autogalaxy.profiles.mass.gNFW

class 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 convergence of the mass profile as a function of the radial coordinate.
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(x**2 + y**2)).
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/pyautogalaxy/envs/latest/lib/python3.11/site-packages/numpy/__init__.py'>, **kwargs)

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/pyautogalaxy/envs/latest/lib/python3.11/site-packages/numpy/__init__.py'>, **kwargs)

potential_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautogalaxy/envs/latest/lib/python3.11/site-packages/numpy/__init__.py'>, **kwargs)

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/pyautogalaxy/envs/latest/lib/python3.11/site-packages/numpy/__init__.py'>)

Returns the convergence of the mass profile as a function of the radial coordinate.

This is used to integrate the convergence profile to compute enclosed masses and the Einstein radius.

Parameters:

grid_radius (float) – The radial distance from the profile centre at which the convergence is evaluated.

Returns:

The convergence at the input radial distance.

Return type:

float