Functions

Object Hierarchy

    GObject
    ╰── NcDensityProfile
        ╰── NcDensityProfileNFW

Description

This object implements the NcDensityProfile class for a Navarro-Frenk-White (NFW) density profile.

The NFW profile is defined as \begin{equation} \rho(r) = \frac{\rho_s}{(r/r_s)(1 + r/r_s)^2}, \end{equation} where $\rho_s$ is ... and $r_s$ is the scale radius, \begin{equation} r_s \equiv \frac{r_{vir}}{c} = \left(\frac{3}{4\pi} \frac{M}{\Delta \overline{\rho}_m(z) c^3}\right)^{1/3}, \end{equation} where $M$ is the virial mass, $\overline{\rho}_m(z)$ is the mean matter density, $\Delta$ is the overdensity parameter (as defined in NcMultiplicityFunc).

The normalized NFW density profile ($u_M(r) = \rho(r) / M$) in the Fourier space is given by \begin{equation} \tilde{u}_M(k) = \frac{1}{m_{nfw}(c)} \left[ \sin(x) \left[\text{Si}((1+c)x) - \text{Si}(x) \right] + \cos(x) \left[\text{Ci}((1+c)x) - \text{Ci}(x) \right] - \frac{\sin(cx)}{(1+c)x} \right], \end{equation} where $x \equiv (1+z)kr_s$, and $\text{Si}(x)$ and $\text{Ci}(x)$ are the sine and cosine integrals, namely. \begin{equation} \text{Si}(x) = \int_0^x \frac{\sin(t)}{t} dt \quad \text{and} \quad \text{Ci}(x) = - \int_x^\infty \frac{\cos(t)}{t} dt. \end{equation}

The concentration parameter is (change this!) \begin{equation} c(M, z) = A_{vir} \left( \frac{M}{2 \times 10^{12} \text{h}^{-1}M_{\odot}}\right)^{B_{vir}} (1+z)^{C_{vir}}. \end{equation}

References: astro-ph/0206508 and arxiv:1010.0744.

Functions

NcDensityProfile *
nc_density_profile_nfw_new (void);

Types and Values