# mypy: disable-error-code="operator,dict-item"
from math import pi
from typing import Optional, Union, Annotated
from caskade import forward, Param
from ..backend_obj import backend, ArrayLike
from ..constants import arcsec_to_rad
from .base import ThinLens, CosmologyType, NameType, ZType
from . import func
__all__ = ("PseudoJaffe",)
[docs]
class PseudoJaffe(ThinLens):
"""
Class representing a Pseudo Jaffe lens in strong gravitational lensing,
based on `Eliasdottir et al 2007 <https://arxiv.org/abs/0710.5636>`_ and
the `lenstronomy` source code.
Attributes
----------
name: string
The name of the Pseudo Jaffe lens.
cosmology: Cosmology
The cosmology used for calculations.
z_l: Optional[Union[ArrayLike, float]]
Redshift of the lens.
*Unit: unitless*
z_s: Optional[Union[ArrayLike, float]]
Redshift of the source.
*Unit: unitless*
x0: Optional[Union[ArrayLike, float]]
x-coordinate of the center of the lens (arcsec).
*Unit: arcsec*
y0: Optional[Union[ArrayLike, float]]
y-coordinate of the center of the lens (arcsec).
*Unit: arcsec*
mass: Optional[Union[ArrayLike, float]]
Total mass of the lens (Msun).
*Unit: Msun*
Rc: Optional[Union[ArrayLike, float]]
Core radius of the lens (arcsec).
*Unit: arcsec*
Rs: Optional[Union[ArrayLike, float]]
Scaling radius of the lens (arcsec).
*Unit: arcsec*
s: float
Softening parameter to prevent numerical instabilities.
*Unit: arcsec*
"""
_null_params = {
"x0": 0.0,
"y0": 0.0,
"mass": 1e12,
"Rc": 0.1,
"Rs": 1.0,
}
def __init__(
self,
cosmology: CosmologyType,
z_l: ZType = None,
z_s: ZType = None,
x0: Annotated[
Optional[Union[ArrayLike, float]],
"X coordinate of the center of the lens",
True,
] = None,
y0: Annotated[
Optional[Union[ArrayLike, float]],
"Y coordinate of the center of the lens",
True,
] = None,
mass: Annotated[
Optional[Union[ArrayLike, float]], "Total mass of the lens", True, "Msol"
] = None,
Rc: Annotated[
Optional[Union[ArrayLike, float]], "Core radius of the lens", True, "arcsec"
] = None,
Rs: Annotated[
Optional[Union[ArrayLike, float]],
"Scaling radius of the lens",
True,
"arcsec",
] = None,
s: Annotated[
float, "Softening parameter to prevent numerical instabilities"
] = 0.0,
name: NameType = None,
):
"""
Initialize the PseudoJaffe class.
Parameters
----------
name: string
The name of the Pseudo Jaffe lens.
cosmology: Cosmology
The cosmology used for calculations.
z_l: Optional[ArrayLike]
Redshift of the lens.
*Unit: unitless*
x0: Optional[ArrayLike]
x-coordinate of the center of the lens.
*Unit: arcsec*
y0: Optional[ArrayLike]
y-coordinate of the center of the lens.
*Unit: arcsec*
mass: Optional[ArrayLike]
Total mass of the lens (Msun).
*Unit: Msun*
Rc: Optional[ArrayLike]
Core radius of the lens.
*Unit: arcsec*
Rs: Optional[ArrayLike]
Scaling radius of the lens.
*Unit: arcsec*
s: float
Softening parameter to prevent numerical instabilities.
*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", valid=(0, None))
self.Rc = Param("Rc", Rc, shape=(), units="arcsec", valid=(0, None))
self.Rs = Param("Rs", Rs, shape=(), units="arcsec", valid=(0, None))
self.s = s
[docs]
@forward
def get_convergence_0(
self,
z_s: Annotated[ArrayLike, "Param"],
z_l: Annotated[ArrayLike, "Param"],
mass: Annotated[ArrayLike, "Param"],
Rc: Annotated[ArrayLike, "Param"],
Rs: Annotated[ArrayLike, "Param"],
):
d_l = self.cosmology.angular_diameter_distance(z_l)
sigma_crit = self.cosmology.critical_surface_density(z_l, z_s)
return mass / (2 * backend.pi * sigma_crit * Rc * Rs * (d_l * arcsec_to_rad) ** 2) # fmt: skip
[docs]
@forward
def mass_enclosed_2d(
self,
theta,
mass: Annotated[ArrayLike, "Param"],
Rc: Annotated[ArrayLike, "Param"],
Rs: Annotated[ArrayLike, "Param"],
):
"""
Calculate the mass enclosed within a two-dimensional radius. Using equation A10 from `Eliasdottir et al 2007 <https://arxiv.org/abs/0710.5636>`_.
