Class
NumCosmoWLSurfaceMassDensity
Description [src]
class NumCosmo.WLSurfaceMassDensity : NumCosmoMath.Model
{
/* No available fields */
}Weak lensing surface mass density.
This object implements the projected surface mass density and related quantities, such as the convergence and tangential shear.
The projected surface mass density is [nc_wl_surface_mass_density_sigma()]
\begin{equation}\label{eq:sigma}
\Sigma (R) = \int \mathrm{d}\chi \, \rho\left(\sqrt{R^2 + \chi^2} \right),
\end{equation}
where $\rho(r)$ is the three-dimensional mass density profile (NcHaloDensityProfile), $r^2 = R^2 + \chi^2$ is a three-dimensional vector in space, $R$ is a
two-dimensional vector from the halo center. In particular, we consider a projection $\Sigma (R)$ onto the lens plane.
$\chi$ is the distance along the line of sight.
The mean surface mass density within a circular aperture of radius $R$ is, [nc_wl_surface_mass_density_sigma_mean()] \begin{equation}\label{eq:sigma_mean} \overline{\Sigma} (<R) = \frac{2}{R^2} \int_0^R \mathrm{d}R^\prime \, R^\prime \Sigma (R^\prime). \end{equation}
The convergence $\kappa (R)$ [nc_wl_surface_mass_density_convergence()] and the shear $\gamma(R)$ [nc_wl_surface_mass_density_shear()] are given by, respectively, \begin{equation}\label{eq:convergence} \kappa (R) = \frac{\Sigma (R)}{\Sigma_{crit}}, \end{equation} * \begin{equation}\label{eq:shear} \gamma (R) = \frac{\Delta\Sigma (R)}{\Sigma_{crit}} = \frac{\overline{\Sigma} (<R) - \Sigma (R)}{\Sigma_{crit}}, \end{equation} where $\Sigma_{crit}$ is the critical surface density [nc_wl_surface_mass_density_sigma_critical()], \begin{equation}\label{eq:sigma_critical} \Sigma_{crit} = \frac{c^2}{4\pi G} \frac{D_s}{D_l D_{ls}}. \end{equation} where $c^2$ is the speed of light squared [ncm_c_c2()], $G$ is the gravitational constant [ncm_c_G()], $D_s$ and $Dl$ are the angular diameter distances to the source and lens, respectively, and $D_{ls}$ is the angular diameter distance between the lens and source.
See, e.g., [Mandelbaum (2006)][XMandelbaum2006], [Umetsu (2012)][XUmetsu2012], [Applegate (2014)][XApplegate2014], [Melchior (2017)][XMelchior2017], [Parroni (2017)][XParroni2017].
Usually $z_{lens} = z_{cluster}, but we define these as two different arguments in order to handle cases where shear signal has been rescaled to a different cluster redshift (following D. Applegate’s code.).
Constructors
nc_wl_surface_mass_density_new
This function allocates memory for a new NcWLSurfaceMassDensity object and sets its properties to the values from
the input arguments.
Functions
nc_wl_surface_mass_density_clear
Atomically decrements the reference count of smd by one. If the reference count drops to 0,
all memory allocated by smd is released. Set pointer to NULL.
Instance methods
nc_wl_surface_mass_density_convergence
Computes the convergence $\kappa(R)$ at R, see Eq $\eqref{eq:convergence}$.
nc_wl_surface_mass_density_convergence_infinity
Computes the convergence $\kappa_\infty(R)$ at R, see Eq $\eqref{eq:convergence}$, and sources at infinite redshift.
nc_wl_surface_mass_density_free
Atomically decrements the reference count of smd by one. If the reference count drops to 0,
all memory allocated by smd is released.
nc_wl_surface_mass_density_magnification
Computes the reduced shear: $$ \mu(R) = \frac{1}{(1 - \kappa(R))^2 - \vert\gamma^2(R) \vert},$$ where $\gamma(R)$ is the shear [nc_wl_surface_mass_density_shear()] and $\kappa(R)$ is the convergence [nc_wl_surface_mass_density_convergence()].
nc_wl_surface_mass_density_prepare_if_needed
Prepares the NcWLSurfaceMassDensity object smd for computation if necessary.
nc_wl_surface_mass_density_reduced_shear
Computes the reduced shear: $$ g(R) = \frac{\gamma(R)}{1 - \kappa(R)},$$ where $\gamma(R)$ is the shear [nc_wl_surface_mass_density_shear()] and $\kappa(R)$ is the convergence [nc_wl_surface_mass_density_convergence()].
nc_wl_surface_mass_density_reduced_shear_array
Computes the reduced shear: $$ g(R) = \frac{\gamma(R)}{1 - \kappa(R)},$$ where $\gamma(R)$ is the shear [nc_wl_surface_mass_density_shear()] and $\kappa(R)$ is the convergence [nc_wl_surface_mass_density_convergence()].
