autogalaxy.profiles.mass.gNFW#

Bases: AbstractgNFW

The elliptical NFW profiles, used to fit the dark matter halo of the lens.

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_s * scale_radius)/lensing_critical_density)
inner_slope (float) – The inner slope of the dark matter halo
scale_radius (float) – The NFW scale radius as an angle on the sky in arc-seconds. For a regular NFW halo, the scale radius is roughly where the log-slope of the profile changes from -1 to -3.

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`	Returns the gNFW convergence at the input elliptical radii (see the class docstring for the closed-form expression and its line-of-sight integral I(eta), eta = xi / r_s).
`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 via the same MGE decomposition used for the deflection angles, so that `grad(psi)` is self-consistent with `deflections_yx_2d_from`.
`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.
`convergence_table_epsrel`
`convergence_table_min_nodes`
`convergence_table_min_points`
`convergence_table_nodes_per_decade`
`convergence_table_pad_decades`
`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`
`latent_parameters`

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]#

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 via the same MGE decomposition used for the deflection angles, so that grad(psi) is self-consistent with deflections_yx_2d_from.

This implementation is inherited by every elliptical and spherical gNFW/NFW variant (NFW, gNFWSph, and the MCR / Virial-mass subclasses), none of which have a closed-form elliptical potential. The MGE decomposer expands the 3D density into a Gaussian sum and integrates each Gaussian’s analytic potential.

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]#

Returns the gNFW convergence at the input elliptical radii (see the class docstring for the closed-form expression and its line-of-sight integral I(eta), eta = xi / r_s).

Small inputs integrate I(eta) with scipy.integrate.quad once per radius, in the numerically stable form of _convergence_integral_from. When there are at least max(convergence_table_min_points, n_nodes) finite positive radii in a 1D NumPy input, I(eta) is instead tabulated with the same stable integral (at convergence_table_epsrel) on a log-spaced eta grid of convergence_table_nodes_per_decade nodes per decade spanning those radii, and interpolated in (log eta, log I) with a cubic spline (see AbstractgNFW for the accuracy of this scheme); both paths agree to ~1e-7. Radii that are zero, negative or non-finite are always integrated per radius with the original integrand form, so their output is unchanged.