| Top | |
|
|
|
GEnum ╰── NcWLSurfaceMassDensityParams GObject ╰── NcmModel ╰── NcWLSurfaceMassDensity
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), Umetsu (2012), Applegate (2014), Melchior (2017), Parroni (2017).
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.).
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.
NcWLSurfaceMassDensity *
nc_wl_surface_mass_density_ref (NcWLSurfaceMassDensity *smd);
Increases the reference count of smd
by one.
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.
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.
void nc_wl_surface_mass_density_prepare (NcWLSurfaceMassDensity *smd,NcHICosmo *cosmo);
Prepares the NcWLSurfaceMassDensity object smd
for computation.
void nc_wl_surface_mass_density_prepare_if_needed (NcWLSurfaceMassDensity *smd,NcHICosmo *cosmo);
Prepares the NcWLSurfaceMassDensity object smd
for computation if necessary.
gdouble nc_wl_surface_mass_density_sigma (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zc);
Computes the surface mass density at R
, see Eq. $\eqref{eq:sigma}$.
gdouble nc_wl_surface_mass_density_sigma_mean (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zc);
Computes the mean surface mass density inside the circle with radius R
, Eq. $\eqref{eq:sigma_mean}$.
gdouble nc_wl_surface_mass_density_sigma_excess (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zc);
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. $\eqref{eq:sigma}$).
gdouble nc_wl_surface_mass_density_sigma_critical (NcWLSurfaceMassDensity *smd,NcHICosmo *cosmo,const gdouble zs,const gdouble zl,const gdouble zc);
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.
gdouble nc_wl_surface_mass_density_sigma_critical_infinity (NcWLSurfaceMassDensity *smd,NcHICosmo *cosmo,const gdouble zl,const gdouble zc);
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.
gdouble nc_wl_surface_mass_density_convergence (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zs,const gdouble zl,const gdouble zc);
Computes the convergence $\kappa(R)$ at R
, see Eq $\eqref{eq:convergence}$.
gdouble nc_wl_surface_mass_density_convergence_infinity (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zl,const gdouble zc);
Computes the convergence $\kappa_\infty(R)$ at R
, see Eq $\eqref{eq:convergence}$, and sources at infinite redshift.
gdouble nc_wl_surface_mass_density_shear (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zs,const gdouble zl,const gdouble zc);
Computes the shear $\gamma(R)$ at R
, see Eq $\eqref{eq:shear}$.
gdouble nc_wl_surface_mass_density_shear_infinity (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zl,const gdouble zc);
Computes the shear $\gamma_\infty (R)$ at R
, see Eq $\eqref{eq:shear}$, and source at infinite redshift.
gdouble nc_wl_surface_mass_density_reduced_shear (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zs,const gdouble zl,const gdouble zc);
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()].
gdouble nc_wl_surface_mass_density_reduced_shear_infinity (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zs,const gdouble zl,const gdouble zc);
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)
gdouble nc_wl_surface_mass_density_magnification (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zs,const gdouble zl,const gdouble zc);
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()].
void nc_wl_surface_mass_density_reduced_shear_optzs_prep (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble R,const gdouble zl,const gdouble zc,NcWLSurfaceMassDensityOptzs *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()].
FIXME
[skip]
gdouble nc_wl_surface_mass_density_reduced_shear_optzs (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,const gdouble zs,const gdouble zl,NcWLSurfaceMassDensityOptzs *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()].
FIXME
GArray * nc_wl_surface_mass_density_sigma_array (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,GArray *R,gdouble fin,gdouble fout,const gdouble zc);
Computes the surface mass density at R
, see Eq. $\eqref{eq:sigma}$.
smd |
||
dp |
||
cosmo |
||
R |
projected radius with respect to the center of the lens / halo. |
[element-type gdouble] |
fin |
factor to multiply $R$, it should be $1$ or the appropriated unit conversion |
|
fout |
factor to multiply $\rho(R)$, it should be $1$ or the appropriated unit conversion |
|
zc |
cluster redshift $z_\mathrm{cluster}$ |
GArray * nc_wl_surface_mass_density_sigma_excess_array (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,GArray *R,gdouble fin,gdouble fout,const gdouble zc);
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. $\eqref{eq:sigma}$).
smd |
||
dp |
||
cosmo |
||
R |
projected radius with respect to the center of the lens / halo. |
[element-type gdouble] |
fin |
factor to multiply $R$, it should be $1$ or the appropriated unit conversion |
|
fout |
factor to multiply $\rho(R)$, it should be $1$ or the appropriated unit conversion |
|
zc |
cluster redshift $z_\mathrm{cluster}$ |
GArray * nc_wl_surface_mass_density_reduced_shear_array (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,GArray *R,gdouble fin,gdouble fout,GArray *zs,const gdouble zl,const gdouble zc);
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()].
smd |
||
dp |
||
cosmo |
||
R |
projected radius with respect to the center of the lens / halo. |
[element-type gdouble] |
fin |
factor to multiply $R$, it should be $1$ or the appropriated unit conversion |
|
fout |
factor to multiply $g(R)$, it should be $1$ or the appropriated unit conversion |
|
zs |
source redshift $z_\mathrm{source}$. |
[element-type gdouble] |
zl |
lens redshift $z_\mathrm{lens}$ |
|
zc |
cluster redshift $z_\mathrm{cluster}$ |
GArray * nc_wl_surface_mass_density_reduced_shear_array_equal (NcWLSurfaceMassDensity *smd,NcHaloDensityProfile *dp,NcHICosmo *cosmo,GArray *R,gdouble fin,gdouble fout,GArray *zs,const gdouble zl,const gdouble zc);
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()].
smd |
||
dp |
||
cosmo |
||
R |
projected radius with respect to the center of the lens / halo. |
[element-type gdouble] |
fin |
factor to multiply $R$, it should be $1$ or the appropriated unit conversion |
|
fout |
factor to multiply $g(R)$, it should be $1$ or the appropriated unit conversion |
|
zs |
source redshift $z_\mathrm{source}$. |
[element-type gdouble] |
zl |
lens redshift $z_\mathrm{lens}$ |
|
zc |
cluster redshift $z_\mathrm{cluster}$ |
#define NC_WL_SURFACE_MASS_DENSITY_DEFAULT_PARAMS_ABSTOL (0.0)
“Roff” property “Roff” double
Scale length of the miscentering probability distribution. FIXME Set correct values (limits) Units: Mpc
Owner: NcWLSurfaceMassDensity
Flags: Read / Write
Default value: 1
“Roff-fit” property“Roff-fit” gboolean
R_{off}:fit.
Owner: NcWLSurfaceMassDensity
Flags: Read / Write
Default value: FALSE
“distance” property“distance” NcDistance *
This property keeps the object NcDistance.
Owner: NcWLSurfaceMassDensity
Flags: Read / Write / Construct Only
“pcc” property “pcc” double
Percentage of correctly centered clusters. Interval: [0.0, 1.0]
Owner: NcWLSurfaceMassDensity
Flags: Read / Write
Default value: 0.8
“pcc-fit” property“pcc-fit” gboolean
p_{cc}:fit.
Owner: NcWLSurfaceMassDensity
Flags: Read / Write
Default value: FALSE