class TestCosmology(object):
def setup(self):
self.arcsec = 2 * np.pi / 360 / 3600
self.zlens = 1
self.zsource = 2
self.angle_diameter = 2 / self.arcsec
self.angle_radius = 0.5 * self.angle_diameter
self.H0 = 70
self.omega_baryon = 0.03
self.omega_DM = 0.25
self.sigma8 = 0.82
curvature = 'flat'
self.ns = 0.9608
cosmo_params = {
'H0': self.H0,
'Om0': self.omega_baryon + self.omega_DM,
'Ob0': self.omega_baryon,
'sigma8': self.sigma8,
'ns': self.ns,
'curvature': curvature
}
self._dm, self._bar = self.omega_DM, self.omega_baryon
self.cosmo = Cosmology(cosmo_kwargs=cosmo_params)
self.geometry = Geometry(self.cosmo, self.zlens, self.zsource,
self.angle_diameter, 'DOUBLE_CONE')
def test_cosmo(self):
da_true = self.cosmo.D_A(0, 1.824)
da_interp = self.cosmo.D_A_z(1.824)
npt.assert_almost_equal(da_true / da_interp, 1, 5)
dc_true = self.cosmo.astropy.comoving_transverse_distance(1.4).value
dc_interp = self.cosmo.D_C_z(1.4)
dc_astropy = self.cosmo.astropy.comoving_distance(1.4).value
npt.assert_almost_equal(dc_true / dc_interp, 1)
npt.assert_almost_equal(dc_astropy / dc_true, 1)
dc_transverse = self.cosmo.D_C_transverse(0.8)
dc = self.cosmo.astropy.comoving_transverse_distance(0.8).value
npt.assert_almost_equal(dc / dc_transverse, 1)
ez = self.cosmo.E_z(0.8)
ez_astropy = self.cosmo.astropy.efunc(0.8)
npt.assert_almost_equal(ez / ez_astropy, 1)
kpc_per_asec = self.cosmo.kpc_proper_per_asec(0.5)
kpc_per_arcsec_true = self.cosmo.astropy.kpc_proper_per_arcmin(
0.5).value / 60
npt.assert_almost_equal(kpc_per_asec, kpc_per_arcsec_true, 2)
rho_crit_0 = self.cosmo.rho_crit(0)
rho_pc = un.Quantity(self.cosmo.astropy.critical_density(0),
unit=un.Msun / un.pc**3)
rho_Mpc = rho_pc.value * (1e+6)**3
npt.assert_almost_equal(rho_crit_0 / rho_Mpc, 1, 3)
rho_crit = self.cosmo.rho_crit(0.6)
rho_pc = un.Quantity(self.cosmo.astropy.critical_density(0.6),
unit=un.Msun / un.m**3)
rho_Mpc = rho_pc.value * self.cosmo.Mpc**3
npt.assert_almost_equal(rho_crit / rho_Mpc, 1, 3)
rho_crit_dark_matter = self.cosmo.rho_dark_matter_crit
rho_crit_DM_astropy = self.cosmo.astropy.critical_density(0.).value * \
self.cosmo.density_to_MsunperMpc * self.cosmo.astropy.Odm(0.)
npt.assert_almost_equal(rho_crit_DM_astropy, rho_crit_dark_matter)
rho_crit = self.cosmo.rho_crit(0.3)
rho_pc = un.Quantity(self.cosmo.astropy.critical_density(0.3),
unit=un.Msun / un.pc**3)
rho_Mpc = rho_pc.value * (1e+6)**3
npt.assert_almost_equal(rho_crit / rho_Mpc, 1, 3)
colossus = self.cosmo.colossus
npt.assert_almost_equal(colossus.Om0,
self.omega_DM + self.omega_baryon)
npt.assert_almost_equal(colossus.Ob0, self.omega_baryon)
npt.assert_almost_equal(colossus.H0, self.H0)
npt.assert_almost_equal(colossus.sigma8, self.sigma8)
npt.assert_almost_equal(colossus.ns, self.ns)
halo_collapse_z = 9.
