autogalaxy.profiles.mass.GaussianGradient

class GaussianGradient

Bases: Gaussian

The elliptical Gaussian light profile with a gradient in its mass to light conversion.

$Psi (r) = Psi_{o} frac{(sigma + 0.01)}{R_{ref}}^{Tau}$

Where:

$Psi (r)$ is the 1D convergence profile of the Gaussian [dimensionless]. $Psi_{o}$ is the base mass-to-light ratio of the profile [dimensionless]. $sigma$ is the sigma value of the Gaussian [arc-seconds]. $r$ is the radius from the centre of the profile [arc-seconds]. $R_{ref}$ is the reference radius where the mass-to-light ratio is equal to $Psi_{o} [arc-seconds]. $Tau$ is the mass-to-light gradient of the profile [dimensionless].

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.

• intensity (float) – Overall intensity normalisation of the light profile (units are dimensionless and derived from the data the light profile’s image is compared too, which is expected to be electrons per second).

• sigma (float) – The sigma value of the Gaussian.

• mass_to_light_ratio_base (float) – The base mass-to-light ratio of the profile, which is the mass-to-light ratio of the Gaussian before it is scaled by values that adjust its mass-to-light ratio based on the reference radius and gradient.

• mass_to_light_gradient (float) – The mass-to-light radial gradient of the profile, whereby positive values means there is more mass per unit light within the reference radius.

• mass_to_light_radius (float) – The radius where the mass-to-light ratio is equal to the base mass-to-light ratio, such that there will be more of less mass per unit light within this radius depending on the mass-to-light gradient.

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	Calculate the projected convergence at a given set of arc-second gridded coordinates.
convergence_func	Returns the convergence of the mass profile as a function of the radial coordinate.
deflections_2d_via_analytic_from	Calculate the deflection angles at a given set of arc-second gridded coordinates.
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 at a given set of arc-second gridded 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.
image_2d_via_radii_from	Calculate the intensity of the Gaussian light profile on a grid of radial coordinates.
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_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
wofz	JAX-compatible Faddeeva function w(z) = exp(-z^2) * erfc(-i z) Based on the Poppe–Wijers / Zaghloul–Ali rational approximations.
zeta_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.
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.