def test_age():
"""Test integrated age against analytical age."""
z = numpy.arange(0, 10.0, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[0.99],[0.01],[0.3]])
cosmo['omega_lambda_0'] = 1. - cosmo['omega_M_0']
cosmo['h'] = 0.7
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
gyr = 1e9 * cc.yr_s
tl = cd.lookback_time(z, **cosmo)
age = cd.age(z, **cosmo)
age_ana = cd.age_flat(z, **cosmo)
pylab.figure(figsize=(6,6))
for i in range(len(linestyle)):
pylab.plot(z, (tl/gyr)[i], ls=linestyle[i], color='0.5')
pylab.plot(z, (age/gyr)[i], ls=linestyle[i], color='r')
pylab.plot(z, (age_ana/gyr)[i], ls=linestyle[i], color='k')
pylab.xlabel("redshift z")
pylab.ylabel(r"age $t_L/$Gyr")
pylab.figure(figsize=(6,6))
for i in range(len(linestyle)):
pylab.plot(z, ((age - age_ana)/age_ana)[i], ls=linestyle[i],
color='k')
# Make sure errors are small:
ntest.assert_array_less((numpy.abs((age - age_ana)/age_ana)[i]),
3e-13)
pylab.xlabel("redshift z")
pylab.ylabel(r"age: (integral - analytical)/analytical")
def lb_time(z, **cosmo):
z = np.atleast_1d(z)
if cosmo == {}:
cosmo_in = {
'omega_M_0': 0.3,
'omega_lambda_0': 0.7,
'omega_k_0': 0.0,
'h': 0.70
}
else:
cosmo_in = cosmo
results = cd.lookback_time(z, **cosmo_in) / 60. / 60. / 24. / 365. / 1.e9
return results
def test_figure6():
"""Plot Hogg fig. 6: The dimensionless lookback time t_L/t_H and age t/t_H.
The three curves are for the three world models,
- Einstein-de Sitter (omega_M, omega_lambda) = (1, 0) [solid]
: Low-density (0.05, 0) [dotted]
-- High lambda, (0.2, 0.8) [dashed]
Hubble distance DH = c / H0
z from 0--5
t/th from 0--1.2
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0], [0.05], [0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0], [0.0], [0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
th = 1 / cd.hubble_z(0, **cosmo)
tl = cd.lookback_time(z, **cosmo)
age = cd.age(z, **cosmo)
pylab.figure(figsize=(6, 6))
for i in range(len(linestyle)):
pylab.plot(z, (tl / th)[i], ls=linestyle[i])
pylab.plot(z, (age / th)[i], ls=linestyle[i])
pylab.xlim(0, 5)
pylab.ylim(0, 1.2)
pylab.xlabel("redshift z")
pylab.ylabel(r"lookback timne $t_L/t_H$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_figure6():
"""Plot Hogg fig. 6: The dimensionless lookback time t_L/t_H and age t/t_H.
The three curves are for the three world models,
- Einstein-de Sitter (omega_M, omega_lambda) = (1, 0) [solid]
: Low-density (0.05, 0) [dotted]
-- High lambda, (0.2, 0.8) [dashed]
Hubble distance DH = c / H0
z from 0--5
t/th from 0--1.2
"""
z = numpy.arange(0, 5.05, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[1.0],[0.05],[0.2]])
cosmo['omega_lambda_0'] = numpy.array([[0.0],[0.0],[0.8]])
cosmo['h'] = 0.5
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
th = 1/ cd.hubble_z(0, **cosmo)
tl = cd.lookback_time(z, **cosmo)
age = cd.age(z, **cosmo)
pylab.figure(figsize=(6,6))
for i in range(len(linestyle)):
pylab.plot(z, (tl/th)[i], ls=linestyle[i])
pylab.plot(z, (age/th)[i], ls=linestyle[i])
pylab.xlim(0,5)
pylab.ylim(0,1.2)
pylab.xlabel("redshift z")
pylab.ylabel(r"lookback timne $t_L/t_H$")
pylab.title("compare to " + inspect.stack()[0][3].replace('test_', '') +
" (astro-ph/9905116v4)")
def test_age():
"""Test integrated age against analytical age."""
