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Functions
Object Hierarchy
GEnum ╰── NcWLSurfaceMassDensityParams GObject ╰── NcmModel ╰── NcWLSurfaceMassDensity
Description
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 (NcDensityProfile), $r^2 = R^2 + \chi^2$ 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 \, \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), Umetsu (2012), Applegate (2014), Melchior (2017), Parroni (2017).
Functions
nc_wl_surface_mass_density_new ()
NcWLSurfaceMassDensity *
nc_wl_surface_mass_density_new (NcDistance *dist
);
This function allocates memory for a new NcWLSurfaceMassDensity object and sets its properties to the values from the input arguments.
nc_wl_surface_mass_density_ref ()
NcWLSurfaceMassDensity *
nc_wl_surface_mass_density_ref (NcWLSurfaceMassDensity *smd
);
Increases the reference count of smd
by one.
nc_wl_surface_mass_density_free ()
void
nc_wl_surface_mass_density_free (NcWLSurfaceMassDensity *smd
);
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_clear ()
void
nc_wl_surface_mass_density_clear (NcWLSurfaceMassDensity **smd
);
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.
nc_wl_surface_mass_density_set_zcluster ()
void nc_wl_surface_mass_density_set_zcluster (NcWLSurfaceMassDensity *smd
,gdouble zcluster
);
Sets the value of the property zcluster.
nc_wl_surface_mass_density_set_zsource ()
void nc_wl_surface_mass_density_set_zsource (NcWLSurfaceMassDensity *smd
,gdouble zsource
);
Sets the value of the property zsource.
nc_wl_surface_mass_density_set_zlens ()
void nc_wl_surface_mass_density_set_zlens (NcWLSurfaceMassDensity *smd
,gdouble zlens
);
Sets the value of the property zlens.
nc_wl_surface_mass_density_sigma ()
gdouble nc_wl_surface_mass_density_sigma (NcWLSurfaceMassDensity *smd
,NcDensityProfile *dp
,NcHICosmo *cosmo
,gdouble R
);
Computes the surface mass density at R
, see Eq. $\eqref{eq:sigma}$.
nc_wl_surface_mass_density_sigma_mean ()
gdouble nc_wl_surface_mass_density_sigma_mean (NcWLSurfaceMassDensity *smd
,NcDensityProfile *dp
,NcHICosmo *cosmo
,gdouble R
);
Computes the mean surface mass density inside the circle with radius R
, Eq. $\eqref{eq:sigma_mean}$.
nc_wl_surface_mass_density_sigma_critical ()
gdouble nc_wl_surface_mass_density_sigma_critical (NcWLSurfaceMassDensity *smd
,NcHICosmo *cosmo
);
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_convergence ()
gdouble nc_wl_surface_mass_density_convergence (NcWLSurfaceMassDensity *smd
,NcDensityProfile *dp
,NcHICosmo *cosmo
,gdouble R
);
Computes the convergence $\kappa(R)$ at R
, see Eq $\eqref{eq:convergence}$.
nc_wl_surface_mass_density_shear ()
gdouble nc_wl_surface_mass_density_shear (NcWLSurfaceMassDensity *smd
,NcDensityProfile *dp
,NcHICosmo *cosmo
,gdouble R
);
Computes the shear $\gamma(R)$ at R
, see Eq $\eqref{eq:shear}$.
nc_wl_surface_mass_density_reduced_shear ()
gdouble nc_wl_surface_mass_density_reduced_shear (NcWLSurfaceMassDensity *smd
,NcDensityProfile *dp
,NcHICosmo *cosmo
,gdouble R
);
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 ()
gdouble nc_wl_surface_mass_density_reduced_shear_infinity (NcWLSurfaceMassDensity *smd
,NcDensityProfile *dp
,NcHICosmo *cosmo
,gdouble R
);
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)
Property Details
The “Roff”
property
“Roff” gdouble
Scale length of the miscentering probability distribution. FIXME Set correct values (limits) Units: Mpc
Flags: Read / Write
Allowed values: [0,2]
Default value: 1
The “distance”
property
“distance” NcDistance *
This property keeps the object NcDistance.
Flags: Read / Write / Construct Only
The “pcc”
property
“pcc” gdouble
Percentage of correctly centered clusters. Interval: [0.0, 1.0]
Flags: Read / Write
Allowed values: [0,1]
Default value: 0.8
The “zcluster”
property
“zcluster” gdouble
This property sets the cluster's redshift.
Flags: Read / Write / Construct
Allowed values: [0,5.5]
Default value: 1
The “zlens”
property
“zlens” gdouble
This property sets the lens' redshift. Usually zlens = zcluster, but we define these two properties in order to handle cases where shear signal has been rescaled to a different cluster redshift (following D. Applegate's code.).
Flags: Read / Write / Construct
Allowed values: [0,5.5]
Default value: 1
The “zsource”
property
“zsource” gdouble
This property sets the source's redshift.
Flags: Read / Write / Construct
Allowed values: [0,6]
Default value: 1.5