def test_hubble(threshold=1e-7):
cosmo = cosmo_wmap_5()
print "Comparing hubble constant with calculations from http://icosmo.org/"
# load external distance calculations
# z H(z)
hz_file = os.path.dirname(os.path.abspath(__file__))
hz_file = os.path.join(hz_file, 'icosmo_testdata', 'h_z.txt')
ic_hz = numpy.loadtxt(hz_file)
z = ic_hz[:, 0]
cd_hz = cd.hubble_z(z, **cosmo) * cc.Mpc_km
label = r"$H(z)$"
pylab.figure()
pylab.plot(z, ic_hz[:, 1], label=label + ' IC', ls=':')
pylab.plot(z, cd_hz, label=label + ' distance.py', ls='-')
pylab.legend(loc='best')
pylab.figure()
diff = (ic_hz[:, 1] - cd_hz) / ic_hz[:, 1]
maxdiff = numpy.max(numpy.abs(diff))
print "Maximum fraction difference in %s is %e." % (label, maxdiff)
if maxdiff > threshold:
print "Warning: difference exceeds threshold %e !!!" % threshold
assert (maxdiff < threshold)
pylab.plot(z, diff, label=label, ls='-')
pylab.legend(loc='best')
def interp_z_dependent_velocity_factors(z, deltaz=1e-3):
from cosmolopy.perturbation import fgrowth
zgrid = np.arange(np.min(z)-deltaz, np.max(z)+deltaz, deltaz)
hz_grid = distance.hubble_z(zgrid, **cosmo)
fgrowth_grid = fgrowth(zgrid, cosmo['omega_M_0'])
a_grid = 1./(1.+zgrid)
tmp_grid = fgrowth_grid*a_grid*hz_grid
from scipy import interpolate
f = interpolate.interp1d(zgrid, tmp_grid)
return f(z)
def calculate_rhoc_cosmopy(redshift=None, aexp=None,
cosmology=_get_cosmology()) :
pass
redshift = check_redshift_kwargs(redshift=redshift,aexp=aexp)
H_z = cdist.hubble_z(redshift, **cosmology) # /s
assert(3.*H_z**2/(8.*np.pi*constants.gravc) == \
cdens.cosmo_densities(**cosmology)[0]*cdist.e_z(redshift,**cosmology)**2)
return 3.*H_z**2/(8.*np.pi*constants.gravc)
def corr_delta_vel(r, z=0.4, kmin=1e-3, kmax=0.2):
# r is in Mpc
a = 1./(1.+z)
hz = distance.hubble_z(z, **cosmo)
fgrowth = perturbation.fgrowth(z, cosmo['omega_M_0'])
k = np.arange(kmin,kmax,kmin)
dk = k[1]-k[0]
corr = []
pk = perturbation.power_spectrum(k, z, **cosmo)
for this_r in r:
this_corr = a*hz*fgrowth/2./np.pi**2. * np.sum(dk*k*pk*spherical_bessel_j1(k*this_r))
corr.append(this_corr)
return np.array(corr)
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_hubble(threshold = 1e-7):
cosmo = cosmo_wmap_5()
print "Comparing hubble constant with calculations from http://icosmo.org/"
# load external distance calculations
# z H(z)
hz_file = os.path.dirname(os.path.abspath(__file__))
hz_file = os.path.join(hz_file, 'icosmo_testdata',
'h_z.txt')
ic_hz = numpy.loadtxt(hz_file)
z = ic_hz[:,0]
cd_hz = cd.hubble_z(z, **cosmo) * cc.Mpc_km
label = r"$H(z)$"
pylab.figure()
pylab.plot(z, ic_hz[:,1],
label=label + ' IC', ls=':')
pylab.plot(z, cd_hz, label=label + ' distance.py', ls='-')
pylab.legend(loc='best')
pylab.figure()
diff = (ic_hz[:,1] - cd_hz) / ic_hz[:,1]
maxdiff = numpy.max(numpy.abs(diff))
print "Maximum fraction difference in %s is %e." % (label,
maxdiff)
if maxdiff > threshold:
print "Warning: difference exceeds threshold %e !!!" % threshold
assert(maxdiff < threshold)
pylab.plot(z,
diff,
label=label, ls='-')
pylab.legend(loc='best')
def integrate_optical_depth(x_ionH, x_ionHe, z, **cosmo):
"""The electron scattering optical depth given ionized filling
factor vs. redshift.
Parameters
----------
x_ionH: array
Ionized fraction of hydrogen as a function of z. Should be [0,1].
x_ionHe: array
Set x_ionHE to X_HeII + 2 * X_HeIII, where X_HeII is the
fraction of helium that is singly ionized, and X_HeII is the
fraction of helium that is doubly ionized. See Notes below.
z: array
Redshift values at which the filling factor is specified.
cosmo: cosmological parameters
uses: 'X_H' and/or 'Y_He', plus parameters needed for hubble_z
Returns
-------
tau: array
The optical depth as a function of z.
Notes
-----
The precision of your result depends on the spacing of the input
arrays. When in doubt, try doubling your z resolution and see if
the optical depth values have converged.
100% singly ionized helium means x_ionHe = 1.0, 100% doubly
ionized helium means x_ionHe = 2.0
If you want helium to be singly ionized at the same rate as
hydrogen, set x_ionHe = x_ionH.
If you want helium to be doubly ionized at the same rate as
hydrogen is ionized, set x_ionHe = 2 * x_ionH.
"""
rho_crit, rho_0, n_He_0, n_H_0 = cden.baryon_densities(**cosmo)
# comoving Mpc^-1
n_p = n_H_0 + 2. * n_He_0
# comoving Mpc^-1
n_e = n_H_0 * x_ionH + n_He_0 * x_ionHe
# fraction of electrons that are free
x = n_e / n_p
H_0 = cc.H100_s * cosmo['h']
# Mpc s^-1 * Mpc^2 * Mpc^-3 / s^-1 -> unitless
tau_star = cc.c_light_Mpc_s * cc.sigma_T_Mpc * n_p
# s^-1
H_z = cd.hubble_z(z, **cosmo)
# Mpc^3 s^-1 * Mpc^-3 / s^-1 -> unitless
integrand = -1. * tau_star * x * ((1. + z)**2.) / H_z
integral = numpy.empty(integrand.shape)
integral[..., 1:] = si.cumtrapz(integrand, z)
integral[..., 0] = 0.0
return numpy.abs(integral)