Validation of SIS model (Numerical vs Analytical)

• This is in reference to Haris et al. (2018)

import numpy as np
from ler.lens_galaxy_population import OpticalDepth
import matplotlib.pyplot as plt
%matplotlib inline

from astropy.cosmology import LambdaCDM
cosmo = LambdaCDM(H0=70, Om0=0.3, Ode0=0.7)

• optical_depth_SIS_hemanta is the numerical solution of the SIS model

od = OpticalDepth(
    z_min=0.001,
    z_max=40,
    optical_depth_function="optical_depth_SIS_hemanta",
    sampler_priors=dict(
        velocity_dispersion="velocity_dispersion_gengamma",
        axis_ratio="axis_ratio_rayleigh",
    ),
    sampler_priors_params=dict(
        velocity_dispersion=dict(vd_min=0., vd_max=600),
        axis_ratio=dict(q_min=0.2, q_max=1),
    ),
    cosmology=cosmo,
    directory="./interpolator_pickle",
    #create_new_interpolator=True,
    )

z_to_Dc interpolator will be generated at ./interpolator_pickle/z_to_Dc/z_to_Dc_3.pickle
Dc_to_z interpolator will be generated at ./interpolator_pickle/Dc_to_z/Dc_to_z_3.pickle
angular_diameter_distance interpolator will be generated at ./interpolator_pickle/angular_diameter_distance/angular_diameter_distance_3.pickle
differential_comoving_volume interpolator will be generated at ./interpolator_pickle/differential_comoving_volume/differential_comoving_volume_3.pickle
velocity_dispersion_gengamma interpolator will be generated at ./interpolator_pickle/velocity_dispersion_gengamma/velocity_dispersion_gengamma_2.pickle
optical_depth_SIS_hemanta interpolator will be generated at ./interpolator_pickle/optical_depth_SIS_hemanta/optical_depth_SIS_hemanta_1.pickle

zs = np.geomspace(0.001, 2, 100)
tau_sis = od.strong_lensing_optical_depth(zs)
tau_sis_haris = od.optical_depth_SIS_haris(zs)

# plot
plt.figure(figsize=(4,4))
plt.plot(zs, tau_sis, label='SIS hemanta')
plt.plot(zs, tau_sis_haris, label='SIS haris')
plt.xlabel('redshift')
plt.ylabel('optical depth')
plt.legend()
plt.grid(alpha=0.5)
plt.show()

zs = np.geomspace(0.001, 40, 100)
tau_sis = od.strong_lensing_optical_depth(zs)
tau_sis_haris = od.optical_depth_SIS_haris(zs)

# plot
plt.figure(figsize=(4,4))
plt.plot(zs, tau_sis, label='SIS hemanta')
plt.plot(zs, tau_sis_haris, label='SIS haris')
plt.xlabel('redshift')
plt.ylabel('optical depth')
plt.legend()
plt.grid(alpha=0.5)
plt.show()

• close enough