age_today = self.cosmo.astropy.age(0.).value
age_z = self.cosmo.astropy.age(halo_collapse_z).value
age = age_today - age_z
npt.assert_almost_equal(age,
self.cosmo.halo_age(0., zform=halo_collapse_z))
npt.assert_almost_equal(self.cosmo.scale_factor(0.7),
self.cosmo.astropy.scale_factor(0.7))
class TestConeGeometry(object):
def setup(self):
self.arcsec = 2 * np.pi / 360 / 3600
self.zlens = 1
self.zsource = 2
self.angle_diameter = 2 / self.arcsec
self.angle_radius = 0.5 * self.angle_diameter
H0 = 70
omega_baryon = 0.0
omega_DM = 0.3
sigma8 = 0.82
curvature = 'flat'
ns = 0.9608
cosmo_params = {
'H0': H0,
'Om0': omega_baryon + omega_DM,
'Ob0': omega_baryon,
'sigma8': sigma8,
'ns': ns,
'curvature': curvature
}
self.cosmo = Cosmology(cosmo_kwargs=cosmo_params)
self._angle_pad = 0.75
self.geometry_double_cone = Geometry(self.cosmo, self.zlens,
self.zsource, self.angle_diameter,
'DOUBLE_CONE', self._angle_pad)
def test_angle_scale(self):
reduced_to_phys = self.geometry_double_cone._cosmo.D_A(0, self.zsource) / \
self.geometry_double_cone._cosmo.D_A(self.zlens, self.zsource)
ratio_double_cone = reduced_to_phys * \
self.cosmo.D_A(self.zlens, self.zsource)/self.cosmo.D_A_z(self.zsource)
angle_scale_zsource = 1 - self._angle_pad * ratio_double_cone
npt.assert_almost_equal(
self.geometry_double_cone.rendering_scale(self.zlens), 1.)
npt.assert_almost_equal(
self.geometry_double_cone.rendering_scale(self.zsource),
angle_scale_zsource)
npt.assert_almost_equal(
self.geometry_double_cone.rendering_scale(self.zlens), 1)
def test_distances_lensing(self):
z = 0.3
radius_physical = self.geometry_double_cone.angle_to_physicalradius(
self.angle_radius, z)
radius = self.geometry_double_cone._cosmo.D_A(
0., z) * self.angle_radius * self.arcsec
npt.assert_almost_equal(radius_physical, radius, 0)
comoving_radius = self.geometry_double_cone.angle_to_comovingradius(
self.angle_radius, z)
npt.assert_almost_equal(comoving_radius, radius_physical * (1 + z), 3)
z = 1
radius_physical = self.geometry_double_cone.angle_to_physicalradius(
self.angle_radius, z)
radius = self.geometry_double_cone._cosmo.D_A(
0., z) * self.angle_radius * self.arcsec
npt.assert_almost_equal(radius_physical, radius, 0)
comoving_radius = self.geometry_double_cone.angle_to_comovingradius(
self.angle_radius, z)
npt.assert_almost_equal(comoving_radius, radius_physical * (1 + z), 3)
z = 1.25
radius_physical = self.geometry_double_cone.angle_to_physicalradius(
self.angle_radius, z)
D_dz = self.geometry_double_cone._cosmo.D_A(self.zlens, z)
D_s = self.geometry_double_cone._cosmo.D_A(0, self.zsource)
D_z = self.geometry_double_cone._cosmo.D_A(0, z)
D_ds = self.geometry_double_cone._cosmo.D_A(self.zlens, self.zsource)
rescale = 1 - self._angle_pad * D_dz * D_s / (D_z * D_ds)
radius = self.geometry_double_cone._cosmo.D_A(
0., z) * self.angle_radius * self.arcsec * rescale
npt.assert_almost_equal(radius_physical, radius, 0)
comoving_radius = self.geometry_double_cone.angle_to_comovingradius(
self.angle_radius, z)
npt.assert_almost_equal(comoving_radius, radius_physical * (1 + z), 3)
def test_volume(self):
cone_arcsec = 3
radius = cone_arcsec * 0.5
angle_pad = 0.7
zlens = 1.
