def check_background_nu(cosmo):
"""
Check that background functions can be run and that the growth functions
exit gracefully in functions with massive neutrinos (not implemented yet).
"""
# Types of scale factor input (scalar, list, array)
a_scl = 0.5
a_lst = [0.2, 0.4, 0.6, 0.8, 1.]
a_arr = np.linspace(0.2, 1., 5)
# growth_factor
assert_raises(CCLError, ccl.growth_factor, cosmo, a_scl)
assert_raises(CCLError, ccl.growth_factor, cosmo, a_lst)
assert_raises(CCLError, ccl.growth_factor, cosmo, a_arr)
# growth_factor_unnorm
assert_raises(CCLError, ccl.growth_factor_unnorm, cosmo, a_scl)
assert_raises(CCLError, ccl.growth_factor_unnorm, cosmo, a_lst)
assert_raises(CCLError, ccl.growth_factor_unnorm, cosmo, a_arr)
# growth_rate
assert_raises(CCLError, ccl.growth_rate, cosmo, a_scl)
assert_raises(CCLError, ccl.growth_rate, cosmo, a_lst)
assert_raises(CCLError, ccl.growth_rate, cosmo, a_arr)
# comoving_radial_distance
assert_(all_finite(ccl.comoving_radial_distance(cosmo, a_scl)))
assert_(all_finite(ccl.comoving_radial_distance(cosmo, a_lst)))
assert_(all_finite(ccl.comoving_radial_distance(cosmo, a_arr)))
# h_over_h0
assert_(all_finite(ccl.h_over_h0(cosmo, a_scl)))
assert_(all_finite(ccl.h_over_h0(cosmo, a_lst)))
assert_(all_finite(ccl.h_over_h0(cosmo, a_arr)))
# luminosity_distance
assert_(all_finite(ccl.luminosity_distance(cosmo, a_scl)))
assert_(all_finite(ccl.luminosity_distance(cosmo, a_lst)))
assert_(all_finite(ccl.luminosity_distance(cosmo, a_arr)))
# scale_factor_of_chi
assert_(all_finite(ccl.scale_factor_of_chi(cosmo, a_scl)))
assert_(all_finite(ccl.scale_factor_of_chi(cosmo, a_lst)))
assert_(all_finite(ccl.scale_factor_of_chi(cosmo, a_arr)))
# omega_m_a
assert_(all_finite(ccl.omega_x(cosmo, a_scl, 'matter')))
assert_(all_finite(ccl.omega_x(cosmo, a_lst, 'matter')))
assert_(all_finite(ccl.omega_x(cosmo, a_arr, 'matter')))
def check_background(cosmo):
"""
Check that background and growth functions can be run.
"""
# Types of scale factor input (scalar, list, array)
a_scl = 0.5
a_lst = [0.2, 0.4, 0.6, 0.8, 1.]
a_arr = np.linspace(0.2, 1., 5)
# growth_factor
assert_( all_finite(ccl.growth_factor(cosmo, a_scl)) )
assert_( all_finite(ccl.growth_factor(cosmo, a_lst)) )
assert_( all_finite(ccl.growth_factor(cosmo, a_arr)) )
# growth_factor_unnorm
assert_( all_finite(ccl.growth_factor_unnorm(cosmo, a_scl)) )
assert_( all_finite(ccl.growth_factor_unnorm(cosmo, a_lst)) )
assert_( all_finite(ccl.growth_factor_unnorm(cosmo, a_arr)) )
# growth_rate
assert_( all_finite(ccl.growth_rate(cosmo, a_scl)) )
assert_( all_finite(ccl.growth_rate(cosmo, a_lst)) )
assert_( all_finite(ccl.growth_rate(cosmo, a_arr)) )
# comoving_radial_distance
assert_( all_finite(ccl.comoving_radial_distance(cosmo, a_scl)) )
assert_( all_finite(ccl.comoving_radial_distance(cosmo, a_lst)) )
assert_( all_finite(ccl.comoving_radial_distance(cosmo, a_arr)) )
# h_over_h0
assert_( all_finite(ccl.h_over_h0(cosmo, a_scl)) )
assert_( all_finite(ccl.h_over_h0(cosmo, a_lst)) )
assert_( all_finite(ccl.h_over_h0(cosmo, a_arr)) )
# luminosity_distance
assert_( all_finite(ccl.luminosity_distance(cosmo, a_scl)) )
assert_( all_finite(ccl.luminosity_distance(cosmo, a_lst)) )
assert_( all_finite(ccl.luminosity_distance(cosmo, a_arr)) )
# scale_factor_of_chi
assert_( all_finite(ccl.scale_factor_of_chi(cosmo, a_scl)) )
assert_( all_finite(ccl.scale_factor_of_chi(cosmo, a_lst)) )
assert_( all_finite(ccl.scale_factor_of_chi(cosmo, a_arr)) )
# omega_m_a
assert_( all_finite(ccl.omega_x(cosmo, a_scl, 'matter')) )
assert_( all_finite(ccl.omega_x(cosmo, a_lst, 'matter')) )
assert_( all_finite(ccl.omega_x(cosmo, a_arr, 'matter')) )
def r_Delta(cosmo, halo_mass, a, Delta=200, is_matter=False):
"""
Calculate the reference radius of a halo.
