Halo Mass Function

frb.halos.hmf.init_hmf()[source]

Initialize the Aemulus Halo Mass Function

WARNING: This uses the original version which codes Tinker+2008 We may refactor to use the more accurate, new version

Returns:: An Aemulus halo mass function emulator.
Return type:: hmfe (hmf_emulator.hmf_emulator)

frb.halos.hmf.frac_in_halos(zvals, Mlow, Mhigh, rmax=1.0)[source]

Calculate the fraction of matter in collapsed halos: over a mass range and at a given redshift

Note that the fraction of DM associated with these halos will be scaled down by an additional factor of f_diffuse

Requires Aemulus HMF to be installed

Parameters:

zvals – ndarray
Mlow – float In h^-1 units already so this will be applied for the halo mass function
Mhigh – float In h^-1 units already
rmax – float Extent of the halo in units of rvir WARNING: This calculation assumes a single concentration for all halos

Returns:

ndarray: rho_halo / rho_m

Return type:

ratios

frb.halos.hmf.halo_incidence(Mlow, zFRB, radius=None, hmfe=None, Mhigh=1e+16, nsample=20, cumul=False)[source]

Calculate the (approximate) average number of intersections to halos of a given minimum mass to a given zFRB.

Requires Aemulus HMF to be installed

Parameters:

Mlow – float Mass of minimum halo in Solar masses The code deals with h^-1 factors so that you do not The minimum value is 2e10
zFRB – float Redshift of the FRB
radius –
Quantity, optional Physical separation from the sightline for the calculation. The calculation will specify this radius as rvir derived from

Mlow unless this is specified. And this rvir will vary with redshift
hmfe (hmf.hmf_emulator, optional) – Halo mass function emulator from Aeumulus
Mhigh – float, optional Mass of maximum halo in Solar masses
nsammple – int, optional Number of samplings in redshift 20 should be enough
cumul – bool, optional Return the cumulative quantities instead

Returns:

If cumul is False Navg: float

Number of average intersections

elif cumul is True zeval: ndarray Ncumul: ndarray

frb.halos.hmf.build_grid(z_FRB=1.0, ntrial=10, seed=12345, Mlow=10000000000.0, r_max=2.0, outfile=None, dz_box=0.1, dz_grid=0.01, f_hot=0.75, verbose=True)[source]

Generate a universe of dark matter halos with DM measurements Mainly an internal function for generating useful output grids.

Requires the Aemulus Halo Mass function

Parameters:

z_FRB – float, optional
ntrial – int, optional
seed – int, optional
Mlow – float, optional h^-1 mass
r_max – float, optional Extent of the halo in units of rvir
outfile – str, optional Write
dz_box – float, optional Size of the slice of the universe for each sub-calculation
dz_grid – float, optional redshift spacing in the DM grid
f_hot – float Fraction of the cosmic fraction of matter in diffuse gas (for DM)

Returns:

ndarray (ntrial, nz) halo_tbl: Table

Table of all the halos intersected

Return type:

DM_grid

Module for halo mass function calculations and related statistical analysis.

Warning

This module is deprecated. The functionality has been moved to frb.halos.models. Please use that module instead for new code.

Functions

frac_in_halos

frb.halos.hmf.frac_in_halos(zvals, Mlow, Mhigh, rmax=1.0)[source]

Calculate the fraction of matter in collapsed halos: over a mass range and at a given redshift

Note that the fraction of DM associated with these halos will be scaled down by an additional factor of f_diffuse

Requires Aemulus HMF to be installed

Parameters:

zvals – ndarray
Mlow – float In h^-1 units already so this will be applied for the halo mass function
Mhigh – float In h^-1 units already
rmax – float Extent of the halo in units of rvir WARNING: This calculation assumes a single concentration for all halos

Returns:

ndarray: rho_halo / rho_m

Return type:

ratios

Calculate the fraction of matter in collapsed halos over a mass range and at a given redshift.

