# mypy: disable-error-code="operator,union-attr,dict-item"
from typing import Optional, Union, Annotated
from caskade import forward, Param
from ..backend_obj import ArrayLike
from .base import ThinLens, NameType, CosmologyType, ZType
from . import func
DELTA = 200.0
__all__ = ("NFW",)
[docs]
class NFW(ThinLens):
"""
NFW lens class. This class models a lens using the Navarro-Frenk-White (NFW) profile.
The NFW profile is a spatial density profile of dark matter halo that arises in
cosmological simulations.
Attributes
-----------
z_l: Optional[ArrayLike]
Redshift of the lens. Default is None.
*Unit: unitless*
z_s: Optional[ArrayLike]
Redshift of the source. Default is None.
*Unit: unitless*
x0: Optional[ArrayLike]
x-coordinate of the lens center in the lens plane. Default is None.
*Unit: arcsec*
y0: Optional[ArrayLike]
y-coordinate of the lens center in the lens plane. Default is None.
*Unit: arcsec*
mass: Optional[ArrayLike]
Mass of the lens. Default is None.
*Unit: Msun*
c: Optional[ArrayLike]
Concentration parameter of the lens. Default is None.
*Unit: unitless*
s: float
Softening parameter to avoid singularities at the center of the lens. Default is 0.0.
*Unit: arcsec*
Methods
-------
get_scale_radius
Returns the scale radius of the lens.
get_scale_density
Returns the scale density of the lens.
get_convergence_s
Returns the dimensionless surface mass density of the lens.
deflection_angle
Computes the deflection angle.
convergence
Computes the convergence (dimensionless surface mass density).
potential
Computes the lensing potential.
"""
_null_params = {
"x0": 0.0,
"y0": 0.0,
"mass": 1e13,
"c": 5.0,
}
def __init__(
self,
cosmology: CosmologyType,
z_l: ZType = None,
z_s: ZType = None,
x0: Annotated[
Optional[Union[ArrayLike, float]], "X coordinate of the lens center", True
] = None,
y0: Annotated[
Optional[Union[ArrayLike, float]], "Y coordinate of the lens center", True
] = None,
mass: Annotated[
Optional[Union[ArrayLike, float]], "Mass of the lens", True
] = None,
c: Annotated[
Optional[Union[ArrayLike, float]],
"Concentration parameter of the lens",
True,
] = None,
s: Annotated[
float,
"Softening parameter to avoid singularities at the center of the lens",
] = 0.0,
name: NameType = None,
):
"""
Initialize an instance of the NFW lens class.
Parameters
----------
name: str
Name of the lens instance.
cosmology: Cosmology
An instance of the Cosmology class which contains
information about the cosmological model and parameters.
z_l: Optional[Union[ArrayLike, float]]
Redshift of the lens. Default is None.
*Unit: unitless*
x0: Optional[Union[ArrayLike, float]]
x-coordinate of the lens center in the lens plane.
Default is None.
*Unit: arcsec*
y0: Optional[Union[ArrayLike, float]]
y-coordinate of the lens center in the lens plane.
Default is None.
*Unit: arcsec*
mass: Optional[Union[ArrayLike, float]]
Mass of the lens. Default is None.
*Unit: Msun*
c: Optional[Union[ArrayLike, float]]
Concentration parameter of the lens. Default is None.
*Unit: unitless*
s: float
Softening parameter to avoid singularities at the center of the lens.
Default is 0.0.
*Unit: arcsec*
"""
super().__init__(cosmology, z_l, name=name, z_s=z_s)
self.x0 = Param("x0", x0, shape=(), units="arcsec")
self.y0 = Param("y0", y0, shape=(), units="arcsec")
self.mass = Param("mass", mass, shape=(), units="Msun")
self.c = Param("c", c, shape=(), units="unitless")
self.s = s
[docs]
@forward
def get_scale_radius(
self,
z_l: Annotated[ArrayLike, "Param"],
mass: Annotated[ArrayLike, "Param"],
c: Annotated[ArrayLike, "Param"],
) -> ArrayLike:
"""
Calculate the scale radius of the lens.
Parameters
----------
z_l: ArrayLike
Redshift of the lens.
*Unit: unitless*
mass: ArrayLike
Mass of the lens.
*Unit: Msun*
c: ArrayLike
Concentration parameter of the lens.
*Unit: unitless*
Returns
-------
ArrayLike
The scale radius of the lens in Mpc.
