autogalaxy.profiles.mass.PowerLawBrokenSph#

class PowerLawBrokenSph[source]#

Bases: PowerLawBroken

Ell, homoeoidal mass model with an inner_slope and outer_slope, continuous in density across break_radius. Position angle is defined to be zero on x-axis and +ve angle rotates the lens anticlockwise

The grid variable is a tuple of (theta_1, theta_2), where each theta_1, theta_2 is itself a 2D array of the x and y coordinates respectively.~

Methods

angle_to_profile_grid_from

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

area_within_curve_list_from

contour_list_from

convergence_1d_from

convergence_2d_from

Returns the dimensionless density kappa=Sigma/Sigma_c (eq.

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://inspirehep.net/literature/419263):

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://inspirehep.net/literature/419263):

convergence_func

deflections_2d_via_potential_2d_from

deflections_yx_2d_from

Returns the complex deflection angle from eq.

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

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.

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

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 potential (see equation 55 https://inspirehep.net/literature/419263):

hyp2f1_series

Computes eq.

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).

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://inspirehep.net/literature/419263):

mass_angular_within_circle_from

Integrate the mass profiles's convergence profile to compute the total mass within a circle of specified radius.

mass_integral

potential_1d_from

potential_2d_from

potential_func

radial_caustic_list_from

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

radial_critical_curve_area_list_from

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

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. :math: r = x**2 + y**2).

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://inspirehep.net/literature/419263):

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://inspirehep.net/literature/419263):

tangential_caustic_list_from

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

tangential_critical_curve_area_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().

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.

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. where the mean convergence is equal to 1.0.

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