \nu \ge 3.907, \end{array} \right.\end{split}\]

where \(\nu=\delta_\mathrm{c}(t)/\sigma(M)\) is the peak height of the halo. The truncation at \(\alpha = 0.3\) is included since Gao et al. (2008)’s fits do not probe this region and extremely large values of \(\alpha\) are numerically troublesome.

(Default implementation)

Parameters

• [scatter] (default 0.0d0) — The scatter (in dex) to assume in the halo concentration distribution at fixed mass.

darkMatterProfileShapeKlypin2015

Dark matter halo shape parameters are computed using the algorithm of Klypin et al. (2016).

Parameters

• [sample] (default var_str('all')) — The sample to use for the halo shape parameter algorithm of Klypin et al. (2016).

• [sample] (default var_str('planck200CritRelaxedMass')) — The sample to use for the halo concentration algorithm of Klypin et al. (2016).