hmvec

hmvec is a fast pure Python/numpy vectorized general halo model and HOD code. Currently, it includes support for (a) 3d power spectra involving NFW, Battaglia electron density profiles and galaxy HODs and (b) 2d power spectra including tSZ, cosmic shear, galaxy-galaxy lensing and CMB lensing.

It calculates a vectorized FFT for a given profile over all points in mass and redshift, but it currently does have one double loop over mass and redshift to interpolate the profile Fourier transforms to the target wavenumbers. Every other part of the code is vectorized. Heavy memory usage can be an issue -- watch out for that!

• Free software: BSD license
• Documentation: in the works

Dependencies

• Python>=2.7 or Python>=3.4
• numpy, scipy, matplotlib
• camb (Python package, recommend using dev branch)

Credits

The theory used here follows the approach outlined in the appendix of arxiv:1810.13423. This code has greatly benefited from comparisons with the implementation written by Moritz Munchmeyer and Matt Johnson for that paper. Some of the HOD functions are copied (and modified) from there.

Installation

Clone this repository and install with symbolic links as follows so that changes you make to the code are immediately reflected.

pip install -e . --user

Usage

One can quickly get the matter power spectrum for desired wavenumbers and redshifts after specifying the mass grid to integrate over. Note that the analytic NFW profile is initialized by default.

import hmvec as hm
zs = np.linspace(0.,3.,20)
ms = np.geomspace(2e10,1e17,200)
ks = np.geomspace(1e-4,100,1001)
hcos = hm.HaloModel(zs,ks,ms=ms)
pmm_1h = hcos.get_power_1halo(name="nfw")
pmm_2h = hcos.get_power_2halo(name="nfw")

You can add functions that implement a profile of your choice. An electron profile from Battaglia 2016 has also been implemented. It needs to be FFTd numerically to get the electron power spectrum, which is done as follows:

hcos.add_battaglia_profile("electron",family="AGN",xmax=20,nxs=5000)
pee_1h = hcos.get_power_1halo(name="electron")
pee_2h = hcos.get_power_2halo(name="electron")

Cross-spectra can also be calculated:

pme_1h = hcos.get_power_1halo("nfw","electron")
pme_2h = hcos.get_power_2halo("nfw","electron")

An HOD can be added as follows:

hcos.add_hod(name="g",mthresh=10**10.5+zs*0.)

and galaxy spectra and cross-spectra with matter and electrons can be calculated just as above by specifying the chosen name for the HOD. If the galaxy number density ngal is provided instead of mthresh, the latter will be found iteratively.

Cosmic Shear / CMB Lensing autospectrum

HaloModel inherits from cosmology.Cosmology which contains some convenient functions involving Limber integrals. To get a cosmic shear power spectrum for example, you first build the total matter power spectrum and pass it to the relevant member function of cosmology.Cosmology,

pmm_1h = hcos.get_power_1halo(name="nfw")
pmm_2h = hcos.get_power_2halo(name="nfw")
Pmm = pmm_1h + pmm_2h

ells = np.linspace(100,600,10)
Cls = hcos.C_kk(ells,zs,ks,Pmm,lzs1=2.5,lzs2=2.5)

Galaxy-galaxy lensing / Galaxy-CMB lensing

Similarly, one can obtain cross-spectra for galaxy-galaxy lensing and galaxy-CMB lensing,

hcos.add_hod(name="g",mthresh=10**10.5+zs*0.)
pgm_1h = hcos.get_power_1halo("nfw","electron")
pgm_2h = hcos.get_power_2halo("nfw","electron")
Pgm = pgm_1h + pgm_2h

ells = np.linspace(100,600,10)
Cls = hcos.C_kg(ells,zs,ks,Pgm,gzs=0.8,lzs=2.5)