def test_delta_sigma(self):
m200 = 1e15
c = 5.0
z = 0.3
nfw = NFW(m200, c, z)
ds = nfw.delta_sigma([0.1, 1.12])
ref_arr = np.array([5.28752650, 1.38772723])
assert_array_almost_equal(ds.value / 1e14, ref_arr)
def test_delta_sigma(self):
m200 = 1e15
c = 5.
z = 0.3
nfw = NFW(m200, c, z)
ds = nfw.delta_sigma([0.1, 1.12])
ref_arr = np.array([5.28752650, 1.38772723])
assert_array_almost_equal(ds.value / 1e14, ref_arr)
def get_delta_sigma(m200, c200, zl, r):
nfw = NFW(m200, c200, zl)
return nfw.delta_sigma(r)
def DStheo(theta, args):
"""
Computes de theoretical :math:`\Delta\Sigma_{NFW}` profile for a given mass
:math:`m_{200}`, z and cosmology.
Parameters
----------
theta: tuple
Parameters for the mcmc
args: dict
Contains the cosmology and other mean values computed from the data
Returns
-------
ds: np.array
The thoretical :math:`\Delta\Sigma_{NFW}` profile
Notes
-----
The parameters for the NFW function are the mass :math:`m_{200}` and the
concentration :math:`c_{200}`. However, in this anlysis, we use the
Duffy et al. (2008) concetration-mass relation to get the profile only
as a function of the mass. See: https://github.com/joergdietrich/NFW for
more details on the NFW function.
"""
runtype = args['runtype']
runconfig = args['runconfig']
if runtype == 'data':
if runconfig == 'Full':
m200, pcc, Am, B0, Rs = theta #M200c [Msun]
elif runconfig == 'OnlyM':
m200 = theta[0]
elif runconfig == 'FixAm':
m200, pcc, B0, Rs = theta
elif runtype == 'cal':
m200 = theta[0]
elif runtype == 'calsys':
if runconfig == 'Full':
m200, pcc, Am, B0, Rs = theta #M200c [Msun]
h = args['h']
z_mean = args['z_mean']
R = args['R'] #in physical [Mpc]
cosmo = args['cosmo'] #astropy cosmology object
cmodel = args[
'cmodel'] #diemer18 (obs.: lastest version of Colossus renamed to diemer19)
twohalo = args['twohalo']
factor2h = args['factor2h'] #boolean, if True multiply 2-halo term by h
cosmodict = args['cosmodict']
omega_m = cosmodict['om']
sigma_crit_inv = args['Sigma_crit_inv']
#Setting up the cosmology for Colossus
params = {
'flat': True,
'H0': cosmodict['h'] * 100.,
'Om0': cosmodict['om'],
'Ob0': cosmodict['ob'],
'sigma8': cosmodict['sigma8'],
'ns': cosmodict['ns']
}
cosmology.addCosmology('myCosmo', params)
cosmoc = cosmology.setCosmology('myCosmo')
cmodel = cmodel
c200c = concentration.concentration(
m200 * h, '200c', z_mean, model=cmodel,
conversion_profile='nfw') #m200c_in is [Msun/h], m200c_out is [Msun/h]
nfw = NFW(m200,
c200c,
z_mean,
cosmology=cosmo,
overdensity_type='critical') #input mass should be in [Msun]
#For DeltaSigma calculation, data and sim, the radius has to be in physical [Mpc]
if runtype == 'cal':
ds = (nfw.delta_sigma(R).value
) / 1.e12 #DeltaSigma is in units of physical [M_sun/Mpc^2]
#This two-halo part was not used in the analysis, the compuation is too slow
if twohalo:
#Adding the 2-halo term
b = bias.haloBias(m200 * h, z_mean, '200c',
model='tinker10') #mass_in is [Msun/h]
outer_term_xi = profile_outer.OuterTermCorrelationFunction(
z=z_mean, bias=b)
p_nfw = profile_nfw.NFWProfile(
M=m200 * h,
c=c200c,
z=z_mean,
mdef='200c',
outer_terms=[outer_term_xi]) #mass_in is [Msun/h]
#Radius in physical kpc/h
two_nfw0 = p_nfw.deltaSigmaOuter((R * 1e3) * h,
interpolate=True,
interpolate_surface_density=False,
min_r_interpolate=1.e-6 * h,
max_r_integrate=2.e5 * h,
max_r_interpolate=2.e5 * h)
two_nfw1 = two_nfw0 / 1.e6 #in physical [h Msun/pc^2]
if factor2h:
two_nfw = h * (two_nfw1 * h
) #something like physical [Msun/(h pc^2)]
else:
two_nfw = (
two_nfw1 * h
) #in physical [Msun/pc^2] #This should be the right one
ds_model = ds + two_nfw #NFW + 2-halo in physical [Msun/pc^2] if factor2h=False
else:
ds_model = ds
return ds_model #physical [M_sun/pc^2]
if runtype == 'data' or runtype == 'calsys':
ds = (
nfw.delta_sigma(R).value
) / 1.e12 #units of h Msun/pc^2 physical (but h=1, so actually is M_sun/pc^2)
sigma = (nfw.sigma(R).value) / 1.e12
# Computing miscetering correction from data
m200p = m200
z = np.array([z_mean])
if runtype == 'data':
cluster = ClusterEnsemble(z,
cosmology=FlatLambdaCDM(H0=100, Om0=0.3),
cm='Diemer18',
cmval=c200c)
misc_off = 0.1326 #here in [Mpc], since h=1
elif runtype == 'calsys':
cluster = ClusterEnsemble(z,
cosmology=FlatLambdaCDM(H0=h * 100,
Om0=omega_m),
cm='Diemer18',
cmval=c200c)
misc_off = 0.1326 / h #input needs to be in units of [Mpc]
if np.shape(m200p) == (1, 1):
m200p = np.reshape(m200p, (1, ))
try:
cluster.m200 = m200p #M200c [Msun]
except TypeError:
cluster.m200 = np.array([m200p])
rbins = R # in physical [Mpc]
offsets = np.ones(cluster.z.shape[0]) * misc_off
cluster.calc_nfw(rbins, offsets=offsets) #NFW with offset
dsigma_offset = cluster.deltasigma_nfw.mean(
axis=0) #physical [M_sun/pc^2], but if h=1 is [h M_sun/pc**2]
DSmisc = dsigma_offset.value #physical [Msun/pc^2]
sigma_offset = cluster.sigma_nfw.mean(
axis=0) #physical [M_sun/pc**2], but if h=1 is [h M_sun/pc**2]
Smisc = sigma_offset.value #physical [Msun/pc^2]
if runconfig == 'OnlyM':
pcc = 0.75
B0 = 0.50
Rs = 2.00
#The final model
full_Sigma = pcc * sigma + (1 - pcc) * Smisc
full_model = pcc * ds + (1 - pcc) * DSmisc
if runconfig == 'Full':
full_model *= Am #shear+photo-z bias correction
elif runconfig == 'OnlyM' or 'FixAm':
full_model = full_model
#Note: R (rbins) and Rs are in physical [Mpc], need to be comoving [Mpc/h]
boost_model = ct.boostfactors.boost_nfw_at_R(rbins * h * (1 + z_mean),
B0, Rs * h * (1 + z_mean))
full_model /= boost_model #boost-factor
full_model /= (1 - full_Sigma * sigma_crit_inv) #Reduced shear
return full_model # in physical [M_sun/pc^2]