.. note:: this is R=(3M/(4*pi*rho_c(a)*Delta))^(1/3), where rho_c is the critical
matter density
Arguments
---------
cosmo : ``pyccl.Cosmology`` object
Cosmological parameters.
halo_mass : float or array_like
Halo mass [Msun].
a : float
Scale factor
Delta : float
Overdensity parameter.
Returns
-------
float or array_like : The halo reference radius in `Mpc`.
"""
omega_factor = 1.
if is_matter:
omega_factor = ccl.omega_x(cosmo, a, 'matter')
prefac = Delta * omega_factor * 1.16217766E12 * (
cosmo['h'] * ccl.h_over_h0(cosmo, a))**2
return (halo_mass / prefac)**(1. / 3.)
def Tb(self, z):
Ez = ccl.h_over_h0(self.C, 1. / (1. + z))
# Note potentially misleading notation:
# Ohi = (comoving density at z) / (critical density at z=0)
Ohi = 4e-4 * (1 + z)**0.6
Tb = 188e-3 * self.C['h'] / Ez * Ohi * (1 + z)**2
return Tb
def cutWedge(self, noise, kperp, kpar, z, NW=3.0):
r = ccl.comoving_radial_distance(self.C, 1 / (1. + z))
H = self.C['H0'] * ccl.h_over_h0(self.C, 1. / (1. + z))
slope = r * H / 3e5 * 1.22 * 0.21 / self.D * NW / 2.0
noiseout = np.copy(noise)
noiseout[np.where(kpar < kperp * slope)] = 1e30
return noiseout
def signal_power(zc, k, mu, cosmo, params):
"""
Return the signal auto- and cross-power spectra.
"""
# Scale factor at central redshift
a = 1. / (1. + zc)
# Get matter power spectrum
pk = ccl.linear_matter_power(cosmo, k, a)
# Get redshift-dep. functions
b = bias(zc, params)
rg = corrfac(zc, params)
f = params['x_f'] * ccl.growth_rate(cosmo, a)
beta = f / b
H = params['x_H'] * ccl.h_over_h0(cosmo, a) * 100. * cosmo['h'] # km/s/Mpc
# Redshift-space suppression factors
D_g = 1. / np.sqrt(1. + 0.5 * (k * mu * sigma_g(zc, params))**2.)
D_u = np.sinc(k * sigma_u(zc, params))
# galaxy-galaxy (dimensionless)
pk_gg = b**2. * (1. + 2. * rg * beta * mu**2. +
beta**2. * mu**4.) * D_g**2. * pk
# galaxy-velocity (units: km/s)
pk_gv = 1.j * a * H * f * b * mu * (rg +
beta * mu**2.) * D_g * D_u / k * pk
#pk_vg = -1. * pk_gv # Complex conjugate
# velocity-velocity (units: [km/s]^2)
pk_vv = (a * H * f * mu)**2. * (D_u / k)**2. * pk
# Multiply all elements by P(k) and return
return pk_gg, pk_gv, pk_vv
def test_tracer_nz_support():
z_max = 1.0
a = np.linspace(1 / (1 + z_max), 1.0, 100)
background_def = {
"a": a,
"chi": ccl.comoving_radial_distance(COSMO, a),
"h_over_h0": ccl.h_over_h0(COSMO, a)
}
calculator_cosmo = ccl.CosmologyCalculator(Omega_c=0.27,
Omega_b=0.045,
h=0.67,
sigma8=0.8,
n_s=0.96,
background=background_def)
z = np.linspace(0., 2., 2000)
n = dndz(z)
with pytest.raises(ValueError):
_ = ccl.WeakLensingTracer(calculator_cosmo, (z, n))
with pytest.raises(ValueError):
_ = ccl.NumberCountsTracer(calculator_cosmo,
has_rsd=False,
dndz=(z, n),
bias=(z, np.ones_like(z)))
with pytest.raises(ValueError):
_ = ccl.CMBLensingTracer(calculator_cosmo, z_source=2.0)
def redshift_space_density(self,
delta_x=None,
velocity_z=None,
sigma_nl=0.,
method='linear'):
"""
Remap the real-space density field to redshift-space using the line-of-
sight velocity field.