zsrc = 1.8
geo = Geometry(self.cosmo,
zlens,
zsrc,
cone_arcsec,
'DOUBLE_CONE',
angle_pad=angle_pad)
astropy = geo._cosmo.astropy
delta_z = 1e-3
dV_pyhalo = geo.volume_element_comoving(0.6, delta_z)
dV = astropy.differential_comoving_volume(0.6).value
dV_astropy = dV * delta_z
steradian = np.pi * (radius * self.arcsec)**2
npt.assert_almost_equal(dV_astropy * steradian, dV_pyhalo, 5)
angle_scale = geo.rendering_scale(1.3)
dV_pyhalo = geo.volume_element_comoving(1.3, delta_z)
dV = astropy.differential_comoving_volume(1.3).value
dV_astropy = dV * delta_z
steradian = np.pi * (radius * angle_scale * self.arcsec)**2
npt.assert_almost_equal(dV_astropy * steradian, dV_pyhalo, 5)
def test_total_volume(self):
cone_arcsec = 4
radius_radians = cone_arcsec * 0.5 * self.cosmo.arcsec
geo = Geometry(self.cosmo,
0.5,
1.5,
cone_arcsec,
'DOUBLE_CONE',
angle_pad=1.)
volume_pyhalo = 0
z = np.linspace(0.0, 1.5, 200)
for i in range(0, len(z) - 1):
delta_z = z[i + 1] - z[i]
volume_pyhalo += geo.volume_element_comoving(z[i], delta_z)
ds = self.cosmo.D_C_z(1.5)
dz = self.cosmo.D_C_z(0.5)
volume_true = 1. / 3 * np.pi * radius_radians**2 * dz**2 * ds
npt.assert_almost_equal(volume_true, volume_pyhalo, 3)
class TestLensCosmo(object):
def setup(self):
kwargs_cosmo = {'Om0': 0.2}
self.cosmo = Cosmology(cosmo_kwargs=kwargs_cosmo)
zlens, zsource = 0.3, 1.7
self.lens_cosmo = LensCosmo(zlens, zsource, self.cosmo)
self.h = self.cosmo.h
self.con = Concentration(self.lens_cosmo)
self._colossus_nfw = NFWProfile
def test_const(self):
D_ds = self.cosmo.D_A(0.3, 1.7)
D_d = self.cosmo.D_A_z(0.3)
D_s = self.cosmo.D_A_z(1.7)
c_Mpc_sec = un.Quantity(c, unit=un.Mpc / un.s)
G_Mpc3_Msun_sec2 = un.Quantity(G, unit=un.Mpc ** 3 / un.s ** 2 / un.solMass)
const = c_Mpc_sec ** 2 / (4 * np.pi * G_Mpc3_Msun_sec2)
sigma_crit_mpc = const.value * D_s / (D_d * D_ds)
sigma_crit_kpc = sigma_crit_mpc * 1000 ** -2
npt.assert_almost_equal(self.lens_cosmo.sigma_crit_lensing/sigma_crit_mpc, 1, 4)
npt.assert_almost_equal(self.lens_cosmo.sigma_crit_lens_kpc/sigma_crit_kpc, 1, 4)
def test_sigma_crit_mass(self):
area = 2.
sigma_crit_mass = self.lens_cosmo.sigma_crit_mass(0.7, area)
sigma_crit = self.lens_cosmo.get_sigma_crit_lensing(0.7, 1.7)
npt.assert_almost_equal(sigma_crit_mass, sigma_crit * area)
def test_colossus(self):
colossus = self.lens_cosmo.colossus
npt.assert_almost_equal(colossus.Om0, 0.2)
def test_truncate_roche(self):
m = 10**9.
norm = 1.4
power = 0.9
r3d = 1000
rt = norm * (m / 10 ** 7) ** (1./3) * (r3d / 50) ** power
rtrunc = self.lens_cosmo.truncation_roche(m, r3d, norm, power)
npt.assert_almost_equal(rt, rtrunc, 3)
def test_LOS_trunc(self):
rt = self.lens_cosmo.LOS_truncation_rN(10**8, 0.2, 90)
rtrunc = self.lens_cosmo.rN_M_nfw_comoving(10**8 * self.lens_cosmo.cosmo.h, 90, 0.2)
npt.assert_almost_equal(rt, 1000 * rtrunc * (1+0.2)**-1 / self.lens_cosmo.cosmo.h)
def test_NFW_concentration(self):
c = self.lens_cosmo.NFW_concentration(10 ** 9, 0.2, model='diemer19', scatter=False)
c2 = self.lens_cosmo.NFW_concentration(10 ** 9, 0.2, model='diemer19', scatter=True)
npt.assert_raises(AssertionError, npt.assert_array_equal, c, c2)
logmhm = 8.
