Overview

The pyRSD.rsd.hzpt module provides functionality for computing various power spectrum and correlation function quantities using Halo Zel’dovich Perturbation Theory (HZPT). See Seljak and Vlah 2015 for an introduction to HZPT.

The Fourier space quantities can be computed from the following classes:

Name	Quantity
HaloZeldovichP00	The dark matter auto power spectrum
HaloZeldovichP01	The dark matter density - radial momentum cross correlation
HaloZeldovichP11	The \(mu^4\) contribution to the radial momentum auto spectrum
HaloZeldovichPhm	The halo - dark matter cross power

And the configuration space quantities can be computed from the following classes:

Name	Quantity
HaloZeldovichCF00	The dark matter auto correlation function
HaloZeldovichCFhm	The halo - dark matter cross correlation function

Initialization

An HZPT instance can be initialized by specifying a cosmology via a pyRSD.rsd.cosmology.Cosmology object and a redshift z.

Note

The objects should be initialized at a specific redshift by passing the z parameter. Once created, the sigma8_z attribute can be adjusted to compute the clustering quantity at different redshifts.

Functions

The HZPT class objects are callable objects; they return either the HZPT power spectrum or correlation function at the specified wavenumber k or separation r. The zeldovich function returns the Zel’dovich term and the broadband function returns the Padé correction term.

Examples

For example, to compute the dark matter auto spectrum for the Planck 2015 cosmology,

from pyRSD.rsd.cosmology import Planck15
from pyRSD.rsd.hzpt import HaloZeldovichP00

# power spectrum at z = 0
P00 = HaloZeldovichP00(Planck15, z=0.)

# compute the full power and each term
k = np.logspace(-2, 0, 100)
Pk = P00(k)
Pzel = P00.zeldovich(k)
Pbb = P00.broadband(k)

# and plot
plt.loglog(k, Pk, label='full P00')
plt.loglog(k, Pzel, label='Zeldovich term')
plt.loglog(k, Pbb, label='broadband term')

Similary, the dark matter correlation function and the various terms can be computed as:

from pyRSD.rsd.hzpt import HaloZeldovichCF00

# correlation function at z = 0
CF = HaloZeldovichCF00(Planck15, z=0.)

# compute the full correlation and each term
r = np.logspace(0, np.log10(150), 100)
xi = CF(r)
xi_zel = CF.zeldovich(r)
xi_bb = CF.broadband(r)

# and plot
plt.loglog(r, r**2 * xi, label='full CF')
plt.loglog(r, r**2 * xi_zel, label='Zeldovich term')
plt.loglog(r, r**2 * xi_bb, label='broadband term')