profiles.density.EinastoDensityProfile.compute_einstein_radius#

EinastoDensityProfile.compute_einstein_radius(z_lens: float, z_source: float, units: str | Unit | None = 'arcsec', G: unyt_quantity | None = None, cosmology: Cosmology | None = None, **kwargs) → unyt_array | unyt_quantity#

Compute the Einstein ring angular radius \(\\theta_E\) for a perfectly aligned source-lens system.

The Einstein radius satisfies:

\[\alpha( \theta_E D_l ) = \theta_E\]

where:

  • \(\alpha\) is the angular deflection angle,

  • \(D_l\) is the angular diameter distance to the lens.

Parameters:

  • z_lens (float) – Redshift of the lens.

  • z_source (float) – Redshift of the source (must satisfy \(z_{\mathrm{source}} > z_{\mathrm{lens}}\)).

  • units (str or Unit, optional) – Desired output units for \(\\theta_E\). Default is arcsec.

  • G (unyt_quantity, optional) – Gravitational constant to use. Defaults to unyt.physical_constants.gravitational_constant.

  • cosmology (astropy.cosmology.Cosmology, optional) – Cosmology used to compute distances. Defaults to pisces_config['physics.default_cosmology'].

  • **kwargs – Additional arguments passed to compute_enclosed_mass().

Returns:

theta_E – Einstein radius in specified angular units.

Return type:

unyt_quantity

Raises:

ValueError – If redshifts are invalid or distances cannot be computed.

Examples

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

profile = HernquistDensityProfile(
    rho_0=0.02, r_s=5
)
theta_E = profile.compute_einstein_radius(
    z_lens=0.3, z_source=2.0, cosmology=Planck18
)

print(f"Einstein radius: {theta_E:.3f}")

See also

compute_deflection_angle(), astropy.cosmology.Cosmology