Parameters:

zvals : ndarray - Redshift values
Mlow : float - Minimum halo mass in h^-1 units
Mhigh : float - Maximum halo mass in h^-1 units
rmax : float, optional - Extent of halo in units of rvir (default: 1.0)

Returns:

ratios : ndarray - rho_halo / rho_m

Note

The fraction of DM associated with these halos will be scaled down by an additional factor of f_diffuse.

Warning

This calculation assumes a single concentration for all halos.

Requirements:

Requires Aemulus HMF to be installed

halo_incidence

frb.halos.hmf.halo_incidence(Mlow, zFRB, radius=None, hmfe=None, Mhigh=1e+16, nsample=20, cumul=False)[source]

Calculate the (approximate) average number of intersections to halos of a given minimum mass to a given zFRB.

Requires Aemulus HMF to be installed

Parameters:

Mlow – float Mass of minimum halo in Solar masses The code deals with h^-1 factors so that you do not The minimum value is 2e10
zFRB – float Redshift of the FRB
radius –
Quantity, optional Physical separation from the sightline for the calculation. The calculation will specify this radius as rvir derived from

Mlow unless this is specified. And this rvir will vary with redshift
hmfe (hmf.hmf_emulator, optional) – Halo mass function emulator from Aeumulus
Mhigh – float, optional Mass of maximum halo in Solar masses
nsammple – int, optional Number of samplings in redshift 20 should be enough
cumul – bool, optional Return the cumulative quantities instead

Returns:

If cumul is False Navg: float

Number of average intersections

elif cumul is True zeval: ndarray Ncumul: ndarray

Calculate the (approximate) average number of intersections to halos of a given minimum mass to a given FRB redshift.

Parameters:

Mlow : float - Mass of minimum halo in Solar masses (minimum: 2e10)
zFRB : float - Redshift of the FRB
radius : Quantity, optional - Physical separation from sightline
hmfe : object, optional - HMF emulator instance
Mhigh : float, optional - Maximum halo mass (default: 1e16)
nsample : int, optional - Number of samples (default: 20)
cumul : bool, optional - Return cumulative values (default: False)

Returns:

Average number of halo intersections

Note

The code handles h^-1 factors automatically. If radius is not specified, it uses rvir derived from Mlow.

Requirements:

Requires Aemulus HMF to be installed

Examples

Calculate matter fraction in halos:

from frb.halos.hmf import frac_in_halos
import numpy as np

# Define redshift range
redshifts = np.linspace(0.1, 1.0, 10)

# Mass range for galaxy-scale halos
mass_min = 1e11  # Solar masses
mass_max = 1e13

# Calculate fractions
fractions = frac_in_halos(redshifts, mass_min, mass_max)

for z, frac in zip(redshifts, fractions):
    print(f"z={z:.1f}: {frac:.3f} of matter in galaxy halos")

Calculate halo incidence along sightline:

from frb.halos.hmf import halo_incidence
from astropy import units as u

# Parameters for FRB sightline
min_mass = 1e12  # Solar masses
frb_redshift = 0.8
impact_radius = 100 * u.kpc

# Calculate average number of halo intersections
n_halos = halo_incidence(min_mass, frb_redshift,
                       radius=impact_radius)

print(f"Expected {n_halos:.2f} halo intersections")

Compare different mass ranges:

from frb.halos.hmf import frac_in_halos
import numpy as np
import matplotlib.pyplot as plt

z_array = np.linspace(0, 2, 50)

# Different mass ranges
dwarf_range = frac_in_halos(z_array, 1e9, 1e11)   # Dwarf galaxies
galaxy_range = frac_in_halos(z_array, 1e11, 1e13) # Normal galaxies
cluster_range = frac_in_halos(z_array, 1e13, 1e15) # Clusters

plt.figure(figsize=(10, 6))
plt.plot(z_array, dwarf_range, label='Dwarf halos (1e9-1e11)')
plt.plot(z_array, galaxy_range, label='Galaxy halos (1e11-1e13)')
plt.plot(z_array, cluster_range, label='Cluster halos (1e13-1e15)')

plt.xlabel('Redshift')
plt.ylabel('Matter fraction in halos')
plt.legend()
plt.title('Halo matter fraction vs redshift')
plt.show()