z = numpy.arange(0, 10.0, 0.05)
cosmo = {}
cosmo['omega_M_0'] = numpy.array([[0.99], [0.01], [0.3]])
cosmo['omega_lambda_0'] = 1. - cosmo['omega_M_0']
cosmo['h'] = 0.7
cd.set_omega_k_0(cosmo)
linestyle = ['-', ':', '--']
gyr = 1e9 * cc.yr_s
tl = cd.lookback_time(z, **cosmo)
age = cd.age(z, **cosmo)
age_ana = cd.age_flat(z, **cosmo)
pylab.figure(figsize=(6, 6))
for i in range(len(linestyle)):
pylab.plot(z, (tl / gyr)[i], ls=linestyle[i], color='0.5')
pylab.plot(z, (age / gyr)[i], ls=linestyle[i], color='r')
pylab.plot(z, (age_ana / gyr)[i], ls=linestyle[i], color='k')
pylab.xlabel("redshift z")
pylab.ylabel(r"age $t_L/$Gyr")
pylab.figure(figsize=(6, 6))
for i in range(len(linestyle)):
pylab.plot(z, ((age - age_ana) / age_ana)[i],
ls=linestyle[i],
color='k')
# Make sure errors are small:
ntest.assert_array_less((numpy.abs((age - age_ana) / age_ana)[i]),
3e-13)
pylab.xlabel("redshift z")
pylab.ylabel(r"age: (integral - analytical)/analytical")
dm = cd.comoving_distance_transverse(z[i], **Cosmology)
#See equation 16 of David Hogg's arXiv:astro-ph/9905116v4
da = cd.angular_diameter_distance(z[i], **Cosmology)
#See equations 18-19 of David Hogg's arXiv:astro-ph/9905116v4
dl = cd.luminosity_distance(z[i], **Cosmology)
#Units are Mpc
dVc = cd.diff_comoving_volume(z[i], **Cosmology)
#The differential comoving volume element dV_c/dz/dSolidAngle.
#Dimensions are volume per unit redshift per unit solid angle.
#Units are Mpc**3 Steradians^-1.
#See David Hogg's arXiv:astro-ph/9905116v4, equation 28
tl = cd.lookback_time(z[i], **Cosmology)
#See equation 30 of David Hogg's arXiv:astro-ph/9905116v4. Units are s.
agetl = cd.age(z[i], **Cosmology)
#Age at z is lookback time at z'->Infinity minus lookback time at z.
tH = 3.09e17 / Cosmology['h']
ez = cd.e_z(z[i], **Cosmology)
#The unitless Hubble expansion rate at redshift z.
#In David Hogg's (arXiv:astro-ph/9905116v4) formalism, this is
#equivalent to E(z), defined in his eq. 14.
if PlotNumber == 1:
val[i] = dm / dh
xtitle = "redshift z"
cosmo = {
'omega_M_0': omegaM,
'omega_lambda_0': omegaL,
'omega_k_0': 0.,
'h': h
}
Nz = 1001
z_grid = np.linspace(0., 5., Nz)
logt_grid = 0. * z_grid
rhoc_grid = 0. * z_grid
for i in range(0, Nz):
logt_grid[i] = np.log10(
distance.lookback_time(z_grid[i], 0., **cosmo) / yr) - 9.
rhoc_grid[i] = density.cosmo_densities(**cosmo)[0] * distance.e_z(
z_grid[i], **cosmo) * M_Sun / Mpc**3
z_spline = splrep(logt_grid[1:], z_grid[1:])
logt_spline = splrep(z_grid[1:], logt_grid[1:])
rhoc_spline = splrep(z_grid[1:], rhoc_grid[1:])
def z_form_vdisp_func(lvdisp):
return splev(0.46 + 0.238 * lvdisp, z_spline)
def z_form_mstar_func(lmstar):
return splev(0.427 + 0.053 * lmstar, z_spline)
dm = cd.comoving_distance_transverse(z[i],**Cosmology)
#See equation 16 of David Hogg's arXiv:astro-ph/9905116v4
da = cd.angular_diameter_distance(z[i],**Cosmology)
#See equations 18-19 of David Hogg's arXiv:astro-ph/9905116v4
dl = cd.luminosity_distance(z[i],**Cosmology)
#Units are Mpc
dVc = cd.diff_comoving_volume(z[i], **Cosmology)
#The differential comoving volume element dV_c/dz/dSolidAngle.
#Dimensions are volume per unit redshift per unit solid angle.
#Units are Mpc**3 Steradians^-1.
#See David Hogg's arXiv:astro-ph/9905116v4, equation 28
tl = cd.lookback_time(z[i],**Cosmology)
#See equation 30 of David Hogg's arXiv:astro-ph/9905116v4. Units are s.
agetl = cd.age(z[i],**Cosmology)
#Age at z is lookback time at z'->Infinity minus lookback time at z.
tH = 3.09e17/Cosmology['h']
ez = cd.e_z(z[i],**Cosmology)
#The unitless Hubble expansion rate at redshift z.
#In David Hogg's (arXiv:astro-ph/9905116v4) formalism, this is
#equivalent to E(z), defined in his eq. 14.
if PlotNumber == 1:
val[i] = dm/dh
xtitle = "redshift z"