Source code for caustics.lenses.func.mass_sheet
from ...backend_obj import backend
from ...utils import translate_rotate
[docs]
def reduced_deflection_angle_mass_sheet(x0, y0, kappa, x, y):
"""
Compute the reduced deflection angles. Here we use the Meneghetti lecture
notes equation 3.84.
Parameters
----------
x0: ArrayLike
x-coordinate of the center of the lens.
*Unit: arcsec*
y0: ArrayLike
y-coordinate of the center of the lens.
*Unit: arcsec*
kappa: Optional[Union[ArrayLike, float]]
Convergence. Surface density normalized by the critical surface density.
*Unit: unitless*
x: ArrayLike
x-coordinates in the lens plane.
*Unit: arcsec*
y: ArrayLike
y-coordinates in the lens plane.
*Unit: arcsec*
Returns
-------
x_component: ArrayLike
Deflection Angle in the x-direction.
*Unit: arcsec*
y_component: ArrayLike
Deflection Angle in the y-direction.
*Unit: arcsec*
"""
x, y = translate_rotate(x, y, x0, y0)
# Meneghetti eq 3.84
return x * kappa, y * kappa
[docs]
def potential_mass_sheet(x0, y0, kappa, x, y):
"""
Compute the lensing potential. Here we use the Meneghetti lecture notes
equation 3.81.
Parameters
----------
x0: ArrayLike
x-coordinate of the center of the lens.
*Unit: arcsec*
y0: ArrayLike
y-coordinate of the center of the lens.
*Unit: arcsec*
kappa: Optional[Union[ArrayLike, float]]
Convergence. Surface density normalized by the critical surface density.
*Unit: unitless*
x: ArrayLike
The x-coordinate of the lens.
*Unit: arcsec*
y: ArrayLike
The y-coordinate of the lens.
*Unit: arcsec*
Returns
-------
ArrayLike
The lensing potential.
*Unit: arcsec^2*
"""
x, y = translate_rotate(x, y, x0, y0)
# Meneghetti eq 3.81
return (kappa / 2) * (x**2 + y**2)
[docs]
def convergence_mass_sheet(kappa, x):
"""
Compute the lensing convergence. In the case of a mass sheet, this is just
the convergence value mapped to the input shape.
Parameters
----------
kappa: Optional[Union[ArrayLike, float]]
Convergence. Surface density normalized by the critical surface density.
*Unit: unitless*
x: ArrayLike
The x-coordinate of the lens. Only used for shape and device.
*Unit: arcsec*
Returns
-------
ArrayLike
The lensing potential.
*Unit: arcsec^2*
"""
# By definition
return kappa * backend.ones_like(x)
