class PowerLawSubhalo(Halo):
"""
The base class for a halo modeled as a power law profile
"""
def __init__(self, mass, x, y, r3d, mdef, z, sub_flag, lens_cosmo_instance,
args, unique_tag):
"""
See documentation in base class (Halos/halo_base.py)
"""
self._prof = SPLCORE()
self._lens_cosmo = lens_cosmo_instance
super(PowerLawSubhalo,
self).__init__(mass, x, y, r3d, mdef, z, sub_flag,
lens_cosmo_instance, args, unique_tag)
@property
def params_physical(self):
"""
See documentation in base class (Halos/halo_base.py)
"""
if not hasattr(self, '_params_physical'):
(concentration, gamma, x_core_halo) = self.profile_args
rhos, rs, _ = self._lens_cosmo.NFW_params_physical(
self.mass, concentration, self.z)
kpc_per_arcsec = self._lens_cosmo.cosmo.kpc_proper_per_asec(self.z)
if 'x_match' in self._args.keys():
x_match = self._args['x_match']
else:
# r_vmax = 2.16 * rs
x_match = 2.16
r_match_arcsec = x_match * rs / kpc_per_arcsec
fx = np.log(1 + x_match) - x_match / (1 + x_match)
m = 4 * np.pi * rs**3 * rhos * fx
r_core_arcsec = x_core_halo * r_match_arcsec / x_match
sigma_crit_mpc = self._lens_cosmo.get_sigma_crit_lensing(
self.z, self._lens_cosmo.z_source)
sigma_crit_arcsec = sigma_crit_mpc * (0.001 * kpc_per_arcsec)**2
rho0 = m / self._prof.mass_3d(r_match_arcsec, sigma_crit_arcsec,
r_core_arcsec, gamma)
# units 1 / arcsec
rho0 *= sigma_crit_arcsec * kpc_per_arcsec**-3
self._params_physical = {'rho0': rho0, 'r_core': x_core_halo * rs}
return self._params_physical
@property
def lenstronomy_params(self):
"""
See documentation in base class (Halos/halo_base.py)
"""
if not hasattr(self, '_lenstronomy_args'):
(concentration, gamma, x_core_halo) = self.profile_args
rhos, rs, _ = self._lens_cosmo.NFW_params_physical(
self.mass, concentration, self.z)
kpc_per_arcsec = self._lens_cosmo.cosmo.kpc_proper_per_asec(self.z)
if 'x_match' in self._args.keys():
x_match = self._args['x_match']
else:
# r_vmax = 2.16 * rs
x_match = 2.16
r_match_arcsec = x_match * rs / kpc_per_arcsec
fx = np.log(1 + x_match) - x_match / (1 + x_match)
m = 4 * np.pi * rs**3 * rhos * fx
r_core_arcsec = x_core_halo * r_match_arcsec / x_match
sigma_crit_mpc = self._lens_cosmo.get_sigma_crit_lensing(
self.z, self._lens_cosmo.z_source)
sigma_crit_arcsec = sigma_crit_mpc * (0.001 * kpc_per_arcsec)**2
rho0 = m / self._prof.mass_3d(r_match_arcsec, sigma_crit_arcsec,
r_core_arcsec, gamma)
sigma0 = rho0 * r_core_arcsec
self._lenstronomy_args = [{
'sigma0': sigma0,
'gamma': gamma,
'center_x': self.x,
'center_y': self.y,
'r_core': r_core_arcsec
}]
return self._lenstronomy_args, None
@property
def lenstronomy_ID(self):
"""
See documentation in base class (Halos/halo_base.py)
"""
return ['SPL_CORE']
@property
def profile_args(self):
"""
See documentation in base class (Halos/halo_base.py)
"""
if not hasattr(self, '_profile_args'):
if self._args['evaluate_mc_at_zlens']:
z_eval = self.z
else:
z_eval = self.z_infall
concentration = self._lens_cosmo.NFW_concentration(
self.mass, z_eval, self._args['mc_model'],
self._args['mc_mdef'], self._args['log_mc'],
self._args['c_scatter'], self._args['c_scatter_dex'],
self._args['kwargs_suppression'],
self._args['suppression_model'])
gamma = self._args['log_slope_halo']
x_core_halo = self._args['x_core_halo']
self._profile_args = (concentration, gamma, x_core_halo)
return self._profile_args
class TestSPLCORE(object):
def setup(self):
self.profile = SPLCORE()
def test_no_potential(self):
npt.assert_raises(Exception, self.profile.function, 0., 0., 0., 0., 0.)
def test_origin(self):
x = 0.
y = 0.
sigma0 = 1.
r_core = 0.1
gamma = 2.4
alpha_x, alpha_y = self.profile.derivatives(x, y, sigma0, r_core,
gamma)
npt.assert_almost_equal(alpha_x, 0.)
npt.assert_almost_equal(alpha_y, 0.)