Parameters:
delta_x (array_like, optional):
Real-space density field.
velocity_z (array_like, optional):
Velocity in the z (line-of-sight) direction (km/s).
sigma_nl (float, optional):
Optionally, add random small-scale incoherent velocities along the
LOS (uncorrelated Gaussian; km/s).
method (str, optional):
Interpolation method to use when performing remapping, using the
`scipy.interpolate.griddata` function. Default: 'linear'.
"""
# Expansion rate (km/s/Mpc)
Hz = 100. * self.cosmo['h'] * ccl.h_over_h0(self.cosmo,
self.scale_factor)
# Empty redshift-space array
delta_s = np.zeros_like(delta_x) - 1. # Default value is -1 (void)
# Loop over x and y pixels
for i in range(delta_x.shape[0]):
for j in range(delta_x.shape[1]):
# Realisation of uncorrelated non-linear velocities
vel_nl = 0.
if sigma_nl > 0.:
vel_nl = sigma_nl * np.random.normal(0., 1., self.z.size)
# Redshift-space z coordinate (negative sign as we will map
# from real coord to redshift-space coord)
s = self.z - (velocity_z[i, j, :] + vel_nl) / Hz
# Apply periodic boundary conditions
length_z = np.max(self.z) - np.min(self.z)
s = (s - np.min(self.z)) % (length_z) + np.min(self.z)
# Use average value of endpoints as fill value
fill_value = 0.5 * (delta_x[i, j, 0] + delta_x[i, j, -1])
# Remap to redshift-space (on regular grid in redshift-space
# with same grid points as in 'z' array)
delta_s[i, j, :] = griddata(points=(s, ),
values=delta_x[i, j, :],
xi=(self.z),
method=method,
fill_value=fill_value)
return delta_s
def _func(m, a):
abs_dzda = 1 / a / a
dc = ccl.comoving_angular_distance(cosmo, a)
ez = ccl.h_over_h0(cosmo, a)
dh = ccl.physical_constants.CLIGHT_HMPC / cosmo['h']
dvdz = dh * dc**2 / ez
dvda = dvdz * abs_dzda
val = hmf.get_mass_function(cosmo, 10**m, a, mdef_other=mdef)
val *= sel(10**m, a)
return val[0, 0] * dvda
def PNoise(self, z, kperp):
"""Thermal noise power spectrum.
Parameters
----------
z : float
Redshift.
kperp : float or array
kperp value(s), in Mpc^-1.
Returns
-------
Pn : float or array
Thermal noise power spectrum, in K^2 Mpc^3.
"""
# Observed wavelength
lam = 0.21 * (1 + z) # m
# Comoving radial distance to redshift z
r = ccl.comoving_radial_distance(self.C, 1 / (1. + z)) # Mpc
# Conversion between kperp and uv-plane (vector norm) u
u = np.asarray(kperp) * r / (2 * np.pi)
# Baseline length corresponding to u
l = u * lam # m
# Number density of baselines in uv plane
Nu = self.nofl(l) * lam**2
# Inaccurate approximation for uv-plane baseline density
#umax=self.Dmax/lam
#Nu=self.Nd**2/(2*np.pi*umax**2)
# Field of view of single dish
FOV = (lam / self.Deff)**2 # sr
# Hubble parameter H(z)
Hz = self.C['H0'] * ccl.h_over_h0(self.C, 1. /
(1. + z)) # km s^-1 Mpc^-1
# Conversion factor from frequency to physical space
y = 3e5 * (1 + z)**2 / (1420e6 * Hz) # Mpc s
# System temperature (sum of telescope and sky temperatures)
Tsys = self.Tsky(1420. / (1 + z)) + self.Tscope # K
# 21cm noise power spectrum (Eq. D4 of paper).
# Hard-codes 2 polarizations
Pn = Tsys**2 * r**2 * y * (lam**4 / self.Ae**2) * 1 / (
2 * Nu * self.ttotal) * (self.Sarea / FOV) # K^2 Mpc^3
# Catastrophically fail if we've gotten negative power spectrum values
if np.any(Pn < 0):
print(Nu, Pn, l, self.nofl(l), self.nofl(l / 2))
stop()
return Pn
def __init__(self, cosmo, z_max=6., n_chi=1024):
self.chi_max = ccl.comoving_radial_distance(cosmo, 1. / (1 + z_max))
chi = np.linspace(0, self.chi_max, n_chi)
a_arr = ccl.scale_factor_of_chi(cosmo, chi)
H0 = cosmo['h'] / ccl.physical_constants.CLIGHT_HMPC
OM = cosmo['Omega_c'] + cosmo['Omega_b']
Ez = ccl.h_over_h0(cosmo, a_arr)
fz = ccl.growth_rate(cosmo, a_arr)
w_arr = 3 * cosmo['T_CMB'] * H0**3 * OM * Ez * chi**2 * (1 - fz)
self._trc = []
self.add_tracer(cosmo, kernel=(chi, w_arr), der_bessel=-1)
def thermal_n(kperp, zz, D=6.0, Ns=256, hex=True):
"""The thermal noise for PUMA -- note noise rescaling from 5->5/4 yr."""
