# autogalaxy.profiles.mass_profiles.SphChameleon¶

class autogalaxy.profiles.mass_profiles.SphChameleon(centre: Tuple[float, float] = (0.0, 0.0), intensity: float = 0.1, core_radius_0: float = 0.01, core_radius_1: float = 0.02, mass_to_light_ratio: float = 1.0)
__init__(centre: Tuple[float, float] = (0.0, 0.0), intensity: float = 0.1, core_radius_0: float = 0.01, core_radius_1: float = 0.02, mass_to_light_ratio: float = 1.0)

The spherica; Chameleon mass profile.

Profile form:
mass_to_light_ratio * intensity * (1.0 / Sqrt(x^2 + (y/q)^2 + core_radius_0^2) - 1.0 / Sqrt(x^2 + (y/q)^2 + (core_radius_0 + core_radius_1)**2.0))
Parameters: centre – The (y,x) arc-second coordinates of the profile centre. elliptical_comps – The first and second ellipticity components of the elliptical coordinate system, where fac = (1 - axis_ratio) / (1 + axis_ratio), ellip_y = fac * sin(2*angle) and ellip_x = fac * cos(2*angle). intensity – Overall intensity normalisation of the light profiles (electrons per second). core_radius_0 (the core size of the first elliptical cored Isothermal profile.) – core_radius_1 (core_radius_0 + core_radius_1 is the core size of the second elliptical cored Isothermal profile.) – We use core_radius_1 here is to avoid negative values.

Methods

 __init__(centre, float] = (0.0, 0.0), …) The spherica; Chameleon mass profile. area_within_tangential_critical_curve_from(grid) caustics_from(grid[, pixel_scale]) convergence_1d_from(grid, Grid1D, …) convergence_2d_from(grid, …) Calculate the projected convergence at a given set of arc-second gridded coordinates. convergence_func(grid_radius) convergence_via_hessian_from(grid[, buffer]) convergence_via_jacobian_from(grid[, jacobian]) cos_and_sin_to_x_axis() Determine the sin and cosine of the angle between the profile’s ellipse and the positive x-axis, counter-clockwise. critical_curves_from(grid[, pixel_scale]) deflection_magnitudes_from(grid) deflections_2d_from(grid, …) Calculate the deflection angles at a given set of arc-second gridded coordinates. deflections_2d_via_potential_2d_from(grid) density_between_circular_annuli(…) Calculate the mass between two circular annuli and compute the density by dividing by the annuli surface area. einstein_mass_angular_from(grid[, pixel_scale]) einstein_radius_from(grid[, pixel_scale]) einstein_radius_via_normalization_from(…) eta_u(u, coordinates) extract_attribute(cls, attr_name) Returns an attribute of a class and its children profiles in the the galaxy as a ValueIrregular or Grid2DIrregular object. from_axis_ratio_and_phi(centre, …) grid_angle_to_profile(grid_thetas) The angle between each angle theta on the grid and the profile, in radians. grid_to_eccentric_radii(grid) Convert a grid of (y,x) coordinates to an eccentric radius, which is (1.0/axis_ratio) * elliptical radius and used to define light profile half-light radii using circular radii. grid_to_elliptical_radii(grid) Convert a grid of (y,x) coordinates to an elliptical radius. grid_to_grid_cartesian(grid, radius) Convert a grid of (y,x) coordinates with their specified circular radii to their original (y,x) Cartesian coordinates. grid_to_grid_radii(grid) Convert a grid of (y, x) coordinates to a grid of their circular radii. hessian_from(grid[, buffer, deflections_func]) image_2d_via_radii_from(grid_radii) Calculate the intensity of the Chamelon light profile on a grid of radial coordinates. jacobian_from(grid) magnification_2d_from(grid) magnification_via_hessian_from(grid[, …]) mass_angular_via_normalization_from(…) mass_angular_within_circle(radius) Integrate the mass profiles’s convergence profile to compute the total mass within a circle of specified radius. mass_integral(x) Routine to integrate an elliptical light profiles - set axis ratio to 1 to compute the luminosity within a circle normalization_via_einstein_radius_from(…) normalization_via_mass_angular_from(…[, …]) potential_1d_from(grid, Grid1D, …) potential_2d_from(grid, …) potential_func(u, y, x) radial_caustic_from(grid[, pixel_scale]) radial_critical_curve_from(grid[, pixel_scale]) radial_eigen_value_from(grid[, jacobian]) rotate_grid_from_reference_frame(grid) 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_via_hessian_from(grid[, buffer]) shear_via_jacobian_from(grid[, jacobian]) shear_yx_via_hessian_from(grid[, buffer]) shear_yx_via_jacobian_from(grid[, jacobian]) tangential_caustic_from(grid[, pixel_scale]) tangential_critical_curve_from(grid[, …]) tangential_eigen_value_from(grid[, jacobian]) transform_grid_from_reference_frame(grid) Transform a grid of (y,x) coordinates from the reference frame of the profile to the original observer reference frame, including a rotation to its original orientation and a translation from the profile’s centre. transform_grid_to_reference_frame(grid) Transform a grid of (y,x) coordinates to the reference frame of the profile, including a translation to its centre and a rotation to it orientation. with_new_normalization(normalization)

Attributes

 angle average_convergence_of_1_radius The radius a critical curve forms for this mass profile, e.g. axis_ratio centre cos_phi ellipticity_rescale has_mass_profile phi_radians sin_phi