kwargs_suppression, suppression_model = {'c_scale': 60., 'c_power': -0.17}, 'polynomial'
c_wdm = self.lens_cosmo.NFW_concentration(10 ** 9, 0.2, model='diemer19', scatter=False, logmhm=logmhm,
kwargs_suppresion=kwargs_suppression, suppression_model=suppression_model)
suppresion = WDM_concentration_suppresion_factor(10**9, 0.2, logmhm, suppression_model, kwargs_suppression)
npt.assert_almost_equal(suppresion * c, c_wdm)
kwargs_suppression, suppression_model = {'a_mc': 0.5, 'b_mc': 0.17}, 'hyperbolic'
c_wdm = self.lens_cosmo.NFW_concentration(10 ** 9, 0.2, model='diemer19', scatter=False, logmhm=logmhm,
kwargs_suppresion=kwargs_suppression,
suppression_model=suppression_model)
suppresion = WDM_concentration_suppresion_factor(10 ** 9, 0.2, logmhm, suppression_model, kwargs_suppression)
npt.assert_almost_equal(suppresion * c, c_wdm)
def test_subhalo_accretion(self):
zi = [self.lens_cosmo.z_accreted_from_zlens(10**8, 0.5)
for _ in range(0, 20000)]
h, b = np.histogram(zi, bins=np.linspace(0.5, 6, 20))
# number at the lens redshift should be about 5x that at redshift 4
ratio = h[0]/h[12]
npt.assert_almost_equal(ratio/5 - 1, 0., 1)
def test_nfw_fundamental_parameters(self):
for z in [0., 0.74, 1.2]:
M, c = 10**8, 17.5
rho_crit_z = self.cosmo.rho_crit(z)
rhos, rs, r200 = self.lens_cosmo.nfwParam_physical_Mpc(M, c, z)
h = self.cosmo.h
_rhos, _rs = self._colossus_nfw.fundamentalParameters(M * h, c, z, '200c')
# output in units (M h^2 / kpc^2, kpc/h)
rhos_col = _rhos * h ** 2 * 1000 ** 3
rs_col = _rs / h / 1000
r200_col = rs * c
npt.assert_almost_equal(rhos/rhos_col, 1, 3)
npt.assert_almost_equal(rs/rs_col, 1, 3)
npt.assert_almost_equal(r200/r200_col, 1, 3)
def _profile(x):
fac = x * (1 + x) ** 2
return 1. / fac
def _integrand(x):
return 4 * np.pi * x ** 2 * _profile(x)
volume = 4 * np.pi/3 * r200 ** 3
integral = quad(_integrand, 0, r200/rs)[0]
mean_density = rhos * rs ** 3 * integral / volume
ratio = mean_density/rho_crit_z
npt.assert_almost_equal(ratio/200, 1., 3)
def test_mhm_convert(self):
mthermal = 5.3
mhm = self.lens_cosmo.mthermal_to_halfmode(mthermal)
mthermal_out = self.lens_cosmo.halfmode_to_thermal(mhm)
npt.assert_almost_equal(mthermal/mthermal_out, 1, 2)
fsl = self.lens_cosmo.mhm_to_fsl(10**8.)
npt.assert_array_less(fsl, 100)
def test_NFW_phys2angle(self):
c = self.lens_cosmo.NFW_concentration(10**8, 0.5, scatter=False)
out = self.lens_cosmo.nfw_physical2angle(10**8, c, 0.5)
out2 = self.lens_cosmo.nfw_physical2angle_fromM(10**8, 0.5)
for (x, y) in zip(out, out2):
npt.assert_almost_equal(x, y)
rhos_kpc, rs_kpc, _ = self.lens_cosmo.NFW_params_physical(10**8, c, 0.5)
rhos_mpc = rhos_kpc * 1000 ** 3
rs_mpc = rs_kpc * 1e-3
rs, theta_rs = self.lens_cosmo.nfw_physical2angle_fromNFWparams(rhos_mpc, rs_mpc, 0.5)
npt.assert_almost_equal(rs, out[0])
npt.assert_almost_equal(theta_rs, out[1])