Source code for lenstronomy.LensModel.Profiles.spp

__author__ = 'sibirrer'


import numpy as np
import scipy.special as special
from lenstronomy.LensModel.Profiles.base_profile import LensProfileBase

__all__ = ['SPP']


[docs]class SPP(LensProfileBase): """ class for circular power-law mass distribution """ param_names = ['theta_E', 'gamma', 'center_x', 'center_y'] lower_limit_default = {'theta_E': 0, 'gamma': 1.5, 'center_x': -100, 'center_y': -100} upper_limit_default = {'theta_E': 100, 'gamma': 2.5, 'center_x': 100, 'center_y': 100}
[docs] def function(self, x, y, theta_E, gamma, center_x=0, center_y=0): """ :param x: set of x-coordinates :type x: array of size (n) :param theta_E: Einstein radius of lens :type theta_E: float. :param gamma: power law slope of mass profile :type gamma: <2 float :returns: function :raises: AttributeError, KeyError """ gamma = self._gamma_limit(gamma) x_ = x - center_x y_ = y - center_y E = theta_E / ((3. - gamma) / 2.) ** (1. / (1. - gamma)) # E = phi_E_spp eta= -gamma + 3 p2 = x_**2+y_**2 s2 = 0. # softening return 2 * E**2/eta**2 * ((p2 + s2)/E**2)**(eta/2)
[docs] def derivatives(self, x, y, theta_E, gamma, center_x=0., center_y=0.): gamma = self._gamma_limit(gamma) xt1 = x - center_x xt2 = y - center_y r2 = xt1*xt1+xt2*xt2 a = np.maximum(r2, 0.000001) r = np.sqrt(a) alpha = theta_E * (r2/theta_E**2) ** (1 - gamma/2.) fac = alpha/r f_x = fac*xt1 f_y = fac*xt2 return f_x, f_y
[docs] def hessian(self, x, y, theta_E, gamma, center_x=0., center_y=0.): gamma = self._gamma_limit(gamma) xt1 = x - center_x xt2 = y - center_y E = theta_E / ((3. - gamma) / 2.) ** (1. / (1. - gamma)) # E = phi_E_spp eta = -gamma + 3. P2 = xt1**2+xt2**2 if isinstance(P2, int) or isinstance(P2, float): a = max(0.000001,P2) else: a=np.empty_like(P2) p2 = P2[P2>0] #in the SIS regime a[P2==0] = 0.000001 a[P2>0] = p2 kappa = 1./eta*(a/E**2)**(eta/2-1)*((eta-2)*(xt1**2+xt2**2)/a+(1+1)) gamma1 = 1./eta*(a/E**2)**(eta/2-1)*((eta/2-1)*(2*xt1**2-2*xt2**2)/a) gamma2 = 4*xt1*xt2*(1./2-1/eta)*(a/E**2)**(eta/2-2)/E**2 f_xx = kappa + gamma1 f_yy = kappa - gamma1 f_xy = gamma2 return f_xx, f_xy, f_xy, f_yy
[docs] @staticmethod def rho2theta(rho0, gamma): """ converts 3d density into 2d projected density parameter :param rho0: :param gamma: :return: """ fac = np.sqrt(np.pi) * special.gamma(1. / 2 * (-1 + gamma)) / special.gamma(gamma / 2.) * 2 / (3 - gamma) * rho0 #fac = theta_E**(gamma - 1) theta_E = fac**(1. / (gamma - 1)) return theta_E
[docs] @staticmethod def theta2rho(theta_E, gamma): """ converts projected density parameter (in units of deflection) into 3d density parameter :param theta_E: :param gamma: :return: """ fac1 = np.sqrt(np.pi) * special.gamma(1. / 2 * (-1 + gamma)) / special.gamma(gamma / 2.) * 2 / (3 - gamma) fac2 = theta_E**(gamma - 1) rho0 = fac2 / fac1 return rho0
[docs] @staticmethod def mass_3d(r, rho0, gamma): """ mass enclosed a 3d sphere or radius r :param r: :param a: :param s: :return: """ mass_3d = 4 * np.pi * rho0 /(-gamma + 3) * r ** (-gamma + 3) return mass_3d
[docs] def mass_3d_lens(self, r, theta_E, gamma): """ :param r: :param theta_E: :param gamma: :return: """ rho0 = self.theta2rho(theta_E, gamma) return self.mass_3d(r, rho0, gamma)
[docs] def mass_2d(self, r, rho0, gamma): """ mass enclosed projected 2d sphere of radius r :param r: :param rho0: :param a: :param s: :return: """ alpha = np.sqrt(np.pi) * special.gamma(1. / 2 * (-1 + gamma)) / special.gamma(gamma / 2.) * r ** (2 - gamma)/(3 - gamma) *np.pi * 2 * rho0 mass_2d = alpha*r return mass_2d
[docs] def mass_2d_lens(self, r, theta_E, gamma): """ :param r: projected radius :param theta_E: Einstein radius :param gamma: power-law slope :return: 2d projected radius enclosed """ rho0 = self.theta2rho(theta_E, gamma) return self.mass_2d(r, rho0, gamma)
[docs] def grav_pot(self, x, y, rho0, gamma, center_x=0, center_y=0): """ gravitational potential (modulo 4 pi G and rho0 in appropriate units) :param x: :param y: :param rho0: :param a: :param s: :param center_x: :param center_y: :return: """ x_ = x - center_x y_ = y - center_y r = np.sqrt(x_**2 + y_**2) mass_3d = self.mass_3d(r, rho0, gamma) pot = mass_3d/r return pot
[docs] @staticmethod def density(r, rho0, gamma): """ computes the density :param x: :param y: :param rho0: :param a: :param s: :return: """ rho = rho0 / r**gamma return rho
[docs] def density_lens(self, r, theta_E, gamma): """ computes the density at 3d radius r given lens model parameterization. The integral in projected in units of angles (i.e. arc seconds) results in the convergence quantity. """ rho0 = self.theta2rho(theta_E, gamma) return self.density(r, rho0, gamma)
[docs] @staticmethod def density_2d(x, y, rho0, gamma, center_x=0, center_y=0): """ projected density :param x: :param y: :param rho0: :param a: :param s: :param center_x: :param center_y: :return: """ x_ = x - center_x y_ = y - center_y r = np.sqrt(x_**2 + y_**2) sigma = np.sqrt(np.pi) * special.gamma(1./2*(-1+gamma))/special.gamma(gamma/2.) * r**(1-gamma) * rho0 return sigma
@staticmethod def _gamma_limit(gamma): """ limits the power-law slope to certain bounds :param gamma: power-law slope :return: bounded power-law slopte """ return gamma