# Some constants.
etaA = 0.7 # Aperture efficiency.
Aeff = etaA * np.pi * (D / 2)**2 # m^2
lam21 = 0.21 * (1 + zz) # m
nuobs = 1420 / (1 + zz) # MHz
# The cosmology-dependent factors.
hub = C['h']
Ez = ccl.h_over_h0(C, 1. / (1. + zz))
chi = ccl.comoving_radial_distance(C, 1 / (1. + zz)) * hub # Mpc/h.
#hub = cc.H(0).value / 100.0
#Ez = cc.H(zz).value / cc.H(0).value
#chi = cc.comoving_distance(zz).value * hub # Mpc/h.
OmHI = 4e-4 * (1 + zz)**0.6 / Ez**2
Tbar = 0.188 * hub * (1 + zz)**2 * Ez * OmHI # K
# Eq. (3.3) of Chen++19
d2V = chi**2 * 2997.925 / Ez * (1 + zz)**2
# Eq. (3.5) of Chen++19
if hex: # Hexagonal array of Ns^2 elements.
n0, c1, c2, c3, c4, c5 = (
Ns / D)**2, 0.5698, -0.5274, 0.8358, 1.6635, 7.3177
uu = kperp * chi / (2 * np.pi)
xx = uu * lam21 / Ns / D # Dimensionless.
nbase = n0 * (c1 + c2 * xx) / (
1 + c3 * xx**c4) * np.exp(-xx**c5) * lam21**2 + 1e-30
#nbase[uu< D/lam21 ]=1e-30
nbase[uu > Ns * D / lam21 * 1.3] = 1e-30
else: # Square array of Ns^2 elements.
n0, c1, c2, c3, c4, c5 = (Ns /
D)**2, 0.4847, -0.33, 1.3157, 1.5974, 6.8390
uu = kperp * chi / (2 * np.pi)
xx = uu * lam21 / Ns / D # Dimensionless.
nbase = n0 * (c1 + c2 * xx) / (
1 + c3 * xx**c4) * np.exp(-xx**c5) * lam21**2 + 1e-30
#nbase[uu< D/lam21 ]=1e-30
nbase[uu > Ns * D / lam21 * 1.4] = 1e-30
# Eq. (3.2) of Chen++19
npol = 2
fsky = 0.5
tobs = 5. * 365.25 * 24. * 3600. # sec.
tobs /= 4.0 # Scale to 1/2-filled array.
Tamp = 62.0 # K
Tgnd = 33.0 # K
Tsky = 2.7 + 25 * (400. / nuobs)**2.75 # K
Tsys = Tamp + Tsky + Tgnd
Omp = (lam21 / D)**2 / etaA
# Return Pth in "cosmological units", with the Tbar divided out.
Pth = (Tsys/Tbar)**2*(lam21**2/Aeff)**2 *\
4*np.pi*fsky/Omp/(npol*1420e6*tobs*nbase) * d2V
return (Pth)
def LSSTSpecParams(C):
biasfunc = lambda z: 0.95 / ccl.growth_factor(C, 1 / (1 + z))
ndens = 49 ## per /arcmin^2, LSST SRD, page 47
dndz = lambda z: z**2 * np.exp(-(z / 0.28)**0.94) ## LSST SRD, page 47
arcminfsky = 1 / (4 * np.pi / (np.pi / (180 * 60))**2)
## volume between z=3
zmax = 3
V = 4 * np.pi**3 / 3 * ccl.comoving_radial_distance(C, 1 / (1 + zmax))**3
dVdz = lambda z: 3e3 / C['h'] * 1 / ccl.h_over_h0(C, 1 / (
1 + z)) * 4 * np.pi * ccl.comoving_radial_distance(C, 1 / (1 + z))**2
norm = ndens / (quad(dndz, 0, zmax)[0] * arcminfsky)
nbarofz = lambda z: norm * dndz(z) / dVdz(z)
return biasfunc, nbarofz, 0, 3, None
def get_battaglia(m,z,delta) :
"""Sets all parameters needed to compute the Battaglia et al. profile."""
fb=cosmo.cosmo.params.Omega_b/cosmo.cosmo.params.Omega_m
ez2=(ccl.h_over_h0(cosmo,1/(1+z)))**2
h=cosmo.cosmo.params.h
mr=m*1E-14
p0=18.1*mr**0.154*(1+z)**(-0.758)
rDelta=R_Delta(cosmo,m,1./(1+z),Delta=delta)*(1+z)
dic={'ups0':0.518*p0*2.52200528E-19*delta*m*h**2*ez2*fb*(1+z)/rDelta,
'rDelta':rDelta,
'xc':0.497*(mr**(-0.00865))*((1+z)**0.731),
'beta':4.35*(mr**0.0393)*((1+z)**0.415)}
return dic
def Ntot(z, mhmin, fsky=1.):
"""
Calculate the total number of dark matter halos above a given mass
threshold, as a function of maximum redshift and sky fraction.
