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])