def virial_temp(mass, z, mu=None, **cosmology):
r"""The Virial temperature for a halo of a given mass.
Calculates the Virial temperature in Kelvin for a halo of a given
mass using equation 26 of Barkana & Loeb.
The transition from neutral to ionized is assumed to occur at temp
= 1e4K. At temp >= 10^4 k, the mean partical mass drops from 1.22
to 0.59 to very roughly account for collisional ionization.
Parameters
----------
mass: array
Mass in Solar Mass units.
z: array
Redshift.
mu: array, optional
Mean mass per particle.
"""
omega_M_0 = cosmology["omega_M_0"]
omega = cden.omega_M_z(z, **cosmology)
d = omega - 1
deltac = 18.0 * math.pi ** 2.0 + 82.0 * d - 39.0 * d ** 2.0
if mu is None:
mu_t = 1.22
else:
mu_t = mu
temp = (
1.98e4
* (mass * cosmology["h"] / 1.0e8) ** (2.0 / 3.0)
* (omega_M_0 * deltac / (omega * 18.0 * math.pi ** 2.0)) ** (1.0 / 3.0)
* ((1 + z) / 10.0)
* (mu_t / 0.6)
)
if mu is None:
# Below is some magic to consistently use mu = 1.22 at temp < 1e4K
# and mu = 0.59 at temp >= 1e4K.
t_crit = 1e4
t_crit_large = 1.22 * t_crit / 0.6
t_crit_small = t_crit
mu = (
(temp < t_crit_small) * 1.22
+ (temp > t_crit_large) * 0.59
+ (1e4 * 1.22 / temp) * (temp >= t_crit_small) * (temp <= t_crit_large)
)
temp = temp * mu / 1.22
return temp
def virial_temp(mass, z, mu=None, **cosmology):
r"""The Virial temperature for a halo of a given mass.
Calculates the Virial temperature in Kelvin for a halo of a given
mass using equation 26 of Barkana & Loeb.
The transition from neutral to ionized is assumed to occur at temp
= 1e4K. At temp >= 10^4 k, the mean partical mass drops from 1.22
to 0.59 to very roughly account for collisional ionization.
Parameters
----------
mass: array
Mass in Solar Mass units.
z: array
Redshift.
mu: array, optional
Mean mass per particle.
"""
omega_M_0 = cosmology['omega_M_0']
omega = cden.omega_M_z(z, **cosmology)
d = omega - 1
deltac = 18. * math.pi**2. + 82. * d - 39. * d**2.
if mu is None:
mu_t = 1.22
else:
mu_t = mu
temp = (1.98e4 * (mass * cosmology['h'] / 1.0e8)**(2.0 / 3.0) *
(omega_M_0 * deltac / (omega * 18. * math.pi**2.))**(1.0 / 3.0) *
((1 + z) / 10.0) * (mu_t / 0.6))
if mu is None:
# Below is some magic to consistently use mu = 1.22 at temp < 1e4K
# and mu = 0.59 at temp >= 1e4K.
t_crit = 1e4
t_crit_large = 1.22 * t_crit / 0.6
t_crit_small = t_crit
mu = ((temp < t_crit_small) * 1.22 + (temp > t_crit_large) * 0.59 +
(1e4 * 1.22 / temp) * (temp >= t_crit_small) *
(temp <= t_crit_large))
temp = temp * mu / 1.22
return temp
def fgrowth(z, omega_M_0, unnormed=False):
r"""Cosmological perturbation growth factor, normalized to 1 at z = 0.
Approximate forumla from Carol, Press, & Turner (1992, ARA&A, 30,
499), "good to a few percent in regions of plausible Omega_M,
Omega_Lambda".
This is proportional to D_1(z) from Eisenstein & Hu (1999 ApJ 511
5) equation 10, but the normalization is different: fgrowth = 1 at
z = 0 and ``D_1(z) = \frac{1+z_\mathrm{eq}}{1+z}`` as z goes
to infinity.
To get D_1 one would just use
::
D_1(z) = (1+z_\mathrm{eq}) \mathtt{fgrowth}(z,\Omega_{M0}, 1)
(see \EH\ equation 1 for z_eq).
::
\mathtt{fgrowth} = \frac{D_1(z)}{D_1(0)}
Setting unnormed to true turns off normalization.
Note: assumes Omega_lambda_0 = 1 - Omega_M_0!
"""
#if cden.get_omega_k_0(**) != 0:
# raise ValueError, "Not valid for non-flat (omega_k_0 !=0) cosmology."
omega = cden.omega_M_z(z,
omega_M_0=omega_M_0,
omega_lambda_0=1. - omega_M_0)
lamb = 1 - omega
a = 1 / (1 + z)
if unnormed:
norm = 1.0
else:
norm = 1.0 / fgrowth(0.0, omega_M_0, unnormed=True)
return (norm * (5. / 2.) * a * omega /
(omega**(4. / 7.) - lamb + (1. + omega / 2.) * (1. + lamb / 70.)))
def fgrowth(z, omega_M_0, unnormed=False):
r"""Cosmological perturbation growth factor, normalized to 1 at z = 0.
Approximate forumla from Carol, Press, & Turner (1992, ARA&A, 30,
499), "good to a few percent in regions of plausible Omega_M,
Omega_Lambda".
This is proportional to D_1(z) from Eisenstein & Hu (1999 ApJ 511
5) equation 10, but the normalization is different: fgrowth = 1 at
z = 0 and ``D_1(z) = \frac{1+z_\mathrm{eq}}{1+z}`` as z goes
to infinity.
To get D_1 one would just use
::
D_1(z) = (1+z_\mathrm{eq}) \mathtt{fgrowth}(z,\Omega_{M0}, 1)
(see \EH\ equation 1 for z_eq).
::
\mathtt{fgrowth} = \frac{D_1(z)}{D_1(0)}
Setting unnormed to true turns off normalization.
Note: assumes Omega_lambda_0 = 1 - Omega_M_0!
"""
#if cden.get_omega_k_0(**) != 0:
# raise ValueError, "Not valid for non-flat (omega_k_0 !=0) cosmology."
omega = cden.omega_M_z(z, omega_M_0=omega_M_0, omega_lambda_0=1.-omega_M_0)
lamb = 1 - omega
a = 1/(1 + z)
if unnormed:
norm = 1.0
else:
norm = 1.0 / fgrowth(0.0, omega_M_0, unnormed=True)
return (norm * (5./2.) * a * omega /
(omega**(4./7.) - lamb + (1. + omega/2.) * (1. + lamb/70.))
)
def f(z):
f = (den.omega_M_z(z, **cosmo))**(cc.gamma)
return f