__author__ = "sibirrer"
import numpy as np
from lenstronomy.LensModel.Profiles.nfw import NFW
import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
__all__ = ["NFW_ELLIPSE"]
[docs]
class NFW_ELLIPSE(LensProfileBase):
"""This class contains functions concerning the NFW profile with an ellipticity
defined in the potential parameterization of alpha_Rs and Rs is the same as for the
spherical NFW profile.
from Glose & Kneib: https://cds.cern.ch/record/529584/files/0112138.pdf
relation are: R_200 = c * Rs
"""
profile_name = "NFW_ELLIPSE"
param_names = ["Rs", "alpha_Rs", "e1", "e2", "center_x", "center_y"]
lower_limit_default = {
"Rs": 0,
"alpha_Rs": 0,
"e1": -0.5,
"e2": -0.5,
"center_x": -100,
"center_y": -100,
}
upper_limit_default = {
"Rs": 100,
"alpha_Rs": 10,
"e1": 0.5,
"e2": 0.5,
"center_x": 100,
"center_y": 100,
}
[docs]
def __init__(self, interpol=False, num_interp_X=1000, max_interp_X=10):
"""
:param interpol: bool, if True, interpolates the functions F(), g() and h()
:param num_interp_X: int (only considered if interpol=True), number of interpolation elements in units of r/r_s
:param max_interp_X: float (only considered if interpol=True), maximum r/r_s value to be interpolated
(returning zeros outside)
"""
self.nfw = NFW(
interpol=interpol, num_interp_X=num_interp_X, max_interp_X=max_interp_X
)
self._diff = 0.0000000001
super(NFW_ELLIPSE, self).__init__()
[docs]
def function(self, x, y, Rs, alpha_Rs, e1, e2, center_x=0, center_y=0):
"""Returns elliptically distorted NFW lensing potential.
:param x: angular position (normally in units of arc seconds)
:param y: angular position (normally in units of arc seconds)
:param Rs: turn over point in the slope of the NFW profile in angular unit
:param alpha_Rs: deflection (angular units) at projected Rs
:param e1: eccentricity component in x-direction
:param e2: eccentricity component in y-direction
:param center_x: center of halo (in angular units)
:param center_y: center of halo (in angular units)
:return: lensing potential
"""
x_, y_ = param_util.transform_e1e2_square_average(
x, y, e1, e2, center_x, center_y
)
R_ = np.sqrt(x_**2 + y_**2)
rho0_input = self.nfw.alpha2rho0(alpha_Rs=alpha_Rs, Rs=Rs)
if Rs < 0.0000001:
Rs = 0.0000001
f_ = self.nfw.nfw_potential(R_, Rs, rho0_input)
return f_
[docs]
def derivatives(self, x, y, Rs, alpha_Rs, e1, e2, center_x=0, center_y=0):
"""Returns df/dx and df/dy of the function, calculated as an elliptically
distorted deflection angle of the spherical NFW profile.
:param x: angular position (normally in units of arc seconds)
:param y: angular position (normally in units of arc seconds)
:param Rs: turn over point in the slope of the NFW profile in angular unit
:param alpha_Rs: deflection (angular units) at projected Rs
:param e1: eccentricity component in x-direction
:param e2: eccentricity component in y-direction
:param center_x: center of halo (in angular units)
:param center_y: center of halo (in angular units)
:return: deflection in x-direction, deflection in y-direction
"""
x_, y_ = param_util.transform_e1e2_square_average(
x, y, e1, e2, center_x, center_y
)
phi_G, q = param_util.ellipticity2phi_q(e1, e2)
cos_phi = np.cos(phi_G)
sin_phi = np.sin(phi_G)
e = param_util.q2e(q)
# e = abs(1 - q)
R_ = np.sqrt(x_**2 + y_**2)
rho0_input = self.nfw.alpha2rho0(alpha_Rs=alpha_Rs, Rs=Rs)
if Rs < 0.0000001:
Rs = 0.0000001
f_x_prim, f_y_prim = self.nfw.nfw_alpha(R_, Rs, rho0_input, x_, y_)
f_x_prim *= np.sqrt(1 - e)
f_y_prim *= np.sqrt(1 + e)
f_x = cos_phi * f_x_prim - sin_phi * f_y_prim
f_y = sin_phi * f_x_prim + cos_phi * f_y_prim
return f_x, f_y
[docs]
def hessian(self, x, y, Rs, alpha_Rs, e1, e2, center_x=0, center_y=0):
"""Returns Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy the
calculation is performed as a numerical differential from the deflection field.
Analytical relations are possible.
:param x: angular position (normally in units of arc seconds)
:param y: angular position (normally in units of arc seconds)
:param Rs: turn over point in the slope of the NFW profile in angular unit
:param alpha_Rs: deflection (angular units) at projected Rs
:param e1: eccentricity component in x-direction
:param e2: eccentricity component in y-direction
:param center_x: center of halo (in angular units)
:param center_y: center of halo (in angular units)
:return: d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
"""
alpha_ra, alpha_dec = self.derivatives(
x, y, Rs, alpha_Rs, e1, e2, center_x, center_y
)
diff = self._diff
alpha_ra_dx, alpha_dec_dx = self.derivatives(
x + diff, y, Rs, alpha_Rs, e1, e2, center_x, center_y
)
alpha_ra_dy, alpha_dec_dy = self.derivatives(
x, y + diff, Rs, alpha_Rs, e1, e2, center_x, center_y
)
f_xx = (alpha_ra_dx - alpha_ra) / diff
f_xy = (alpha_ra_dy - alpha_ra) / diff
f_yx = (alpha_dec_dx - alpha_dec) / diff
f_yy = (alpha_dec_dy - alpha_dec) / diff
return f_xx, f_xy, f_yx, f_yy
[docs]
def mass_3d_lens(self, r, Rs, alpha_Rs, e1=1, e2=0):
"""
:param r: radius (in angular units)
:param Rs:
:param alpha_Rs:
:param e1:
:param e2:
:return:
"""
return self.nfw.mass_3d_lens(r, Rs, alpha_Rs)
[docs]
def density_lens(self, r, Rs, alpha_Rs, e1=1, e2=0):
"""Computes the density at 3d radius r given lens model parameterization. The
integral in the LOS projection of this quantity results in the convergence
quantity.
:param r: 3d radios
:param Rs: turn-over radius of NFW profile
:param alpha_Rs: deflection at Rs
:return: density rho(r)
"""
return self.nfw.density_lens(r, Rs, alpha_Rs)