autogalaxy.profiles.mass.PowerLaw

class PowerLaw

Bases: PowerLawCore

Represents an elliptical power-law density distribution.

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.

• einstein_radius (float) – The arc-second Einstein radius.

• slope (float) – The density slope of the power-law (lower value -> shallower profile, higher value -> steeper profile).

Methods

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).
angle_to_profile_grid_from	The angle between each angle theta on the grid and the profile, in radians.
axis_ratio	The ratio of the minor-axis to major-axis (b/a) of the ellipse defined by profile (0.0 > q > 1.0).
convergence_2d_from	Returns the two dimensional projected convergence on a grid of (y,x) arc-second coordinates.
convergence_func	Returns the convergence of the mass profile as a function of the radial coordinate.
deflection_func
deflections_2d_via_potential_2d_from	Returns the 2D deflection angles of the mass profile by numerically differentiating the lensing potential on the input grid.
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.
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_radius_rescaled	Rescale the einstein radius by slope and axis_ratio, to reduce its degeneracy with other mass-profiles parameters.
elliptical_radii_grid_from	Convert a grid of (y,x) coordinates to their elliptical radii values: :math: (x^2 + (y^2/q))^0.5
ellipticity_rescale	A rescaling factor applied to account for the ellipticity of the mass profile when computing the Einstein radius from the average convergence equals unity criterion.
extract_attribute	Returns an attribute of a class and its children profiles in the galaxy as a ValueIrregular or Grid2DIrregular object.
has	Returns True if any attribute of this profile is an instance of the input class cls, else False.
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	Integrand used by mass_angular_within_circle_from to compute the total projected mass within a circle.
potential_2d_from	Calculate the potential on a grid of (y,x) arc-second coordinates.
potential_func	Returns the integrand of the lensing potential at a single point, used in numerical integration schemes for computing the potential from the mass profile's convergence.
radial_deflection_from
radial_grid_from	Convert a grid of (y, x) coordinates, to their radial distances from the profile centre (e.g. :math: r = sqrt(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.
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.
vmapped_deflections_from

Attributes

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.
unit_mass

potential_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautogalaxy/envs/latest/lib/python3.11/site-packages/numpy/__init__.py'>, **kwargs)

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

Parameters:

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

deflections_yx_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautogalaxy/envs/latest/lib/python3.11/site-packages/numpy/__init__.py'>, **kwargs)

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

For coordinates (0.0, 0.0) the analytic calculation of the deflection angle gives a NaN. Therefore, coordinates at (0.0, 0.0) are shifted slightly to (1.0e-8, 1.0e-8).

This code is an adaption of Tessore & Metcalf 2015: https://arxiv.org/abs/1507.01819

Parameters:

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

convergence_func(grid_radius, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautogalaxy/envs/latest/lib/python3.11/site-packages/numpy/__init__.py'>)

Returns the convergence of the mass profile as a function of the radial coordinate.

This is used to integrate the convergence profile to compute enclosed masses and the Einstein radius.

Parameters:

grid_radius (float) – The radial distance from the profile centre at which the convergence is evaluated.

Returns:

The convergence at the input radial distance.

Return type:

float

static potential_func(u, y, x, axis_ratio, slope, core_radius, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautogalaxy/envs/latest/lib/python3.11/site-packages/numpy/__init__.py'>)

Returns the integrand of the lensing potential at a single point, used in numerical integration schemes for computing the potential from the mass profile’s convergence.

Parameters:

• u – The integration variable.

• y – The y-coordinate of the point at which the potential is evaluated.

• x – The x-coordinate of the point at which the potential is evaluated.