"""
# Calculate cumulative number density n(>M_min) as a fn of M_min and redshift
ndens = nm(z, mhmin=mhmin)
# Integrate over comoving volume of lightcone
r = ccl.comoving_radial_distance(cosmo, a) # Comoving distance, r
H = 100. * cosmo['h'] * ccl.h_over_h0(cosmo, a) # H(z) in km/s/Mpc
Ntot = integrate.cumtrapz(ndens * r**2. / H, z, initial=0.)
Ntot *= 4. * np.pi * fsky * C_kms
return Ntot
def _norm(self, cosmo, M, a, b):
"""Computes the normalisation factor of the Arnaud profile.
.. note:: Normalisation factor is given in units of ``eV/cm^3``. \
(Arnaud et al., 2009)
"""
aP = 0.12 # Arnaud et al.
h70 = cosmo["h"] / 0.7
P0 = 6.41 # reference pressure
K = 1.65 * h70**2 * P0 * (h70 / 3e14)**(2 / 3 + aP) # prefactor
PM = (M * (1 - b))**(2 / 3 + aP) # mass dependence
Pz = ccl.h_over_h0(cosmo, a)**(8 / 3) # scale factor (z) dependence
P = K * PM * Pz
return P
def kernel(self, cosmo, a, **kwargs):
"""The galaxy number overdensity window function."""
unit_norm = 3.3356409519815204e-04 # 1/c
Hz = ccl.h_over_h0(cosmo, a) * cosmo["h"]
z = 1 / a - 1
w = kwargs["width"]
nz_new = self.nzf(self.z_avg + (1 / w) * (self.z - self.z_avg))
nz_new /= simps(nz_new, x=self.z)
nzf_new = interp1d(self.z,
nz_new,
kind="cubic",
bounds_error=False,
fill_value=0)
return Hz * unit_norm * nzf_new(z)
def test_iswcl():
# Cosmology
Ob = 0.05
Oc = 0.25
h = 0.7
COSMO = ccl.Cosmology(Omega_b=Ob,
Omega_c=Oc,
h=h,
n_s=0.96,
sigma8=0.8,
transfer_function='bbks')
# CCL calculation
ls = np.arange(2, 100)
zs = np.linspace(0, 0.6, 256)
nz = np.exp(-0.5 * ((zs - 0.3) / 0.05)**2)
bz = np.ones_like(zs)
tr_n = ccl.NumberCountsTracer(COSMO,
has_rsd=False,
dndz=(zs, nz),
bias=(zs, bz))
tr_i = ccl.ISWTracer(COSMO)
cl = ccl.angular_cl(COSMO, tr_n, tr_i, ls)
# Benchmark from Eq. 6 in 1710.03238
pz = nz / simps(nz, x=zs)
H0 = h / ccl.physical_constants.CLIGHT_HMPC
# Prefactor
prefac = 3 * COSMO['T_CMB'] * (Oc + Ob) * H0**3 / (ls + 0.5)**2
# H(z)/H0
ez = ccl.h_over_h0(COSMO, 1. / (1 + zs))
# Linear growth and derivative
dz = ccl.growth_factor(COSMO, 1. / (1 + zs))
gz = np.gradient(dz * (1 + zs), zs[1] - zs[0]) / dz
# Comoving distance
chi = ccl.comoving_radial_distance(COSMO, 1 / (1 + zs))
# P(k)
pks = np.array([
ccl.nonlin_matter_power(COSMO, (ls + 0.5) / (c + 1E-6), 1. / (1 + z))
for c, z in zip(chi, zs)
]).T
# Limber integral
cl_int = pks[:, :] * (pz * ez * gz)[None, :]
clbb = simps(cl_int, x=zs)
clbb *= prefac
assert np.all(np.fabs(cl / clbb - 1) < 1E-3)
def signal_covariance(zc, cosmo, params):
"""
Signal power spectrum matrix, containing (cross-)spectra for gg, gv, vv.
These are simply the galaxy auto-, galaxy-velocity cross-, and velocity
auto-spectra.
"""
# Scale factor at central redshift
a = 1. / (1. + zc)
# Grid of Fourier wavenumbers
k = np.logspace(KMIN, KMAX, NK)
mu = np.linspace(-1., 1., NMU)
K, MU = np.meshgrid(k, mu)
# Get matter power spectrum
pk = ccl.linear_matter_power(cosmo, k, a=1.)