Extended halo calculations:

from frb.halos.hmf import frac_in_halos
import numpy as np

# Calculate with extended halo profiles
z_test = 0.5
mass_min = 1e12
mass_max = 1e14

# Standard virial radius
frac_1rvir = frac_in_halos([z_test], mass_min, mass_max, rmax=1.0)[0]

# Extended to 2 virial radii
frac_2rvir = frac_in_halos([z_test], mass_min, mass_max, rmax=2.0)[0]

# Extended to 3 virial radii
frac_3rvir = frac_in_halos([z_test], mass_min, mass_max, rmax=3.0)[0]

print(f"Matter fraction at z={z_test}:")
print(f"  1 rvir: {frac_1rvir:.4f}")
print(f"  2 rvir: {frac_2rvir:.4f}")
print(f"  3 rvir: {frac_3rvir:.4f}")

boost_factor = frac_2rvir / frac_1rvir
print(f"Boost factor (2 rvir): {boost_factor:.2f}")

Statistical analysis of halo encounters:

from frb.halos.hmf import halo_incidence
from astropy import units as u
import numpy as np

# Range of FRB redshifts
frb_redshifts = np.linspace(0.1, 2.0, 20)

# Different halo mass thresholds
mass_thresholds = [1e11, 1e12, 1e13]  # Solar masses
radius = 50 * u.kpc

results = {}
for mass_min in mass_thresholds:
    encounters = []
    for z_frb in frb_redshifts:
        n_enc = halo_incidence(mass_min, z_frb, radius=radius)
        encounters.append(n_enc)
    results[mass_min] = encounters

# Plot results
import matplotlib.pyplot as plt
plt.figure(figsize=(10, 6))

for mass_min, encounters in results.items():
    plt.plot(frb_redshifts, encounters,
            label=f'M > {mass_min:.0e} Msun')

plt.xlabel('FRB Redshift')
plt.ylabel('Average Number of Halo Encounters')
plt.title(f'Halo Encounters vs FRB Redshift (R < {radius})')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()

Cumulative analysis:

from frb.halos.hmf import halo_incidence
from astropy import units as u

# Parameters
mass_min = 1e12
z_frb = 1.0
radius = 100 * u.kpc

# Get cumulative encounters
cumul_encounters = halo_incidence(mass_min, z_frb, radius=radius,
                                cumul=True, nsample=100)

print(f"Cumulative halo encounters: {cumul_encounters}")

Redshift evolution study:

from frb.halos.hmf import frac_in_halos
import numpy as np

# Study evolution from z=0 to z=3
z_range = np.linspace(0, 3, 100)

# Different mass ranges
mass_ranges = [
    (1e10, 1e11, 'Low mass'),
    (1e11, 1e12, 'Intermediate mass'),
    (1e12, 1e13, 'High mass'),
    (1e13, 1e15, 'Cluster mass')
]

import matplotlib.pyplot as plt
fig, axes = plt.subplots(2, 2, figsize=(12, 10))
axes = axes.ravel()

for i, (m_low, m_high, label) in enumerate(mass_ranges):
    fractions = frac_in_halos(z_range, m_low, m_high)

    axes[i].plot(z_range, fractions, 'b-', linewidth=2)
    axes[i].set_title(f'{label} halos')
    axes[i].set_xlabel('Redshift')
    axes[i].set_ylabel('Matter fraction')
    axes[i].grid(True, alpha=0.3)
    axes[i].text(0.1, 0.9, f'{m_low:.0e} - {m_high:.0e} Msun',
                transform=axes[i].transAxes,
                bbox=dict(boxstyle='round', facecolor='wheat'))

plt.tight_layout()
plt.suptitle('Halo Matter Fraction Evolution', y=1.02)
plt.show()