# autogalaxy.profiles.mass.PowerLawBroken#

class PowerLawBroken[source]#

Bases: `MassProfile`

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` rtype: `convergence_1d_from` rtype: `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` rtype: `float` `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` rtype: `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. `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. `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`
convergence_2d_from(grid)[source]#

Returns the dimensionless density kappa=Sigma/Sigma_c (eq. 1)

deflections_yx_2d_from(grid, max_terms=20)[source]#

Returns the complex deflection angle from eq. 18 and 19

static hyp2f1_series(t, q, r, z, max_terms=20)[source]#

Computes eq. 26 for a radius r, slope t, axis ratio q, and coordinates z.