autogalaxy.profiles.mass.NFWSph

class NFWSph

Bases: NFW

Parameters:

• centre (Tuple[float, float]) – The (y,x) arc-second coordinates of the profile centre.

• kappa_s (float) – The overall normalization of the dark matter halo (\(\kappa_s = \rho_s r_s / \Sigma_{\rm crit}\)).

• scale_radius (float) – The NFW scale radius \(r_s\), 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	Analytic calculation convergence from Heyrovský & Karamazov 2024
convergence_2d_via_cse_from	Calculate the projected 2D convergence from a grid of (y,x) arc second coordinates, by computing and summing the convergence of each individual cse used to decompose the mass profile.
convergence_cse_1d_from	One dimensional function which is solved to decompose a convergence profile in cored steep ellipsoids, given by equation (14) of Oguri 2021 (https://arxiv.org/abs/2106.11464).
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
decompose_convergence_via_cse	Decompose the convergence of the elliptical NFW mass profile into cored steep elliptical (cse) profiles.
deflection_func_sph
deflections_2d_via_analytic_from	Calculate the deflection angles at a given set of arc-second gridded coordinates.
deflections_2d_via_cse_from
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_via_cse_from	Returns the deflection angles of a 1d cored steep ellisoid (CSE) profile, given by equation (19) and (20) of Oguri 2021 (https://arxiv.org/abs/2106.11464).
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	Calculate the potential at a given set of arc-second gridded 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.
potential_func_sph
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.
shear_yx_2d_from	Analytic calculation shear from Heyrovský & Karamazov 2024
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_analytic_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)

Calculate the deflection angles at a given set of arc-second gridded coordinates.

Parameters:

grid (Union[ndarray, Grid2D, Grid2DIrregular]) – The grid of (y,x) arc-second coordinates the deflection angles are computed on.

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

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)

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

Parameters:

grid (Union[ndarray, Grid2D, Grid2DIrregular]) – The grid of (y,x) arc-second coordinates the deflection angles are computed on.

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