from lenstronomy.LensModel.Profiles.hernquist import Hernquist
import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase
import numpy as np
__all__ = ["Hernquist_Ellipse"]
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class Hernquist_Ellipse(LensProfileBase):
"""This class contains functions for the elliptical Hernquist profile.
Ellipticity is defined in the potential.
"""
param_names = ["sigma0", "Rs", "e1", "e2", "center_x", "center_y"]
lower_limit_default = {
"sigma0": 0,
"Rs": 0,
"e1": -0.5,
"e2": -0.5,
"center_x": -100,
"center_y": -100,
}
upper_limit_default = {
"sigma0": 100,
"Rs": 100,
"e1": 0.5,
"e2": 0.5,
"center_x": 100,
"center_y": 100,
}
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def __init__(self):
self.spherical = Hernquist()
self._diff = 0.00000001
super(Hernquist_Ellipse, self).__init__()
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def function(self, x, y, sigma0, Rs, e1, e2, center_x=0, center_y=0):
"""Returns double integral of NFW profile."""
x_, y_ = param_util.transform_e1e2_square_average(
x, y, e1, e2, center_x, center_y
)
f_ = self.spherical.function(x_, y_, sigma0, Rs)
return f_
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def derivatives(self, x, y, sigma0, Rs, e1, e2, center_x=0, center_y=0):
"""Returns df/dx and df/dy of the function (integral of NFW)"""
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)
f_x_prim, f_y_prim = self.spherical.derivatives(x_, y_, sigma0, Rs)
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
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def hessian(self, x, y, sigma0, Rs, e1, e2, center_x=0, center_y=0):
"""Returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx,
d^f/dy^2."""
alpha_ra, alpha_dec = self.derivatives(
x, y, sigma0, Rs, e1, e2, center_x, center_y
)
diff = self._diff
alpha_ra_dx, alpha_dec_dx = self.derivatives(
x + diff, y, sigma0, Rs, e1, e2, center_x, center_y
)
alpha_ra_dy, alpha_dec_dy = self.derivatives(
x, y + diff, sigma0, 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
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def density(self, r, rho0, Rs, e1=0, e2=0):
"""Computes the 3-d density.
:param r: 3-d radius
:param rho0: density normalization
:param Rs: Hernquist radius
:return: density at radius r
"""
return self.spherical.density(r, rho0, Rs)
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def density_lens(self, r, sigma0, Rs, e1=0, e2=0):
"""Density as a function of 3d radius in lensing parameters This function
converts the lensing definition sigma0 into the 3d density.
:param r: 3d radius
:param sigma0: rho0 * Rs (units of projected density)
:param Rs: Hernquist radius
:return: enclosed mass in 3d
"""
return self.spherical.density_lens(r, sigma0, Rs)
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def density_2d(self, x, y, rho0, Rs, e1=0, e2=0, center_x=0, center_y=0):
"""Projected density along the line of sight at coordinate (x, y)
:param x: x-coordinate
:param y: y-coordinate
:param rho0: density normalization
:param Rs: Hernquist radius
:param center_x: x-center of the profile
:param center_y: y-center of the profile
:return: projected density
"""
return self.spherical.density_2d(x, y, rho0, Rs, center_x, center_y)
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def mass_2d_lens(self, r, sigma0, Rs, e1=0, e2=0):
"""Mass enclosed projected 2d sphere of radius r Same as mass_2d but with input
normalization in units of projected density.
:param r: projected radius
:param sigma0: rho0 * Rs (units of projected density)
:param Rs: Hernquist radius
:return: mass enclosed 2d projected radius
"""
return self.spherical.mass_2d_lens(r, sigma0, Rs)
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def mass_2d(self, r, rho0, Rs, e1=0, e2=0):
"""Mass enclosed projected 2d sphere of radius r.
:param r: projected radius
:param rho0: density normalization
:param Rs: Hernquist radius
:return: mass enclosed 2d projected radius
"""
return self.spherical.mass_2d(r, rho0, Rs)
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def mass_3d(self, r, rho0, Rs, e1=0, e2=0):
"""Mass enclosed a 3d sphere or radius r.
:param r: 3-d radius within the mass is integrated (same distance units as
density definition)
:param rho0: density normalization
:param Rs: Hernquist radius
:return: enclosed mass
"""
return self.spherical.mass_3d(r, rho0, Rs)
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def mass_3d_lens(self, r, sigma0, Rs, e1=0, e2=0):
"""Mass enclosed a 3d sphere or radius r in lensing parameterization.
:param r: 3-d radius within the mass is integrated (same distance units as
density definition)
:param sigma0: rho0 * Rs (units of projected density)
:param Rs: Hernquist radius
:return: enclosed mass
"""
return self.spherical.mass_3d_lens(r, sigma0, Rs)