autogalaxy.profiles.mass.cNFW#

Bases: AbstractgNFW

Parameters:

centre (Tuple[float, float]) – The (y,x) arc-second coordinates of the profile centre.
ell_comps (Tuple[float, float]) – The first and second ellipticity components of the elliptical coordinate system.
kappa_s (float) – The overall normalization of the dark matter halo (\(\kappa_s = \rho_0 D_d r_s / \Sigma_{\rm crit}\)).
scale_radius (float) – The cored NFW scale radius \(r_s\), as an angle on the sky in arcseconds.
core_radius (float) – The cored NFW core radius \(r_c\), as an angle on the sky in arcseconds.

Methods

`angle`	The position angle in degrees of the major-axis of the ellipse defined by profile, defined counter clockwise from the positive x-axis (0.0 > angle > 180.0).
`angle_radians`	The position angle in radians of the major-axis of the ellipse defined by profile, defined counter clockwise from the positive x-axis (0.0 > angle > 2pi).
`angle_to_profile_grid_from`	The angle between each angle theta on the grid and the profile, in radians.
`axis_ratio`	The ratio of the minor-axis to major-axis (b/a) of the ellipse defined by profile (0.0 > q > 1.0).
`concentration`
`concentration_func`
`convergence_2d_from`	Calculate the projected convergence at a given set of arc-second gridded coordinates.
`convergence_func`	Radial projected convergence kappa(r), reusing the MGE-of-3D-density decomposition (the same machinery convergence_2d_from uses with three_D=True) evaluated at the radial coordinate grid_radius.
`coord_func_f`
`coord_func_g`	Vectorized version of the original looped coord_func_g_jit.
`coord_func_h`
`deflections_2d_via_mge_from`
`deflections_2d_via_potential_2d_from`	Returns the 2D deflection angles of the mass profile by numerically differentiating the lensing potential on the input grid.
`deflections_yx_2d_from`	Returns the 2D deflection angles of the mass profile from a 2D grid of Cartesian (y,x) coordinates.
`delta_concentration`
`density_3d_func`
`density_between_circular_annuli`	Calculate the mass between two circular annuli and compute the density by dividing by the annuli surface area.
`eccentric_radii_grid_from`	Convert a grid of (y,x) coordinates to an eccentric radius: :math: axis_ratio^0.5 (x^2 + (y^2/q))^0.5
`elliptical_radii_grid_from`	Convert a grid of (y,x) coordinates to their elliptical radii values: :math: (x^2 + (y^2/q))^0.5
`extract_attribute`	Returns an attribute of a class and its children profiles in the galaxy as a ValueIrregular or Grid2DIrregular object.
`has`	Returns True if any attribute of this profile is an instance of the input class cls, else False.
`mass_angular_within_circle_from`	Integrate the mass profiles's convergence profile to compute the total mass within a circle of specified radius.
`mass_at_200_solar_masses`
`mass_integral`	Integrand used by mass_angular_within_circle_from to compute the total projected mass within a circle.
`potential_2d_from`	Returns the 2D lensing potential of the mass profile from a 2D grid of Cartesian (y,x) coordinates.
`potential_func`	Returns the integrand of the lensing potential at a single point, used in numerical integration schemes for computing the potential from the mass profile's convergence.
`radial_deflection_from`
`radial_grid_from`	Convert a grid of (y, x) coordinates, to their radial distances from the profile centre (e.g. :math: r = sqrt(x2 + y2)).
`radius_at_200`	Returns r_{200m} for this halo in arcseconds
`rho_at_scale_radius_solar_mass_per_kpc3`	The Cosmic average density is defined at the redshift of the profile.
`rotated_grid_from_reference_frame_from`	Rotate a grid of (y,x) coordinates which have been transformed to the elliptical reference frame of a profile back to the original unrotated coordinate grid reference frame.
`transformed_from_reference_frame_grid_from`	Transform a grid of (y,x) coordinates from the reference frame of the profile to the original observer reference frame.
`transformed_to_reference_frame_grid_from`	Transform a grid of (y,x) coordinates to the reference frame of the profile.
`vmapped_deflections_from`

Attributes

`average_convergence_of_1_radius`	The radius a critical curve forms for this mass profile, e.g. where the mean convergence is equal to 1.0.
`ellipticity_rescale`	A rescaling factor applied to account for the ellipticity of the mass profile when computing the Einstein radius from the average convergence equals unity criterion.
`epsrel`

deflections_yx_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>, **kwargs)[source]#

Returns the 2D deflection angles of the mass profile from a 2D grid of Cartesian (y,x) coordinates.

The deflection angle α(θ) at image-plane position θ describes how a light ray is bent by the gravitational field of the lens. The source-plane position β is then:

β = θ − α(θ)

Deflection angles are the single most important output of a mass profile — every other lensing quantity (convergence, shear, magnification, critical curves, caustics) can be derived from them.

Parameters:: grid (Union[ndarray, Grid2D, Grid2DIrregular]) – The 2D (y, x) coordinates where the deflection angles are evaluated.
Returns:: The (y, x) deflection angles at every coordinate on the input grid.
Return type:: aa.VectorYX2D

deflections_2d_via_mge_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>, **kwargs)[source]#

density_3d_func(r, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>)[source]#

convergence_func(grid_radius, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>)[source]#

Radial projected convergence kappa(r), reusing the MGE-of-3D-density decomposition (the same machinery convergence_2d_from uses with three_D=True) evaluated at the radial coordinate grid_radius.

cNFW has no closed-form radial convergence helper, so this delegates to the MGE Gaussian sum. This hook is reached by MGEDecomposer.decompose_convergence_via_mge (three_D=False, not used by cNFW) and by radial mass integration (mass_integral -> mass_angular_within_circle_from -> Einstein radius).

The result is the q-independent radial profile (like NFW.convergence_func): ellipticity is re-introduced by the MGE machinery elsewhere, so no sigmas_factor rescale is applied (sigmas_factor=1.0). Verified to match convergence_2d_from for the spherical case and to be q-independent for the elliptical case.

convergence_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>, **kwargs)[source]#

Calculate the projected convergence at a given set of arc-second gridded coordinates.

Parameters:: grid (Union[ndarray, Grid2D, Grid2DIrregular]) – The grid of (y,x) arc-second coordinates the convergence is computed on.

potential_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>, **kwargs)[source]#

Returns the 2D lensing potential of the mass profile from a 2D grid of Cartesian (y,x) coordinates.

The lensing potential ψ(θ) is the gravitational (Shapiro) time-delay term. It quantifies how much the passage of light through the gravitational field delays its arrival relative to a straight-line path in empty space.

The potential enters directly into the Fermat potential:

φ(θ) = ½ |θ − β|² − ψ(θ)

which governs time delays between multiple lensed images of the same source.

Parameters:: grid (Union[ndarray, Grid2D, Grid2DIrregular]) – The 2D (y, x) coordinates where the lensing potential is evaluated.
Returns:: The lensing potential ψ(θ) at every coordinate on the input grid.
Return type:: aa.Array2D