import numpy as np
[docs]def vel_disp_function_CPV2007(vel_disp_grid):
"""Evaluate the velocity dispersion function from the fit on SDSS DR6
by [1]_ on a provided grid and normalizes the result to unity, so it can
be used as a PMF from which to draw the velocity dispersion.
Parameters
----------
vel_disp_grid : array-like
a grid of velocity dispersion values in km/s
Note
----
The returned array is normalized to unity and we treat it as a PMF from which to sample
the velocity dispersion. We also use the exact fit values also used in LensPop ([2]_).
References
----------
.. [1] Choi, Yun-Young, Changbom Park, and Michael S. Vogeley. "Internal and collective properties of galaxies in the Sloan Digital Sky Survey." The Astrophysical Journal 658.2 (2007): 884.
.. [2] Collett, Thomas E. "The population of galaxy–galaxy strong lenses in forthcoming optical imaging surveys." The Astrophysical Journal 811.1 (2015): 20.
Returns
-------
array-like, same shape as `vel_disp_grid`
the velocity dispersion function evaluated at `vel_disp_grid`
"""
#h = true_H0/100.0
#phi_star = 8.0*1.e-3
sig_star = 161.0 # km/s
alpha = 2.32
beta = 2.67
#beta_over_gamma = 2.43827086163172 # beta/gamma(alpha/beta) for alpha=2.32, beta=2.67
dn = (vel_disp_grid/sig_star)**alpha
dn *= np.exp(-(vel_disp_grid/sig_star)**beta)
#dn *= beta_over_gamma
dn *= 1.0/vel_disp_grid
#dn *= phi_star * h**3.0
return dn