# Get redshift-dep. functions
b = bias(zc, params)
rg = corrfac(zc, params)
f = params['x_f'] * ccl.growth_rate(cosmo, a)
beta = f / b
H = params['x_H'] * ccl.h_over_h0(cosmo, a) * 100. * cosmo['h'] # km/s/Mpc
# Redshift-space suppression factors
D_g = 1. / np.sqrt(1. + 0.5 * (K * MU * sigma_g(zc, params))**2.)
D_u = np.sinc(K * sigma_u(zc, params))
# Build 2x2 matrix of mu- and k-dependent pre-factors of P(k)
fac = np.zeros((2, 2, mu.size, k.size)).astype(complex)
# galaxy-galaxy (dimensionless)
fac[0, 0] = b**2. * (1. + 2. * rg * beta * MU**2. +
beta**2. * MU**4.) * D_g**2.
# galaxy-velocity (units: km/s)
fac[0, 1] = 1.j * a * H * f * b * MU * (rg + beta * MU**2.) * D_g * D_u / K
fac[1, 0] = -1. * fac[0, 1] # Complex conjugate
# velocity-velocity (units: [km/s]^2)
fac[1, 1] = (a * H * f * MU)**2. * (D_u / K)**2.
# Multiply all elements by P(k) and return
return fac * pk[np.newaxis, np.newaxis, np.newaxis, :]
def PNoise(self, z, kperp):
""" Thermal noise power in Mpc^3 """
lam = 0.21 * (1 + z)
r = ccl.comoving_radial_distance(self.C, 1 / (1. + z))
u = kperp * r / (2 * np.pi)
l = u * lam
Nu = self.nofl(l) * lam**2
#umax=self.Dmax/lam
#Nu=self.Nd**2/(2*np.pi*umax**2)
FOV = (lam / self.Deff)**2
Hz = self.C['H0'] * ccl.h_over_h0(self.C, 1. / (1. + z))
y = 3e5 * (1 + z)**2 / (1420e6 * Hz)
Tsys = self.Tsky(1420. / (1 + z)) + self.Tscope
Pn = Tsys**2 * r**2 * y * (lam**4 / self.Ae**2) * 1 / (
2 * Nu * self.ttotal) * (self.Sarea / FOV)
if np.any(Pn < 0):
print(Nu, Pn, l, self.nofl(l), self.nofl(l / 2))
stop()
return Pn
def R_Delta(cosmo, M, a, Delta=500, is_matter=False, squeeze=True, **kwargs):
"""
Calculate the reference radius of a halo.
.. note:: This is ``R = (3M/(4*pi*rho_c(a)*Delta))^(1/3)``, where rho_c is
the critical matter density at scale factor ``a``.
Arguments
---------
cosmo: ~pyccl.core.Cosmology
Cosmology object.
M : float or array_like
Halo mass [Msun].
a : float or array_like
Scale factor
Delta : float
Overdensity parameter.
is_matter : bool
True when R_Delta is calculated using the average matter density.
False when R_Delta is calculated using the critical density.
squeeze : bool
Whether to squeeze extra dimensions.
**kwargs : dict
Parametrisation of the profiles and cosmology.
Returns
-------
float or array_like : The halo reference radius in `Mpc`.
"""
# Input handling
M, a = np.atleast_1d(M, a)
if is_matter:
omega_factor = ccl.omega_x(cosmo, a, "matter")
else:
omega_factor = 1
c1 = (cosmo["h"] * ccl.h_over_h0(cosmo, a))**2
prefac = 1.16217766e12 * Delta * omega_factor * c1
R = (M[..., None] / prefac)**(1 / 3)
return R.squeeze() if squeeze else R
def _norm(self, cosmo, M, a, b):
"""Computes the normalisation factor of the Arnaud profile.
.. note:: Normalisation factor is given in units of ``eV/cm^3``. \
(Arnaud et al., 2009)
"""
aP = 0.12 # Arnaud et al.
h70 = cosmo["h"] / 0.7
# Value from Planck 2013 (Planck intermediate results: V.Pressure profiles of galaxy clusters from
# the Sunyaev - Zeldovich effect
P0 = 6.41 # reference pressure
# Values from Arnaud et al., 2010
# P0 = 8.403*h70**(-3./2)
K = 1.65 * h70**2 * P0 * (h70 / 3e14)**(2 / 3 + aP) # prefactor
PM = (M * (1 - b))**(2 / 3 + aP) # mass dependence
Pz = ccl.h_over_h0(cosmo, a)**(8 / 3) # scale factor (z) dependence
P = K * PM * Pz
return P
def norm(self, cosmo, M, a, b, squeeze=True):
"""Computes the normalisation factor of the Arnaud profile.
