autogalaxy.profiles.mass.PointMass

class PointMass

Bases: MassProfile

Represents a point-mass.

Parameters:

• centre (Tuple[float, float]) – The (y,x) arc-second coordinates of the profile centre.

• einstein_radius (float) – The arc-second Einstein radius of the point-mass.

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 2D convergence of the mass profile from a 2D grid of Cartesian (y,x) coordinates.
convergence_func	Returns the convergence of the mass profile as a function of the radial coordinate.
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	Returns the 2D deflection angles of the mass profile from a 2D grid of Cartesian (y,x) 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
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	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	Returns the 2D lensing potential of the mass profile from a 2D grid of Cartesian (y,x) 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_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.

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.
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.
is_point_mass

convergence_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>, **kwargs)

Returns the 2D convergence of the mass profile from a 2D grid of Cartesian (y,x) coordinates.

The convergence κ(θ) is the dimensionless surface mass density of the lens, defined as the projected surface mass density Σ(θ) divided by the critical surface mass density Σ_cr:

κ(θ) = Σ(θ) / Σ_cr

Physically, κ = 1 on the Einstein ring. Regions with κ > 1 produce multiple images.

Parameters:

grid (Union[ndarray, Grid2D, Grid2DIrregular]) – The 2D (y, x) coordinates where the convergence is evaluated.

Returns:

The convergence κ(θ) at every coordinate on the input grid.

Return type:

aa.Array2D

potential_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>, **kwargs)

Returns the 2D lensing potential of the mass profile from a 2D grid of Cartesian (y,x) coordinates.

The lensing potential ψ(θ) is the gravitational (Shapiro) time-delay term. It quantifies how much the passage of light through the gravitational field delays its arrival relative to a straight-line path in empty space.

The potential enters directly into the Fermat potential:

φ(θ) = ½ |θ − β|² − ψ(θ)

which governs time delays between multiple lensed images of the same source.

Parameters:

grid (Union[ndarray, Grid2D, Grid2DIrregular]) – The 2D (y, x) coordinates where the lensing potential is evaluated.

Returns:

The lensing potential ψ(θ) at every coordinate on the input grid.

Return type:

aa.Array2D

deflections_yx_2d_from(grid, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautolens/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>, **kwargs)

Returns the 2D deflection angles of the mass profile from a 2D grid of Cartesian (y,x) coordinates.

The deflection angle α(θ) at image-plane position θ describes how a light ray is bent by the gravitational field of the lens. The source-plane position β is then:

β = θ − α(θ)

Deflection angles are the single most important output of a mass profile — every other lensing quantity (convergence, shear, magnification, critical curves, caustics) can be derived from them.

Parameters:

grid (Union[ndarray, Grid2D, Grid2DIrregular]) – The 2D (y, x) coordinates where the deflection angles are evaluated.

Returns:

The (y, x) deflection angles at every coordinate on the input grid.

Return type:

aa.VectorYX2D

property is_point_mass