def dvc_dzdomega(z):
'''
comoving volume element
dV_c/(d\Omega dz) at redshift z (Mpc^3/h^3)
Args:
z, redshift, float.
Returns:
float, comoving volume element (Mpc^3/h^3)
'''
return C*1e-3/COSMO.Hz(z)*LITTLEH\
*COSMO.luminosityDistance(z)**2./(1.+z)**2.
def zmstar_lilly13(mstar, z, params):
'''
equation 40 from Lilly et al. 2013
Args:
mstar,float,stellar mass (msolar/h)
z, float, redshift
params, dictionary of parameters
Returns:
float, metallicity of galactic gas following the MZR from
Lilly et al. 2013.
'''
y = 10.**params['LILLY13']['LOGYIELD']
z0 = params['LILLY13']['Z0DY'] * y
lam=params['LILLY13']['LOADING10']\
*(mstar/LITTLEH/1e10)**params['LILLY13']['LOADINGPOW']
eps=params['LILLY13']['DEPLETION10']**-1.\
*(mstar/LITTLEH/1e10)**params['LILLY13']['DEPLETIONPOW']\
*(1+z)**params['LILLY13']['DEPLETION_EV_POW']
r = params['LILLY13']['RETURN_FRAC']
alphaeps = params['LILLY13']['DEPLETION_EV_POW']
if z <= 2:
ssfr = 1. / (1. - r) * 0.07 * (mstar / LITTLEH /
10**10.5)**(-0.1) * (1. + z)**3.
dlogmudz = (3. - alphaeps) / (1 + z)
else:
ssfr = 1. / (1. - r) * 0.3 * (mstar / LITTLEH /
10**10.5)**(-0.1) * (1. + z)**(5. / 3.)
dlogmudz = (5. / 3. - alphaeps) / (1 + z)
mu = ssfr / eps
dzdt = -COSMO.Hz(z) * (1. + z) / KPC * 1e9 * YEAR #convert H(z) to Gyr^-1
zeq = np.log10(z0 + y / (1. + lam / (1. - r) + mu + dlogmudz * dzdt / eps /
(1. - r)))
return zeq
def power_lin(k, z):
'''
linear matter power spectrum
Args:
k, float, wavenumber (comoving h/Mpc)
z, float, redshift
Returns:
linear matter power spectrum (Mpc/h)^3
'''
return COSMO.matterPowerSpectrum(k, z)
def mTb_emiss(z21, rhohi=1.):
'''
mean emission brightness temperature (K)
Args:
z21, float,redshift
rhohi, hi density in Msol Mpc^-3 h^2
Returns:
brightness temperature (K)
'''
return 3.*HPLANCK*1e-3*C**3.*A10/(32.*PI*KBOLTZMANN*MP*F21**2.)\
*(1+z21)**2./COSMO.Hz(z21)/(KPC*1e3)**2.*MSOL*rhohi\
*LITTLEH**2.
def dldsobs_agn(freq_obs, zem, alpha, F0=1.4e9):
'''
Compute the derivive of luminosity with respect to observed flux
for agn.
Args:
freq_obs observed frequency
zem, emission redshift.
alpha, power law for emission: L=L0(f/F0)^alpha
F0, reference frequency
Returns: dL/dS_obs (W/Hz/Jy)
'''
output = 4.*PI*COSMO.luminosityDistance(zem)**2.\
*(F0/(1.+zem)/freq_obs)**alpha/(1.+zem)/LITTLEH**2.#This is output in Mpc^2
output = output * JY * (1e3 * KPC)**2.
return output
def instrument_counts(z, survey_area, smin, smax, channel_width, rms, params):
'''
Calculate the number of absorbers per comoving redshift interval
detected at the nsigma level.
Args:
z, redshift
survey_area, area of survey (steradians)
channel_width, specral resolution (Hz)
rms, noise level/beam per spectral channel (Jy/bm)
params, dictionary of model parameters
nsigma, detection threshold above rms.
Returns:
Number of detected absorbers per redshift interval.
'''
s_min = rms * 10.**SNR_INTERP_MIN
g = lambda x: rb.dn_dlogs_domega(10.**x,z)\
*dn_dr(10.**x/rms,channel_width,z,params)
output = integrate.quad(g, np.max([np.log10(smin), s_min]),
np.log10(smax))[0] #dN/dr_com
output = survey_area * output * C * 1e-3 / COSMO.Hz(z) * LITTLEH #dN/dz
return output
def dn_dz_tau(tau, z, params):
'''
number of absorbers per redshift interval with optical depths greater than
tau.
Args:
tau, optical depth
z, redshift
params, dictionary of model parameters
Returns: number of absorbers per redshift interval (along LoS) with optical
depths greater than tau
'''
splkey = ('dn_dz_tau', z) + dict2tuple(params)
if not SPLINE_DICT.has_key(splkey):
tauvals = np.logspace(TAU_INTERP_MIN, TAU_INTERP_MAX, N_INTERP_TAU)
dnvals = np.zeros_like(tauvals)
for taunum, tauval in enumerate(tauvals):
g=lambda x:sigma_tau(tauval,10.**x,z,params)*massfunc(10.**x,z)\
*C*1e-3/COSMO.Hz(z)*LITTLEH
dnvals[taunum] = integrate.quad(g, M_INTERP_MIN, M_INTERP_MAX)[0]
SPLINE_DICT[splkey] = interp.interp1d(np.log(tauvals), dnvals)
return SPLINE_DICT[splkey](np.log(tau))
def dn_dlogtau_dz(tau, z, params, recompute=False):
'''
compute the number of optical depth features per redshift interval
per optical depth interval.
Args:
z, redshift
tau, optical depth
params, model parameters
Returns:
average number of optical depth features between tau and tau+d_tau
and redshift z and dz in a los on the sky.
'''
splkey = ('dn_dlogtau_domega_dz', z) + dict2tuple(params)
if not SPLINE_DICT.has_key(splkey) or recompute:
tauvals = np.logspace(TAU_INTERP_MIN, TAU_INTERP_MAX, N_INTERP_TAU)
dnvals = np.zeros_like(tauvals)
for taunum, tauval in enumerate(tauvals):
g=lambda x: massfunc(10.**x,z)*dsigma_dtau(tauval,10.**x,z,params)\
*tauval*np.log(10.)
dnvals[taunum]=integrate.quad(g,M_INTERP_MIN,M_INTERP_MAX)[0]\
*1e-3*C/COSMO.Hz(z)*LITTLEH
print dnvals
SPLINE_DICT[splkey] = interp.interp1d(np.log(tauvals), dnvals)
return SPLINE_DICT[splkey](np.log(tau))