def power_law_anisotropy(self, r, kwargs_profile, kwargs_anisotropy,
kwargs_light):
"""
equation (19) in Suyu+ 2010
:param r:
:return:
"""
# first term
theta_E = kwargs_profile['theta_E']
gamma = kwargs_profile['gamma']
r_ani = kwargs_anisotropy['r_ani']
a = 0.551 * kwargs_light['r_eff']
rho0_r0_gamma = self._rho0_r0_gamma(theta_E, gamma)
prefac1 = 4 * np.pi * const.G * a**(-gamma) * rho0_r0_gamma / (3 -
gamma)
prefac2 = r * (r + a)**3 / (r**2 + r_ani**2)
hyp1 = vel_util.hyp_2F1(a=2 + gamma,
b=gamma,
c=3 + gamma,
z=1. / (1 + r / a))
hyp2 = vel_util.hyp_2F1(a=3, b=gamma, c=1 + gamma, z=-a / r)
fac = r_ani**2 / a**2 * hyp1 / (
(2 + gamma) * (r / a + 1)**(2 + gamma)) + hyp2 / (gamma *
(r / a)**gamma)
sigma2_dim_less = prefac1 * prefac2 * fac
return sigma2_dim_less * (self.cosmo.arcsec2phys_lens(1.) * const.Mpc /
1000)**2
def sigma_r2(self, r, a, gamma, rho0_r0_gamma, r_ani):
"""
equation (19) in Suyu+ 2010
"""
# first term
prefac1 = 4*np.pi * const.G * a**(-gamma) * rho0_r0_gamma / (3-gamma)
prefac2 = r * (r + a)**3/(r**2 + r_ani**2)
hyp1 = vel_util.hyp_2F1(a=2+gamma, b=gamma, c=3+gamma, z=1./(1+r/a))
hyp2 = vel_util.hyp_2F1(a=3, b=gamma, c=1+gamma, z=-a/r)
fac = r_ani**2/a**2 * hyp1 / ((2+gamma) * (r/a + 1)**(2+gamma)) + hyp2 / (gamma*(r/a)**gamma)
return prefac1 * prefac2 * fac * (self._cosmo.arcsec2phys_lens(1.) * const.Mpc / 1000) ** 2
def _F(self, a, z, beta_inf):
"""
the hypergeometric function 2F1 (a, 1 +beta_inf, a + 1, z)
:param a:
:param z:
:return:
"""
if isinstance(z, int) or isinstance(z, float):
return velocity_util.hyp_2F1(a=a, b=1 + beta_inf, c=a + 1, z=z)
else:
_F_array = []
for z_i in z:
_F_array.append(
velocity_util.hyp_2F1(a=a, b=1 + beta_inf, c=a + 1, z=z_i))
return np.array(_F_array, dtype=float)
def _sigma_r2(self, r, a, gamma, rho0_r0_gamma, r_ani):
"""
equation (19) in Suyu+ 2010
"""
# first term
prefac1 = 4 * np.pi * const.G * a**(-gamma) * rho0_r0_gamma / (3 -
gamma)
prefac2 = r * (r + a)**3 / (r**2 + r_ani**2)
# TODO check whether interpolation functions can speed this up
hyp1 = vel_util.hyp_2F1(a=2 + gamma,
b=gamma,
c=3 + gamma,
z=1. / (1 + r / a))
hyp2 = vel_util.hyp_2F1(a=3, b=gamma, c=1 + gamma, z=-a / r)
fac = r_ani**2 / a**2 * hyp1 / (
(2 + gamma) * (r / a + 1)**(2 + gamma)) + hyp2 / (gamma *
(r / a)**gamma)
return prefac1 * prefac2 * fac * (const.arcsec * self._cosmo.dd *
const.Mpc)**2