.. note:: Normalisation factor is given in units of ``eV/cm^3``. \
(Arnaud et al., 2009)
"""
# Input handling
M, a = np.atleast_1d(M), np.atleast_1d(a)
aP = 0.12 # Arnaud et al.
h70 = cosmo["h"] / 0.7
P0 = 6.41 # reference pressure
K = 1.65 * h70 * P0 * (h70 / 3e14)**(2 / 3 + aP) # prefactor
PM = (M * (1 - b))**(2 / 3 + aP) # mass dependence
Pz = ccl.h_over_h0(cosmo, a)**(8 / 3) # scale factor (z) dependence
P = K * PM[..., None] * Pz
return P.squeeze() if squeeze else P
def freq_array(self, redshift=None):
"""
Return frequency array coordinates (in the z direction of the box).
This approximates the frequency channel width to be constant across the
box, which is only a good approximation in the distant observer
approximation.
Parameters:
redshift (float, optional):
Redshift to evaluate the centre of the box at. Default: Same value
as ``self.redshift``.
Returns:
freqs (array_like):
Frequencies, in MHz. Frequency decreases as z coordinate
increases.
"""
# Check redshift
if redshift is None:
redshift = self.redshift
a = 1. / (1. + redshift)
# Calculate central frequency of box
freq_centre = a * self.line_freq
# Comoving voxel size
dx = self.Lz / self.N
# Convert comoving voxel size to frequency channel size
# df / dr = df / da * (dr / da)^-1 = f0 * (a^2 H) / c
Hz = 100. * self.cosmo['h'] * ccl.h_over_h0(self.cosmo, a) # km/s/Mpc
df = dx * self.line_freq * (a**2. * Hz) / (C / 1e3
) # Same units as line_freq
# Comoving units in z direction: place origin in centre of box
freqs = freq_centre \
+ df * (np.arange(self.N) - 0.5*(self.N - 1.))
# Frequency is decreasing with increasing z coordinate
return freqs[::-1]
def signal_amplitude(self, redshift=None, formula='powerlaw'):
"""
Brightness temperature Tb(z), in mK. Several different expressions for the
21cm line brightness temperature are available:
Parameters:
redshift (float, optional):
Central redshift to evaluate the signal amplitude at. If not
specified, uses `self.box.redshift`.
formula (str, optional):
Which fitting formula to use for the brightness temperature. Some
of the options are a function of Omega_HI(z)
- ``powerlaw``: Simple power-law fit to Mario's updated data
(powerlaw M_HI function with alpha=0.6) (Default)
- ``hall``: From Hall, Bonvin, and Challinor.
"""
if redshift is None:
redshift = self.box.redshift
z = redshift
# Calculate OmegaHI(z)
omegaHI = self.Omega_HI(redshift=redshift)
# Select which formula to use
if formula == 'powerlaw':
# Mario Santos' fit, used in Bull et al. (2015)
Tb = 5.5919e-02 + 2.3242e-01 * z - 2.4136e-02 * z**2.
elif formula == 'hall':
# From Hall et al.
E = ccl.h_over_h0(self.box.cosmo, 1. / (1. + z))
Tb = 188. * self.box.cosmo['h'] * omegaHI * (1. + z)**2. / E
else:
raise ValueError("No formula found with name '%s'" % formula)
return Tb
def Tb(self, z):
"""Approximation for mean 21cm brightness temperature.
This is reasonably up-to-date, and comes from Eq. B1
in the CV 21cm paper.
Parameters
----------
z : float or array
Redshift(s).
Returns
-------
Tb : float or array
Temperature value(s), in K.
"""
z = np.asarray(z)
Ez = ccl.h_over_h0(self.C, 1. / (1. + z))
# Note potentially misleading notation:
# Ohi = (comoving density at z) / (critical density at z=0)
Ohi = 4e-4 * (1 + z)**0.6
Tb = 188e-3 * self.C['h'] / Ez * Ohi * (1 + z)**2
return Tb
def cutWedge(self, noise, kperp, kpar, z, NW=3.0):
"""Cut the foreground wedge from a 2d noise power spectrum.
Parameters
----------
noise : array[nkpar,nkperp]
2d noise power spectrum.
kperp : array[nkpar,nkperp]
2d array where columns are kperp values (in Mpc^-1) and rows are identical.
kpar : array[nkpar,nkperp]
2d array where rows are kpar values (in Mpc^-1) and columns are identical.
z : float
Redshift.
NW : float, optional
Multiplier defining wedge in terms of primary beam.
(default = 3)
Returns
-------
Pn : array[nkpar,nkperp]
2d noise power spectrum where modes within wedge have noise set to
large value.
