def barrier_density(z, zeta=40, var_m=None, m=None, m_min=None):
"""
Equation 4
"""
delta_c = barkana_loeb_2001.critical_overdensity_collapse(z)
K_zeta = erfinv(1. - 1. / zeta)
if var_m is None:
var_m = barkana_loeb_2001.matter_variance(z, M=m, power_spectra=None)
if m_min is None: m_min = minimum_source_mass(z, Tvir=1e4)
var_min = barkana_loeb_2001.matter_variance(z, M=m_min, power_spectra=None)
return delta_c - np.sqrt(2 * (var_min - var_m)) * K_zeta
def linear_fit_barrier(m, z, zeta=40, var_m=None):
B0 = barrier_density(z, zeta=zeta, var_m=0)
B1 = (barrier_density(z, zeta=zeta, var_m=0.1) -
barrier_density(z, zeta=zeta, var_m=0)) / 0.1
if var_m is None:
var_m = barkana_loeb_2001.matter_variance(z, M=m, power_spectra=None)
return B0 + B1 * var_m
def mass_function(m, z, zeta=40):
rho_mean_ = mean_density(z) #Solar_mass/Mpc^3
B0 = barrier_density(z, zeta=zeta, var_m=0)
def f(x):
m = np.exp(x)
y = barkana_loeb_2001.matter_variance(z, M=m)
return np.sqrt(y)
if type(m) == np.float:
sig2 = barkana_loeb_2001.matter_variance(z, M=m, power_spectra=None)
Bm = linear_fit_barrier(m, z, zeta=zeta, var_m=None)
dsigdm = derivative(f, np.log(m), order=15)
else:
sig2 = np.array([
barkana_loeb_2001.matter_variance(z, M=m1, power_spectra=None)
for m1 in m
])
Bm = np.array(
[linear_fit_barrier(m1, z, zeta=zeta, var_m=None) for m1 in m])
dsigdm = np.array([derivative(f, np.log(m1), order=15) for m1 in m])
m_dndm = np.sqrt(2 / np.pi) * rho_mean_ * np.abs(dsigdm) * B0 * np.exp(
-Bm**2 / (2 * sig2)) / sig2 / m
return m_dndm
def b_mz(m, z, zeta=40):
Bm = functions.linear_fit_barrier(m, z, zeta=zeta)
B0 = functions.barrier_density(z, zeta=zeta, var_m=0)
var_m = barkana_loeb_2001.matter_variance(z, M=m, power_spectra=None)
return 1 + B0**2 / var_m / Bm
def f(x):
m = np.exp(x)
y = barkana_loeb_2001.matter_variance(z, M=m)
return np.sqrt(y)