NumCosmo

Surface Mass Density

Surface Mass Density

Description

Example written in Python to compute: (i) the surface mass density, its mean and excess, (ii) the convergence, shear and reduced shear.

Running

To try this example you must have PyGObject installed, and numcosmo built with –enable-introspection option. To run the examples without installing follow the instructions here.

example_wl_surface_mass_density.py:

#!/usr/bin/env python

import math
import numpy as np
import matplotlib.pyplot as plt

try:
  import gi
  gi.require_version('NumCosmo', '1.0')
  gi.require_version('NumCosmoMath', '1.0')
except:
  pass

from gi.repository import NumCosmo as Nc
from gi.repository import NumCosmoMath as Ncm

Ncm.cfg_init ()

#
#  New homogeneous and isotropic cosmological model NcHICosmoDEXcdm 
#
cosmo = Nc.HICosmo.new_from_name (Nc.HICosmo, "NcHICosmoDEXcdm")
cosmo.omega_x2omega_k ()
cosmo.param_set_by_name ("Omegak",    0.0)

#
#  New cosmological distance objects optimizied to perform calculations
#  up to redshift 2.0.
#
dist = Nc.Distance.new (1.0)

#
# New matter density profile 
#
nfw = Nc.DensityProfile.new_from_name ("NcDensityProfileNFW{'Delta':<200.0>}") 
nfw.param_set_by_name ('cDelta', 4.0) # 4 as Douglas. In LCDM c = 5 corresponds to cluster masses. (see Lokas and G. Mamon, astro-ph/0002395) 
nfw.param_set_by_name ('MDelta', 1.e15)
mdelta = 1.e15
cdelta = 4.0
delta = 200.0

zcluster = 1.0
zsource = 1.5

#
# New weak lensing surface mass density
#
smd = Nc.WLSurfaceMassDensity.new (dist)

#
#  Setting values for the cosmological model, those not set keep their
#  default values. Remember to use the _orig_ version to set the original
#  parameters when a reparametrization is used.
#
cosmo.props.H0     = 70.0
cosmo.props.Omegab = 0.045
cosmo.props.Omegac = 0.255
cosmo.props.Omegax = 0.7
cosmo.param_set_by_name ("Omegak", 0.0) # This line sets a flat universe, modifying Omega_x (small difference). 
#This is necessary since CLASS require the inclusion of the radiation density. 

dist.prepare (cosmo)

npoints = 500
r_a = np.logspace(math.log10(5.e-3), 2., npoints, endpoint=True)

Sigma = []
meanSigma = []
DeltaSigma = []
convergence = []
shear = []
reduced_shear = []
reduced_shear_inf = []

for i in range(0, npoints): 
  ri       = r_a[i]
  Sig      = smd.sigma (nfw, cosmo, ri, zcluster)  
  meanSig  = smd.sigma_mean (nfw, cosmo, ri, zcluster)
  kappa    = smd.convergence (nfw, cosmo, ri, zsource, zcluster, zcluster)
  sh       = smd.shear (nfw, cosmo, ri, zsource, zcluster, zcluster)
  reds     = smd.reduced_shear (nfw, cosmo, ri, zsource, zcluster, zcluster)
  reds_inf = smd.reduced_shear_infinity (nfw, cosmo, ri, zsource, zcluster, zcluster)
  
  Sigma.append (Sig)
  meanSigma.append (meanSig)
  DeltaSigma.append (meanSig - Sig) 
  convergence.append (kappa)
  shear.append (sh)
  reduced_shear.append (reds)
  reduced_shear_inf.append (reds_inf)
  
  print (ri, Sig, meanSig, kappa, sh, reds)  

fig = plt.figure(figsize=(6, 5)) #in inches
ax = plt.subplot()

ax.plot(r_a, Sigma, label=r'$\Sigma(R)$') 
ax.plot(r_a, meanSigma, label=r'Mean $\overline{\Sigma}(<R)$')
ax.plot(r_a, DeltaSigma, label=r'Excess/differential  $\Delta{\Sigma}(R)$')
            
ax.set_xlabel(r'$R$ [Mpc]', fontsize=14)
ax.set_ylabel(r'Surface Mass Density', fontsize=12)
ax.set_xscale('log')
ax.set_yscale('log')

ax.annotate(r'$[\Sigma] = M_\odot/Mpc^2$', xy=(0.65, 0.8), xycoords='axes fraction', fontsize=12)
ax.set_title (r'NFW, $c_{200} = 4$, $M_{200} = 10^{15} \, M_\odot$')

plt.legend(loc = 3)

plt.savefig ('wl_smd_sigmas.svg')
plt.show ()
plt.clf ()  

ax = plt.subplot()

ax.plot(r_a, convergence, label=r'Convergence $\kappa (R)$')  
ax.plot(r_a, shear, label=r'Shear $\gamma (R)$')
ax.plot(r_a, reduced_shear, label=r'Reduced Shear $g(R)$')
ax.plot(r_a, reduced_shear_inf, label=r'Reduced Shear $g_\infty(R)$')
            
ax.set_xlabel(r'$R$ [Mpc]', fontsize=14)
ax.set_xscale('log')
ax.set_yscale('log')

ax.set_title (r'NFW, $c_{200} = 4$, $M_{200} = 10^{15} \, M_\odot$')

plt.legend(loc = 1)

plt.savefig('wl_smd_convergence_shear.svg')
plt.show()

Figure 1: Surface Mass Density

wl_smd_sigmas.svg

Figure 1: Surface mass density (smd) $\Sigma(R)$, the mean smd $\overline{\Sigma}(<R)$ and the differential smd $\Delta\Sigma(R) = \overline{\Sigma}(<R) - \Sigma(R)$. We computed these functions using the Navarro-Frenk-White (NFW) mass density profile, with $c_\Delta = 4$ (concentration parameter), $M_\Delta = 10^{15} \, M_\odot$ and $\Delta = 200$. Lens redshift $z_l = 1.0$ and source redshift $z_s = 1.5$.

Figure 2: Other lensing functions

wl_smd_convergence_shear.svg

Figure 2: Convergence $\kappa (R)$, shear $\gamma (R)$, reduced shear $g(R)$, and reduced shear (infinite source redshit) $g_\infty(R)$. We computed these functions using the Navarro-Frenk-White (NFW) mass density profile, with $c_\Delta = 4$ (concentration parameter), $M_\Delta = 10^{15} \, M_\odot$ and $\Delta = 200$. Lens redshift $z_l = 1.0$ and source redshift $z_s = 1.5$.

Example Directory