skypy.halos.mass.halo_mass_function

skypy.halos.mass.halo_mass_function(M, wavenumber, power_spectrum, growth_function, cosmology, collapse_function, params)

Halo mass function. This function computes the halo mass function, defined in equation 7.46 in [1].

Parameters:

M(nm,) array_like

Array for the halo mass, in units of solar mass.

wavenumber(nk,) array_like

Array of wavenumbers at which the power spectrum is evaluated, in units of Mpc-1.

power_spectrum: (nk,) array_like

Linear power spectrum at redshift 0 in Mpc3.

growth_functionfloat

The growth function evaluated at a given redshift for the given cosmology.

cosmologyastropy.cosmology.Cosmology

Cosmology object providing methods for the evolution history of omega_matter and omega_lambda with redshift.

collapse_function: function

Collapse function to choose from a variety of models: sheth_tormen_collapse_function, press_schechter_collapse_function.

params: tuple

List of parameters that determines the model used for the collapse function.

Returns:

mass_function: (nm,) array_like

Halo mass function for a given mass array, cosmology and redshift, in units of Mpc-3 Msun-1.

References

[1]

Mo, H. and van den Bosch, F. and White, S. (2010), Cambridge University Press, ISBN: 9780521857932.

Examples

>>> import numpy as np
>>> from skypy.halos import mass
>>> from skypy.power_spectrum import eisenstein_hu

This example will compute the halo mass function for elliptical and spherical collapse, for a Planck15 cosmology at redshift 0. The power spectrum is given by the Eisenstein and Hu fitting formula:

>>> from astropy.cosmology import Planck15
>>> cosmo = Planck15
>>> D0 = 1.0
>>> k = np.logspace(-3, 1, num=1000, base=10.0)
>>> A_s, n_s = 2.1982e-09, 0.969453
>>> Pk = eisenstein_hu(k, A_s, n_s, cosmo, kwmap=0.02, wiggle=True)

The Sheth and Tormen mass function at redshift 0:

>>> m = 10**np.arange(9.0, 12.0, 2)
>>> mass.sheth_tormen_mass_function(m, k, Pk, D0, cosmo)
array([2.730976...e-11, 5.202592...e-13])

And the Press-Schechter mass function at redshift 0:

>>> mass.press_schechter_mass_function(m, k, Pk, D0, cosmo)
array([2.945662...e-11, 6.573908...e-13])

For any other collapse models:

>>> params_model = (0.3, 0.7, 0.3, 1.686)
>>> mass.halo_mass_function(m, k, Pk, D0, cosmo,
...     mass.ellipsoidal_collapse_function, params=params_model)
array([2.536209...e-11, 4.832517...e-13])