Note

This module has been deprecated as it no longer functions correctly and is unmaintained. The code has been moved to the yt attic. If you’d like to take it over, please do!

# Halo Mass Function¶

The Halo Mass Function extension is capable of outputting the halo mass function for a collection halos (input), and/or an analytical fit over a given mass range for a set of specified cosmological parameters. This extension is based on code generously provided by Brian O’Shea.

## General Overview¶

A halo mass function can be created for the halos identified in a cosmological simulation, as well as analytic fits using any arbitrary set of cosmological parameters. In order to create a mass function for simulated halos, they must first be identified (using HOP, FOF, or Rockstar, see Halo Finding and Analysis) and loaded as a halo dataset object. The distribution of halo masses will then be found, and can be compared to the analytic prediction at the same redshift and using the same cosmological parameters as were used in the simulation. Care should be taken in this regard, as the analytic fit requires the specification of cosmological parameters that are not necessarily stored in the halo or simulation datasets, and must be specified by the user. Efforts have been made to set reasonable defaults for these parameters, but setting them to identically match those used in the simulation will produce a much better comparison.

Analytic halo mass functions can also be created without a halo dataset by providing either a simulation dataset or specifying cosmological parameters by hand. yt includes 5 analytic fits for the halo mass function which can be selected.

## Analytical Fits¶

There are five analytical fits to choose from.

We encourage reading each of the primary sources. In general, we recommend the Warren fitting function because it matches simulations over a wide range of masses very well. The Warren fitting function is the default (equivalent to not specifying fitting_function in HaloMassFcn(), below). The Tinker fit is for the $$\Delta=300$$ fits given in the paper, which appears to fit HOP threshold=80.0 fairly well.

## Basic Halo Mass Function Creation¶

The simplest way to create a halo mass function object is to simply pass it no arguments and let it use the default cosmological parameters.

from yt.analysis_modules.halo_mass_function.api import *

hmf = HaloMassFcn()

This will create a HaloMassFcn object off of which arrays holding the information about the analytic mass function hang. Creating the halo mass function for a set of simulated halos requires only the loaded halo dataset to be passed as an argument. This also creates the analytic mass function using all parameters that can be extracted from the halo dataset, at the same redshift, spanning a similar range of halo masses.

from yt.mods import *
from yt.analysis_modules.halo_mass_function.api import *

hmf = HaloMassFcn(halos_ds=my_halos)

A simulation dataset can be passed along with additional cosmological parameters to create an analytic mass function.

from yt.mods import *
from yt.analysis_modules.halo_mass_function.api import *

hmf = HaloMassFcn(simulation_ds=my_ds, omega_baryon0=0.05, primordial_index=0.96,
sigma8 = 0.8, log_mass_min=5, log_mass_max=9)

The analytic mass function can be created for a set of arbitrary cosmological parameters without any dataset being passed as an argument.

from yt.mods import *
from yt.analysis_modules.halo_mass_function.api import *

hmf = HaloMassFcn(omega_baryon0=0.05, omega_matter0=0.27,
omega_lambda0=0.73, hubble0=0.7, this_redshift=10,
log_mass_min=5, log_mass_max=9, fitting_function=5)

## Keyword Arguments¶

• simulation_ds (Simulation dataset object) The loaded simulation dataset, used to set cosmological parameters. Default : None.
• halos_ds (Halo dataset object) The halos from a simulation to be used for creation of the halo mass function in the simulation. Default : None.
• make_analytic (bool) Whether or not to calculate the analytic mass function to go with the simulated halo mass function. Automatically set to true if a simulation dataset is provided. Default : True.
• omega_matter0 (float) The fraction of the universe made up of matter (dark and baryonic). Default : 0.2726.
• omega_lambda0 (float) The fraction of the universe made up of dark energy. Default : 0.7274.
• omega_baryon0 (float) The fraction of the universe made up of baryonic matter. This is not always stored in the dataset and should be checked by hand. Default : 0.0456.
• hubble0 (float) The expansion rate of the universe in units of 100 km/s/Mpc. Default : 0.704.
• sigma8 (float) The amplitude of the linear power spectrum at z=0 as specified by the rms amplitude of mass-fluctuations in a top-hat sphere of radius 8 Mpc/h. This is not always stored in the dataset and should be checked by hand. Default : 0.86.
• primoridal_index (float) This is the index of the mass power spectrum before modification by the transfer function. A value of 1 corresponds to the scale-free primordial spectrum. This is not always stored in the dataset and should be checked by hand. Default : 1.0.
• this_redshift (float) The current redshift. Default : 0.
• log_mass_min (float) The log10 of the mass of the minimum of the halo mass range. This is set automatically by the range of halo masses if a simulated halo dataset is provided. If a halo dataset if not provided and no value is specified, it will be set to 5. Units: M_solar Default : None.
• log_mass_max (float) The log10 of the mass of the maximum of the halo mass range. This is set automatically by the range of halo masses if a simulated halo dataset is provided. If a halo dataset if not provided and no value is specified, it will be set to 16. Units: M_solar Default : None.
• num_sigma_bins (float) The number of bins (points) to use for the calculation of the analytic mass function. Default : 360.
• fitting_function (int) Which fitting function to use. 1 = Press-Schechter, 2 = Jenkins, 3 = Sheth-Tormen, 4 = Warren, 5 = Tinker Default : 4.

## Outputs¶

A HaloMassFnc object has several arrays hanging off of it containing the

• masses_sim: Halo masses from simulated halos. Units: M_solar
• n_cumulative_sim: Number density of halos with mass greater than the corresponding mass in masses_sim. Units: comoving Mpc^-3
• masses_analytic: Masses used for the generation of the analytic mass function. Units: M_solar
• n_cumulative_analytic: Number density of halos with mass greater then the corresponding mass in masses_analytic. Units: comoving Mpc^-3
• dndM_dM_analytic: Differential number density of halos, (dn/dM)*dM.

After the mass function has been created for both simulated halos and the corresponding analytic fits, they can be plotted though something along the lines of

import yt
from yt.analysis_modules.halo_mass_function.api import *
import matplotlib.pyplot as plt

hmf = HaloMassFcn(halos_ds=my_halos)

plt.loglog(hmf.masses_sim, hmf.n_cumulative_sim)
plt.loglog(hmf.masses_analytic, hmf.n_cumulative_analytic)

Attached to hmf is the convenience function write_out, which saves the halo mass function to a text file. (continued from above) .. code-block:: python

hmf.write_out(prefix=’hmf’, analytic=True, simulated=True)

This writes the files hmf-analytic.dat with columns:

• mass [Msun]
• cumulative number density of halos [comoving Mpc^-3]
• (dn/dM)*dM (differential number density of halos) [comoving Mpc^-3]

and the file hmf-simulated.dat with columns:

• mass [Msun]
• cumulative number density of halos [comoving Mpc^-3]