profiles.density.DoublePowerLawDensityProfile.compute_deflection_angle#

Compute the gravitational lensing deflection angle at projected radius \(R\).

Supports both physical and angular deflection:

Physical Deflection (length units):

\[\alpha_{\mathrm{phys}}(R) = \frac{4 G M(<R)}{c^2 R}\]
Angular Deflection (default, angular units):

\[\alpha_{\mathrm{ang}}(R) = \alpha_{\mathrm{phys}}(R) \times \frac{D_{ls}}{D_s}\]

where:

\(M(<R)\) is the enclosed mass at projected radius \(R\)
\(D_l\), \(D_s\), \(D_{ls}\) are angular diameter distances to lens, source, and between lens and source, respectively.

Parameters:

R (unyt_quantity or unyt_array) – Projected radius in the lens plane with length units.
mode ({"physical", "angular"}, optional) – Type of deflection to compute. Default is angular.
units (str or Unit, optional) – Output units. For angular deflection, defaults to arcsec.
G (unyt_quantity, optional) – Gravitational constant to use. Defaults to unyt.physical_constants.gravitational_constant.
z_lens (float, optional) – Redshift of the lens (required for angular mode if distances not provided).
z_source (float, optional) – Redshift of the source (required for angular mode if distances not provided).
D_l (unyt_quantity, optional) – Angular diameter distance to the lens.
D_s (unyt_quantity, optional) – Angular diameter distance to the source.
D_ls (unyt_quantity, optional) – Angular diameter distance between lens and source.
cosmology (astropy.cosmology.Cosmology, optional) – Cosmology used to compute distances if not provided. Defaults to pisces_config['physics.default_cosmology'].
**kwargs – Additional arguments passed to compute_enclosed_mass().

Returns:

alpha – Deflection angle at each radius, in specified units.

Return type:

unyt_quantity or unyt_array

Raises:

ValueError – If necessary distances are missing or redshifts are inconsistent.

Examples

import unyt
from astropy.cosmology import Planck18
from pisces.profiles.density import (
    NFWDensityProfile,
)

profile = NFWDensityProfile(rho_0=0.03, r_s=15)
R = unyt.array.unyt_array([1, 5, 10], "kpc")

alpha_arcsec = profile.compute_deflection_angle(
    R,
    mode="angular",
    units="arcsec",
    z_lens=0.3,
    z_source=2.0,
    cosmology=Planck18,
)

print(alpha_arcsec)

profiles.density.DoublePowerLawDensityProfile.compute_deflection_angle#

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