*Unit: Mpc*
"""
critical_density = self.cosmology.critical_density(z_l)
return func.scale_radius_nfw(critical_density, mass, c, DELTA)
[docs]
@forward
def get_scale_density(
self,
z_l: Annotated[ArrayLike, "Param"],
c: Annotated[ArrayLike, "Param"],
) -> ArrayLike:
"""
Calculate the scale density of the lens.
Parameters
----------
z_l: ArrayLike
Redshift of the lens.
*Unit: unitless*
c: ArrayLike
Concentration parameter of the lens.
*Unit: unitless*
Returns
-------
ArrayLike
The scale density of the lens in solar masses per Mpc cubed.
*Unit: Msun/Mpc^3*
"""
critical_density = self.cosmology.critical_density(z_l)
return func.scale_density_nfw(critical_density, c, DELTA)
[docs]
@forward
def physical_deflection_angle(
self,
x: ArrayLike,
y: ArrayLike,
z_l: Annotated[ArrayLike, "Param"],
x0: Annotated[ArrayLike, "Param"],
y0: Annotated[ArrayLike, "Param"],
mass: Annotated[ArrayLike, "Param"],
c: Annotated[ArrayLike, "Param"],
) -> tuple[ArrayLike, ArrayLike]:
"""
Compute the physical deflection angle.
Parameters
----------
x: ArrayLike
x-coordinates in the lens plane.
*Unit: arcsec*
y: ArrayLike
y-coordinates in the lens plane.
*Unit: arcsec*
Returns
-------
x_component: ArrayLike
The x-component of the reduced deflection angle.
*Unit: arcsec*
y_component: ArrayLike
The y-component of the reduced deflection angle.
*Unit: arcsec*
"""
d_l = self.cosmology.angular_diameter_distance(z_l)
critical_density = self.cosmology.critical_density(z_l)
return func.physical_deflection_angle_nfw(
x0, y0, mass, c, critical_density, d_l, x, y, DELTA=DELTA, s=self.s
)
[docs]
@forward
def reduced_deflection_angle(self, x, y, z_s, z_l):
d_s = self.cosmology.angular_diameter_distance(z_s)
d_ls = self.cosmology.angular_diameter_distance_z1z2(z_l, z_s)
deflection_angle_x, deflection_angle_y = self.physical_deflection_angle(x, y)
return func.reduced_from_physical_deflection_angle(
deflection_angle_x, deflection_angle_y, d_s, d_ls
)
[docs]
@forward
def convergence(
self,
x: ArrayLike,
y: ArrayLike,
z_s: Annotated[ArrayLike, "Param"],
z_l: Annotated[ArrayLike, "Param"],
x0: Annotated[ArrayLike, "Param"],
y0: Annotated[ArrayLike, "Param"],
mass: Annotated[ArrayLike, "Param"],
c: Annotated[ArrayLike, "Param"],
) -> ArrayLike:
"""
Compute the convergence (dimensionless surface mass density).
Parameters
----------
x: ArrayLike
x-coordinates in the lens plane.
*Unit: arcsec*
y: ArrayLike
y-coordinates in the lens plane.
*Unit: arcsec*
Returns
-------
ArrayLike
The convergence (dimensionless surface mass density).
*Unit: unitless*
"""
critical_surface_density = self.cosmology.critical_surface_density(z_l, z_s)
critical_density = self.cosmology.critical_density(z_l)
d_l = self.cosmology.angular_diameter_distance(z_l)
return func.convergence_nfw(
critical_surface_density,
critical_density,
x0,
y0,
mass,
c,
x,
y,
d_l,
DELTA=DELTA,
s=self.s,
)
[docs]
@forward
def potential(
self,
x: ArrayLike,
y: ArrayLike,
z_s: Annotated[ArrayLike, "Param"],
z_l: Annotated[ArrayLike, "Param"],
x0: Annotated[ArrayLike, "Param"],
y0: Annotated[ArrayLike, "Param"],
mass: Annotated[ArrayLike, "Param"],
c: Annotated[ArrayLike, "Param"],
) -> ArrayLike:
"""
Compute the lensing potential.
Parameters
----------
x: ArrayLike
x-coordinates in the lens plane.
*Unit: arcsec*
y: ArrayLike
y-coordinates in the lens plane.
*Unit: arcsec*
Returns
-------
ArrayLike
The lensing potential.
*Unit: arcsec^2*
"""
critical_surface_density = self.cosmology.critical_surface_density(z_l, z_s)
critical_density = self.cosmology.critical_density(z_l)
d_l = self.cosmology.angular_diameter_distance(z_l)
return func.potential_nfw(
critical_surface_density,
critical_density,
x0,
y0,
mass,
c,
d_l,
x,
y,
DELTA=DELTA,
s=self.s,
)