fxx, fyy, fxy = self.profile.hessian(x, y, sigma0, r_core, gamma)
kappa = self.profile.density_2d(x, y, sigma0 / r_core, r_core, gamma)
npt.assert_almost_equal(fxx, kappa)
npt.assert_almost_equal(fyy, kappa)
npt.assert_almost_equal(fxy, 0.)
r = 0.01
xmin = 0.001
rmin = self.profile._safe_r_division(r, 1., xmin)
npt.assert_equal(rmin, r)
r = 1e-9
rmin = self.profile._safe_r_division(r, 1., xmin)
npt.assert_equal(rmin, xmin)
xmin = 1e-2
r = np.logspace(-3, 0, 100)
inds = np.where(r < xmin)
rmin = self.profile._safe_r_division(r, 1., xmin)
npt.assert_almost_equal(rmin[inds], xmin)
def test_g_function(self):
gamma = 2.5
rc = 0.01
rho0 = 1.
R = 5.
args = (rho0, rc, gamma)
mass_numerical = quad(self._mass_integrand3d, 0, R, args=args)[0]
mass_analytic = self.profile.mass_3d(R, rho0, rc, gamma)
npt.assert_almost_equal(mass_analytic, mass_numerical)
gamma = 2.
args = (rho0, rc, gamma)
mass_numerical = quad(self._mass_integrand3d, 0, R, args=args)[0]
mass_analytic = self.profile.mass_3d(R, rho0, rc, gamma)
npt.assert_almost_equal(mass_analytic, mass_numerical)
gamma = 3.
args = (rho0, rc, gamma)
mass_numerical = quad(self._mass_integrand3d, 0, R, args=args)[0]
mass_analytic = self.profile.mass_3d(R, rho0, rc, gamma)
npt.assert_almost_equal(mass_analytic, mass_numerical)
gamma = 1.4
args = (rho0, rc, gamma)
mass_numerical = quad(self._mass_integrand3d, 0, R, args=args)[0]
mass_analytic = self.profile.mass_3d(R, rho0, rc, gamma)
npt.assert_almost_equal(mass_analytic, mass_numerical)
sigma0 = rho0 * rc
mass_analytic_from_sigm0 = self.profile.mass_3d_lens(
R, sigma0, rc, gamma)
npt.assert_almost_equal(mass_analytic_from_sigm0, mass_numerical)
def test_f_function(self):
gamma = 2.5
rc = 0.01
rho0 = 1.
R = 5.
args = (rho0, rc, gamma)
mass_numerical = quad(self._mass_integrand2d, 0, R, args=args)[0]
mass_analytic = self.profile.mass_2d(R, rho0, rc, gamma)
npt.assert_almost_equal(mass_analytic, mass_numerical)
sigma0 = rho0 * rc
mass_analytic_from_sigm0 = self.profile.mass_2d_lens(
R, sigma0, rc, gamma)
npt.assert_almost_equal(mass_analytic_from_sigm0, mass_numerical)
gamma = 2.
args = (rho0, rc, gamma)
mass_numerical = quad(self._mass_integrand2d, 0, R, args=args)[0]
mass_analytic = self.profile.mass_2d(R, rho0, rc, gamma)
npt.assert_almost_equal(mass_analytic, mass_numerical)
sigma0 = rho0 * rc
mass_analytic_from_sigm0 = self.profile.mass_2d_lens(
R, sigma0, rc, gamma)
npt.assert_almost_equal(mass_analytic_from_sigm0, mass_numerical)
gamma = 3.
args = (rho0, rc, gamma)
mass_numerical = quad(self._mass_integrand2d, 0, R, args=args)[0]
mass_analytic = self.profile.mass_2d(R, rho0, rc, gamma)
npt.assert_almost_equal(mass_analytic, mass_numerical)
sigma0 = rho0 * rc
mass_analytic_from_sigm0 = self.profile.mass_2d_lens(
R, sigma0, rc, gamma)
npt.assert_almost_equal(mass_analytic_from_sigm0, mass_numerical)
gamma = 1.4
args = (rho0, rc, gamma)
mass_numerical = quad(self._mass_integrand2d, 0, R, args=args)[0]
mass_analytic = self.profile.mass_2d(R, rho0, rc, gamma)
npt.assert_almost_equal(mass_analytic, mass_numerical)
sigma0 = rho0 * rc
mass_analytic_from_sigm0 = self.profile.mass_2d_lens(
R, sigma0, rc, gamma)
npt.assert_almost_equal(mass_analytic_from_sigm0, mass_numerical)
def _mass_integrand3d(self, r, rho0, rc, gamma):
return 4 * np.pi * r**2 * rho0 * rc**gamma / (rc**2 + r**2)**(gamma /
2)
def _mass_integrand2d(self, r, rho0, rc, gamma):
return 2 * np.pi * r * self.profile.density_2d(r, 0, rho0, rc, gamma)