autogalaxy.profiles.mass.NFWMCRDuffySph#
- class NFWMCRDuffySph[source]#
Bases:
NFWSph
The spherical NFW profiles, used to fit the dark matter halo of the lens.
- Parameters:
centre (
Tuple
[float
,float
]) – The (y,x) arc-second coordinates of the profile centre.kappa_s – The overall normalization of the dark matter halo (kappa_s = (rho_s * scale_radius)/lensing_critical_density)
scale_radius – The arc-second radius where the average density within this radius is 200 times the critical density of the Universe..
Methods
angle_to_profile_grid_from
The angle between each angle theta on the grid and the profile, in radians.
area_within_curve_list_from
concentration
Computes the NFW halo concentration, c_{200m}
concentration_func
contour_list_from
convergence_1d_from
convergence_2d_from
Analytic calculation convergence from Heyrovský & Karamazov 2024
convergence_2d_via_cse_from
Calculate the projected 2D convergence from a grid of (y,x) arc second coordinates, by computing and summing the convergence of each individual cse used to decompose the mass profile.
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://inspirehep.net/literature/419263):
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://inspirehep.net/literature/419263):
convergence_2d_via_mge_from
Calculate the projected convergence at a given set of arc-second gridded coordinates.
convergence_cse_1d_from
One dimensional function which is solved to decompose a convergence profile in cored steep ellipsoids, given by equation (14) of Oguri 2021 (https://arxiv.org/abs/2106.11464).
convergence_func
convergence_func_gaussian
coord_func
coord_func_f
coord_func_f_jit
coord_func_g
coord_func_g_jit
coord_func_h
decompose_convergence_via_cse
Decompose the convergence of the elliptical NFW mass profile into cored steep elliptical (cse) profiles.
decompose_convergence_via_mge
deflection_func
deflection_func_sph
deflections_2d_via_analytic_from
Calculate the deflection angles at a given set of arc-second gridded coordinates.
deflections_2d_via_cse_from
deflections_2d_via_integral_from
Calculate the deflection angles at a given set of arc-second gridded coordinates.
deflections_2d_via_mge_from
deflections_2d_via_potential_2d_from
deflections_via_cse_from
Returns the deflection angles of a 1d cored steep ellisoid (CSE) profile, given by equation (19) and (20) of Oguri 2021 (https://arxiv.org/abs/2106.11464).
deflections_yx_2d_from
delta_concentration
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_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.
elliptical_radii_grid_from
Convert a grid of (y,x) coordinates to their elliptical radii values: :math: (x^2 + (y^2/q))^0.5
eta
see Eq.(6) of 1906.00263
extract_attribute
Returns an attribute of a class and its children profiles in the galaxy as a ValueIrregular or Grid2DIrregular 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 potential (see equation 55 https://inspirehep.net/literature/419263):
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).
kesi
see Eq.(6) of 1906.08263
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://inspirehep.net/literature/419263):
mass_angular_within_circle_from
Integrate the mass profiles's convergence profile to compute the total mass within a circle of specified radius.
mass_at_200_solar_masses
Returns M_{200m} of this NFW halo, in solar masses, at the given cosmology.
mass_integral
potential_1d_from
potential_2d_from
Calculate the potential at a given set of arc-second gridded coordinates.
potential_func
potential_func_sph
radial_caustic_list_from
Returns all radial caustics of the lensing system, which are computed as follows:
radial_critical_curve_area_list_from
Returns the surface area within each radial critical curve as a list, the calculation of which is described in the function radial_critical_curve_list_from().
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. :math: r = x**2 + y**2).
radius_at_200
Returns r_{200m} for this halo in arcseconds
rho_at_scale_radius_solar_mass_per_kpc3
The Cosmic average density is defined at the redshift of the profile.
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_yx_2d_from
Analytic calculation shear from Heyrovský & Karamazov 2024
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://inspirehep.net/literature/419263):
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://inspirehep.net/literature/419263):
tabulate_integral
Tabulate an integral over the convergence of deflection potential of a mass profile.
tangential_caustic_list_from
Returns all tangential caustics of the lensing system, which are computed as follows:
tangential_critical_curve_area_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().
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.
zeta_from
The key part to compute the deflection angle of each Gaussian.
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. where the mean convergence is equal to 1.0.
axis_ratio
The ratio of the minor-axis to major-axis (b/a) of the ellipse defined by profile (0.0 > q > 1.0).
ellipticity_rescale
epsrel