# autogalaxy.profiles.mass.IsothermalSph#

class IsothermalSph[source]#

Bases: `Isothermal`

Represents a spherical isothermal density distribution, which is equivalent to the spherical power-law density distribution for the value slope: float = 2.0

Parameters

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(). `convergence_1d_from` rtype `convergence_2d_from` Calculate the projected convergence on a grid of (y,x) arc-second 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_func` rtype `float` `deflection_func` `deflections_2d_via_potential_2d_from` `deflections_yx_2d_from` Calculate the deflection angles on a grid of (y,x) arc-second coordinates. `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 `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). `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_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 `potential_2d_from` Calculate the potential on a grid of (y,x) arc-second 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. `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_2d_from` Calculate the (gamma_y, gamma_x) shear vector field on a grid of (y,x) arc-second coordinates. `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): `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`

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). `einstein_radius_rescaled` Rescale the einstein radius by slope and axis_ratio, to reduce its degeneracy with other mass-profiles parameters. `ellipticity_rescale` `unit_mass`
property axis_ratio#

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

potential_2d_from(grid)[source]#

Calculate the potential on a grid of (y,x) arc-second coordinates.

Parameters

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

deflections_yx_2d_from(grid)[source]#

Calculate the deflection angles on a grid of (y,x) arc-second coordinates.

Parameters

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