autogalaxy.profiles.mass.gNFW#

class gNFW[source]#

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 arc-second radius where the average density within this radius is 200 times the critical density of the Universe..

Methods

angle_to_profile_grid_from

The angle between each angle theta on the grid and the profile, in radians.

area_within_tangential_critical_curve_list_from

Returns the surface area within each tangential critical curve as a list, the calculation of which is described in the function tangential_critical_curve_list_from().

concentration

concentration_func

convergence_1d_from

rtype

Union[ndarray, Grid1D, Grid2D, Grid2DIterate, Grid2DIrregular]

convergence_2d_from

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

convergence_2d_via_hessian_from

Returns the convergence of the lensing object, which is computed from the 2D deflection angle map via the Hessian using the expression (see equation 56 https://www.tau.ac.il/~lab3/MICROLENSING/JeruLect.pdf):

convergence_2d_via_jacobian_from

Returns the convergence of the lensing object, which is computed from the 2D deflection angle map via the Jacobian using the expression (see equation 58 https://www.tau.ac.il/~lab3/MICROLENSING/JeruLect.pdf):

convergence_2d_via_mge_from

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

convergence_func

rtype

float

convergence_func_gaussian

coord_func_f

coord_func_f_float_jit

coord_func_f_jit

coord_func_g

coord_func_g_float_jit

coord_func_g_jit

coord_func_h

decompose_convergence_via_mge

deflection_func

deflections_2d_via_integral_from

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

deflections_2d_via_mge_from

deflections_2d_via_potential_2d_from

deflections_yx_2d_from

delta_concentration

density_between_circular_annuli

Calculate the mass between two circular annuli and compute the density by dividing by the annuli surface area.

dict

A dictionary representation of the instance comprising a type field which contains the entire class path by which the type can be imported and constructor arguments.

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

einstein_mass_angular_from

Returns the Einstein radius corresponding to the area within the tangential critical curve.

einstein_mass_angular_list_from

Returns a list of the angular Einstein massses corresponding to the area within each tangential critical curve.

einstein_radius_from

Returns the Einstein radius corresponding to the area within the tangential critical curve.

einstein_radius_list_from

Returns a list of the Einstein radii corresponding to the area within each tangential critical curve.

einstein_radius_via_normalization_from

elliptical_radii_grid_from

Convert a grid of (y,x) coordinates to their elliptical radii values: :math: (x^2 + (y^2/q))^0.5

eta

see Eq.(6) of 1906.00263

extract_attribute

Returns an attribute of a class and its children profiles in the the galaxy as a ValueIrregular or Grid2DIrregular object.

from_dict

Instantiate an instance of a class from its dictionary representation.

from_json

Load the dictable object to a .json file, whereby all attributes are converted from the .json file's dictionary representation to create the instance of the object

has

Does this instance have an attribute which is of type cls?

hessian_from

Returns the Hessian of the lensing object, where the Hessian is the second partial derivatives of the the potential (see equation 55 https://www.tau.ac.il/~lab3/MICROLENSING/JeruLect.pdf):

jacobian_from

Returns the Jacobian of the lensing object, which is computed by taking the gradient of the 2D deflection angle map in four direction (positive y, negative y, positive x, negative x).

kesi

see Eq.(6) of 1906.08263

magnification_2d_from

Returns the 2D magnification map of lensing object, which is computed as the inverse of the determinant of the jacobian.

magnification_2d_via_hessian_from

Returns the 2D magnification map of lensing object, which is computed from the 2D deflection angle map via the Hessian using the expressions (see equation 60 https://www.tau.ac.il/~lab3/MICROLENSING/JeruLect.pdf):

mass_angular_via_normalization_from

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

normalization_via_einstein_radius_from

normalization_via_mass_angular_from

output_to_json

Output the dictable object to a .json file, whereby all attributes are converted to a dictionary representation first.

potential_1d_from

rtype

Union[ndarray, Grid1D, Grid2D, Grid2DIterate, Grid2DIrregular]

potential_2d_from

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

potential_func

radial_caustic_list_from

Returns all radial caustics of the lensing system, which are computed as follows:

radial_critical_curve_list_from

Returns all radial critical curves of the lensing system, which are computed as follows:

radial_eigen_value_from

Returns the radial eigen values of lensing jacobian, which are given by the expression:

radial_grid_from

Convert a grid of (y, x) coordinates, to their radial distances from the profile centre (e.g.

radius_at_200

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_via_hessian_from

Returns the 2D (y,x) shear vectors of the lensing object, which are computed from the 2D deflection angle map via the Hessian using the expressions (see equation 57 https://www.tau.ac.il/~lab3/MICROLENSING/JeruLect.pdf):

shear_yx_2d_via_jacobian_from

Returns the 2D (y,x) shear vectors of the lensing object, which are computed from the 2D deflection angle map via the Jacobian using the expression (see equation 58 https://www.tau.ac.il/~lab3/MICROLENSING/JeruLect.pdf):

tabulate_integral

Tabulate an integral over the convergence of deflection potential of a mass profile.

tangential_caustic_list_from

Returns all tangential caustics of the lensing system, which are computed as follows:

tangential_critical_curve_list_from

Returns all tangential critical curves of the lensing system, which are computed as follows:

tangential_eigen_value_from

Returns the tangential eigen values of lensing jacobian, which are given by the expression:

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.

with_new_normalization

zeta_from

The key part to compute the deflection angle of each Gaussian.

Attributes

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).

average_convergence_of_1_radius

The radius a critical curve forms for this mass profile, e.g.

axis_ratio

The ratio of the minor-axis to major-axis (b/a) of the ellipse defined by profile (0.0 > q > 1.0).

ellipticity_rescale

epsrel

deflections_2d_via_integral_from(grid, tabulate_bins=1000)[source]#

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

Parameters
  • grid (Union[ndarray, Grid2D, Grid2DIterate, Grid2DIrregular]) – The grid of (y,x) arc-second coordinates the deflection angles are computed on.

  • tabulate_bins – The number of bins to tabulate the inner integral of this profile.

potential_2d_from(grid, tabulate_bins=1000)[source]#

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

Parameters
  • grid (Union[ndarray, Grid2D, Grid2DIterate, Grid2DIrregular]) – The grid of (y,x) arc-second coordinates the deflection angles are computed on.

  • tabulate_bins – The number of bins to tabulate the inner integral of this profile.