"""
# Comoving radial distance to redshift z
r = ccl.comoving_radial_distance(self.C, 1 / (1. + z)) # Mpc
# Hubble parameter H(z)
H = self.C['H0'] * ccl.h_over_h0(self.C, 1. /
(1. + z)) # km s^-1 Mpc^-1
# Slope that defines wedge as kpar < kperp * slope.
# See Eq. C1 from the CV 21cm paper.
slope = r * H / 3e5 * 1.22 * 0.21 / self.D * NW / 2.0 # dimensionless
# Boost noise for modes within wedge
noiseout = np.copy(noise)
noiseout[np.where(kpar < kperp * slope)] = 1e30
return noiseout
def get_E2Omega_m(self, z):
a = 1.0/(1.0+z)
return ccl.omega_x(self.be_cosmo, a, "matter")*(ccl.h_over_h0(self.be_cosmo, a))**2
def rDelta(m, zz, Delta):
"""Returns r_Delta
"""
hn = ccl.h_over_h0(cosmo, 1. / (1 + zz))
rhoc = RHOCRIT0 * hn * hn
return (3 * m / (4 * np.pi * Delta * rhoc))**0.333333333 * (1 + zz)
def check_background(cosmo):
"""
Check that background and growth functions can be run.
"""
# Types of scale factor input (scalar, list, array)
a_scl = 0.5
is_comoving = 0
a_lst = [0.2, 0.4, 0.6, 0.8, 1.]
a_arr = np.linspace(0.2, 1., 5)
# growth_factor
assert_(all_finite(ccl.growth_factor(cosmo, a_scl)))
assert_(all_finite(ccl.growth_factor(cosmo, a_lst)))
assert_(all_finite(ccl.growth_factor(cosmo, a_arr)))
# growth_factor_unnorm
assert_(all_finite(ccl.growth_factor_unnorm(cosmo, a_scl)))
assert_(all_finite(ccl.growth_factor_unnorm(cosmo, a_lst)))
assert_(all_finite(ccl.growth_factor_unnorm(cosmo, a_arr)))
# growth_rate
assert_(all_finite(ccl.growth_rate(cosmo, a_scl)))
assert_(all_finite(ccl.growth_rate(cosmo, a_lst)))
assert_(all_finite(ccl.growth_rate(cosmo, a_arr)))
# comoving_radial_distance
assert_(all_finite(ccl.comoving_radial_distance(cosmo, a_scl)))
assert_(all_finite(ccl.comoving_radial_distance(cosmo, a_lst)))
assert_(all_finite(ccl.comoving_radial_distance(cosmo, a_arr)))
# comoving_angular_distance
assert_(all_finite(ccl.comoving_angular_distance(cosmo, a_scl)))
assert_(all_finite(ccl.comoving_angular_distance(cosmo, a_lst)))
assert_(all_finite(ccl.comoving_angular_distance(cosmo, a_arr)))
# h_over_h0
assert_(all_finite(ccl.h_over_h0(cosmo, a_scl)))
assert_(all_finite(ccl.h_over_h0(cosmo, a_lst)))
assert_(all_finite(ccl.h_over_h0(cosmo, a_arr)))
# luminosity_distance
assert_(all_finite(ccl.luminosity_distance(cosmo, a_scl)))
assert_(all_finite(ccl.luminosity_distance(cosmo, a_lst)))
assert_(all_finite(ccl.luminosity_distance(cosmo, a_arr)))
# scale_factor_of_chi
assert_(all_finite(ccl.scale_factor_of_chi(cosmo, a_scl)))
assert_(all_finite(ccl.scale_factor_of_chi(cosmo, a_lst)))
assert_(all_finite(ccl.scale_factor_of_chi(cosmo, a_arr)))
# omega_m_a
assert_(all_finite(ccl.omega_x(cosmo, a_scl, 'matter')))
assert_(all_finite(ccl.omega_x(cosmo, a_lst, 'matter')))
assert_(all_finite(ccl.omega_x(cosmo, a_arr, 'matter')))
# Fractional density of different types of fluid
assert_(all_finite(ccl.omega_x(cosmo, a_arr, 'dark_energy')))
assert_(all_finite(ccl.omega_x(cosmo, a_arr, 'radiation')))
assert_(all_finite(ccl.omega_x(cosmo, a_arr, 'curvature')))
assert_(all_finite(ccl.omega_x(cosmo, a_arr, 'neutrinos_rel')))
assert_(all_finite(ccl.omega_x(cosmo, a_arr, 'neutrinos_massive')))
# Check that omega_x fails if invalid component type is passed
assert_raises(ValueError, ccl.omega_x, cosmo, a_scl, 'xyz')
# rho_crit_a
assert_(all_finite(ccl.rho_x(cosmo, a_scl, 'critical', is_comoving)))
assert_(all_finite(ccl.rho_x(cosmo, a_lst, 'critical', is_comoving)))
assert_(all_finite(ccl.rho_x(cosmo, a_arr, 'critical', is_comoving)))
# rho_m_a
assert_(all_finite(ccl.rho_x(cosmo, a_scl, 'matter', is_comoving)))
assert_(all_finite(ccl.rho_x(cosmo, a_lst, 'matter', is_comoving)))
assert_(all_finite(ccl.rho_x(cosmo, a_arr, 'matter', is_comoving)))