Parameters
----------
theta: ArrayLike
Radius at which to calculate enclosed mass (arcsec).
*Unit: arcsec*
Returns
-------
ArrayLike
The mass enclosed within the given radius.
*Unit: Msun*
"""
return func.mass_enclosed_2d_pseudo_jaffe(theta, mass, Rc, Rs)
[docs]
@staticmethod
def central_convergence(
rho_0,
Rc,
Rs,
critical_surface_density,
):
"""
Compute the central convergence.
Parameters
-----------
rho_0: ArrayLike
Central mass density.
*Unit: Msun/Mpc^3*
Rc: ArrayLike
Core radius of the lens (must be in Mpc).
*Unit: Mpc*
Rs: ArrayLike
Scaling radius of the lens (must be in Mpc).
*Unit: Mpc*
cosmology: Cosmology
The cosmology used for calculations.
Returns
--------
ArrayLike
The central convergence.
*Unit: unitless*
"""
return pi * rho_0 * Rc * Rs / ((Rc + Rs) * critical_surface_density) # fmt: skip
[docs]
@forward
def reduced_deflection_angle(
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"],
Rc: Annotated[ArrayLike, "Param"],
Rs: Annotated[ArrayLike, "Param"],
) -> tuple[ArrayLike, ArrayLike]:
"""Calculate the deflection angle.
Parameters
----------
x: ArrayLike
x-coordinate of the lens.
*Unit: arcsec*
y: ArrayLike
y-coordinate of the lens.
*Unit: arcsec*
Returns
--------
x_component: ArrayLike
x-component of the deflection angle.
*Unit: arcsec*
y_component: ArrayLike
y-component of the deflection angle.
*Unit: arcsec*
"""
d_l = self.cosmology.angular_diameter_distance(z_l)
critical_surface_density = self.cosmology.critical_surface_density(z_l, z_s)
return func.reduced_deflection_angle_pseudo_jaffe(x0, y0, mass, Rc, Rs, x, y, d_l, critical_surface_density) # fmt: skip
[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"],
Rc: Annotated[ArrayLike, "Param"],
Rs: Annotated[ArrayLike, "Param"],
) -> ArrayLike:
"""
Compute the lensing potential. This calculation is based on equation A18 from `Eliasdottir et al 2007 <https://arxiv.org/abs/0710.5636>`_.
Parameters
--------
x: ArrayLike
x-coordinate of the lens.
*Unit: arcsec*
y: ArrayLike
y-coordinate of the lens.
*Unit: arcsec*
Returns
--------
ArrayLike
The lensing potential (arcsec^2).
*Unit: arcsec^2*
"""
d_l = self.cosmology.angular_diameter_distance(z_l) # Mpc
d_s = self.cosmology.angular_diameter_distance(z_s) # Mpc
d_ls = self.cosmology.angular_diameter_distance_z1z2(z_l, z_s) # Mpc
return func.potential_pseudo_jaffe(x0, y0, mass, Rc, Rs, x, y, d_l, d_s, d_ls) # fmt: skip
[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"],
Rc: Annotated[ArrayLike, "Param"],
Rs: Annotated[ArrayLike, "Param"],
) -> ArrayLike:
"""
Calculate the projected mass density, based on equation A6.
Parameters
-----------
x: ArrayLike
x-coordinate of the lens.
*Unit: arcsec*
y: ArrayLike
y-coordinate of the lens.
*Unit: arcsec*
Returns
-------
ArrayLike
The projected mass density.
*Unit: unitless*
"""
d_l = self.cosmology.angular_diameter_distance(z_l)
critical_surface_density = self.cosmology.critical_surface_density(z_l, z_s)
return func.convergence_pseudo_jaffe(
x0, y0, mass, Rc, Rs, x, y, d_l, critical_surface_density
)