nc_wl_surface_mass_density_reduced_shear_array_equal
Computes the reduced shear: $$ g(R) = \frac{\gamma(R)}{1 - \kappa(R)},$$ where $\gamma(R)$ is the shear [nc_wl_surface_mass_density_shear()] and $\kappa(R)$ is the convergence [nc_wl_surface_mass_density_convergence()].
nc_wl_surface_mass_density_reduced_shear_infinity
Computes the reduced shear assuming a lensed source at infinite redshift: $$ g(R) = \frac{\beta_s(zb)\gamma(R)}{1 - \beta_s(zb) \kappa(R)}, $$ where $\gamma(R)$ is the shear [nc_wl_surface_mass_density_shear()], $\kappa(R)$ is the convergence [nc_wl_surface_mass_density_convergence()], $z_b$ is the background-galaxy redshift and $$\beta_s = \frac{D_s}{D_l D_{ls}} \frac{D_\infty}{D_l D_{l\infty}}.$$ See [Applegate (2014)][XApplegate2014].
nc_wl_surface_mass_density_reduced_shear_optzs
Computes the reduced shear: $$ g(R) = \frac{\gamma(R)}{1 - \kappa(R)},$$ where $\gamma(R)$ is the shear [nc_wl_surface_mass_density_shear()] and $\kappa(R)$ is the convergence [nc_wl_surface_mass_density_convergence()].
nc_wl_surface_mass_density_reduced_shear_optzs_prep
Computes the reduced shear: $$ g(R) = \frac{\gamma(R)}{1 - \kappa(R)},$$ where $\gamma(R)$ is the shear [nc_wl_surface_mass_density_shear()] and $\kappa(R)$ is the convergence [nc_wl_surface_mass_density_convergence()].
nc_wl_surface_mass_density_shear_infinity
Computes the shear $\gamma_\infty (R)$ at R, see Eq $\eqref{eq:shear}$, and source at infinite redshift.
nc_wl_surface_mass_density_sigma
Computes the surface mass density at R, see Eq. $\eqref{eq:sigma}$.
nc_wl_surface_mass_density_sigma_array
Computes the surface mass density at R, see Eq. $\eqref{eq:sigma}$.
nc_wl_surface_mass_density_sigma_critical
Computes the critical surface density, \begin{equation}\label{eq:def:SigmaC} \Sigma_c = \frac{c^2}{4\pi G} \frac{D_s}{D_l D_{ls}}, \end{equation} where $c^2$ is the speed of light squared [ncm_c_c2 ()], $G$ is the gravitational constant in units of $m^3/s^2 M_\odot^{-1}$ [ncm_c_G_mass_solar()], $D_s$ ($D_l$) is the angular diameter distance from the observer to the source (lens), and $D_{ls}$ is the angular diameter distance between the lens and the source.
nc_wl_surface_mass_density_sigma_critical_infinity
Computes the critical surface density, \begin{equation}\label{eq:def:SigmaC} \Sigma_c = \frac{c^2}{4\pi G} \frac{D_\infty}{D_l D_{l\infty}}, \end{equation} where $c^2$ is the speed of light squared [ncm_c_c2 ()], $G$ is the gravitational constant in units of $m^3/s^2 M_\odot^{-1}$ [ncm_c_G_mass_solar()], $D_\infty$ ($D_l$) is the angular diameter distance from the observer to the source at infinite redshift (lens), and $D_{l\infty}$ is the angular diameter distance between the lens and the source.
nc_wl_surface_mass_density_sigma_excess
Computes difference between the mean surface mass density inside the circle with radius R (Eq. $\eqref{eq:sigma_mean}$) and the surface mass density at R (Eq. $\eqref{eq:sigma}$).
nc_wl_surface_mass_density_sigma_excess_array
Computes difference between the mean surface mass density inside the circle with radius R (Eq. $\eqref{eq:sigma_mean}$) and the surface mass density at R (Eq. $\eqref{eq:sigma}$).
nc_wl_surface_mass_density_sigma_mean
Computes the mean surface mass density inside the circle with radius R, Eq. $\eqref{eq:sigma_mean}$.
Properties
NumCosmo.WLSurfaceMassDensity:Roff
Scale length of the miscentering probability distribution. FIXME Set correct values (limits) Units: Mpc.
Properties inherited from NcmModel (9)
NumCosmoMath.Model:implementation
NumCosmoMath.Model:name
NumCosmoMath.Model:nick
NumCosmoMath.Model:params-types
NumCosmoMath.Model:reparam
NumCosmoMath.Model:scalar-params-len
NumCosmoMath.Model:sparam-array
NumCosmoMath.Model:submodel-array
NumCosmoMath.Model:vector-params-len
Signals
Signals inherited from GObject (1)
GObject::notify
The notify signal is emitted on an object when one of its properties has its value set through g_object_set_property(), g_object_set(), et al.