Halo Modeling

Module for DM Halo calculations

frb.halos.models.init_hmf()

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:

frb.halos.models.frac_in_halos(zvals, Mlow, Mhigh, rmax=1.0)

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.models.halo_incidence(Mlow, zFRB, radius=None, hmfe=None, Mhigh=1e+16, nsample=20, cumul=False)

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 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.models.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)

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

frb.halos.models.stellarmass_from_halomass(log_Mhalo, z=0, params=None)

Stellar mass from Halo Mass from Moster+2013 https://doi.org/10.1093/mnras/sts261

Parameters:

• log_Mhalo (float) – log_10 halo mass in solar mass units.

• z (float, optional) – halo redshift. Assumed to be 0 by default.

Returns:

log_10 galaxy stellar mass

in solar mass units.

Return type:

log_mstar (float)

frb.halos.models.halomass_from_stellarmass(log_mstar, z=0, randomize=False)

Halo mass from Stellar mass (Moster+2013). Inverts the function stellarmass_from_halomass numerically.

Parameters:

• log_mstar (float or numpy.ndarray) – log_10 stellar mass in solar mass units.

• z (float, optional) – galaxy redshift

Returns:

log_10 halo mass

in solar mass units.

Return type:

log_Mhalo (float)

frb.halos.models.stellarmass_from_halomass_kravtsov(log_mhalo)

Stellar mass from Halo Mass from Kravtsov+2018. https://ui.adsabs.harvard.edu/abs/2018AstL…44….8K/abstract

Caution: This relation is valid for low z (z~0). Higher z values may require a scaled relation. :param log_mhalo: log_10 halo mass :type log_mhalo: float

Returns:

log_10 galaxy

Return type:

log_mstar (float)

frb.halos.models.halomass_from_stellarmass_kravtsov(log_mstar)

Inverts the function frb.halos.models.stellarmass_from_halomass_kravtsov. :param log_mstar: log_10 stellar mass :type log_mstar: float or numpy.ndarray

Returns:

log_10 halo mass

Return type:

log_mhalo (float)

class frb.halos.models.ModifiedNFW(log_Mhalo=12.2, c=7.67, f_hot: float = None, log_MCGM: float = None, alpha=0.0, y0=1.0, z=0.0, cosmo=FlatLambdaCDM(name='Planck18', H0=<Quantity 67.66 km / (Mpc s)>, Om0=0.30966, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.04897), fb=0.15814118710844152, **kwargs)

Bases: object

Generate a modified NFW model, e.g. Mathews & Prochaska 2017 for the hot, virialized gas.

Parameters:

• log_Mhalo – float, optional log10 of the Halo mass [dark matter + baryons] (solar masses)

• log_MCGM – float, optional log10 of the CGM mass (solar masses) If provided, this sets f_hot [this is its only use]

• c – float, optional concentration of the halo

• f_hot – float, optional Fraction of the total “expected” baryons in this hot (aka CGM) phase Will likely use this for all diffuse gas

• alpha – float, optional Parameter to modify NFW profile power-law

• y0 – float, optional Parameter to modify NFW profile position.

• z – float, optional Redshift of the halo

• cosmo – astropy cosmology, optional Cosmology of the universe.

H0

Quantity; Hubble constant

fb

float; Cosmic fraction of baryons (stars+dust+gas) in the entire halo Default to 0.16

r200

Quantity Virial radius

rho0

Quantity Density normalization

M_b

Quantity Mass in baryons of the

__init__(log_Mhalo=12.2, c=7.67, f_hot: float = None, log_MCGM: float = None, alpha=0.0, y0=1.0, z=0.0, cosmo=FlatLambdaCDM(name='Planck18', H0=<Quantity 67.66 km / (Mpc s)>, Om0=0.30966, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.04897), fb=0.15814118710844152, **kwargs)

setup_param(cosmo)

Setup key parameters of the model

Parameters:

cosmo – astropy cosmology Cosmology of the universe

fy_dm(y)

Enclosed mass function for the Dark Matter NFW Assumes the NFW profile

Parameters:

y (float or ndarray) – y = c(r/r200)

Returns:

f_y

Return type:

float or ndarray

fy_b(y)

Enclosed mass function for the baryons

Parameters

y: float or ndarray

Returns:

f_y – Enclosed mass

Return type:

float or ndarray

ne(xyz)

Calculate n_e from n_H with a correction for Helium Assume 25% mass is Helium and both electrons have been stripped

Parameters:

xyz (ndarray (3, npoints)) – Coordinate(s) in kpc

Returns:

n_e – electron density in cm**-3

Return type:

float or ndarray

nH(xyz)

Calculate the Hydrogen number density Includes a correction for Helium

Parameters:

xyz (ndarray) – Coordinate(s) in kpc

Returns:

nH – Density in cm**-3

Return type:

float or ndarray

rho_b(xyz)

Mass density in baryons in the halo; modified

Parameters:

xyz (ndarray) – Position (assumes kpc)

Returns:

rho – Density in g / cm**-3

Return type:

Quantity

Ne_Rperp(Rperp, step_size=<Quantity 0.1 kpc>, rmax=1.0, add_units=True, cumul=False)

Calculate N_e at an input impact parameter Rperp Just a simple sum in steps of step_size

This integrates through the entire halo. Use half if this is for the host

Parameters:

• Rperp (Quantity) – Impact parameter, typically in kpc

• step_size (Quantity, optional) – Step size used for numerical integration (sum)

• rmax (float, optional) – Maximum radius for integration in units of r200

• add_units (bool, optional) – Speed up calculations by avoiding units

• cumul (bool, optional)

Returns:

• if cumul –

  zval: ndarray (kpc)

  z-values where z=0 is the midplane

  Ne_cumul: ndarray

  Cumulative Ne values (pc cm**-3)

• else –

  Ne: Quantity

  Column density of total electrons

RM_Rperp(Rperp, Bparallel, step_size=<Quantity 0.1 kpc>, rmax=1.0, add_units=True, cumul=False, zmax=None)

Calculate RM at an input impact parameter Rperp Just a simple sum in steps of step_size Assumes a constant Magnetic field

Parameters:

• Rperp (Quantity) – Impact parameter, typically in kpc

• (Quantity) (Bparallel) – Magnetic field

• step_size (Quantity, optional) – Step size used for numerical integration (sum)

• rmax (float, optional) – Maximum radius for integration in units of r200

• add_units (bool, optional) – Speed up calculations by avoiding units

• cumul (bool, optional)

• zmax (float, optional) – Maximum distance along the sightline to integrate. Default is rmax*rvir

Returns:

• if cumul –

  zval: ndarray (kpc)

  z-values where z=0 is the midplane

  Ne_cumul: ndarray

  Cumulative Ne values (pc cm**-3)

• else –

  RM: Quantity

  Column density of total electrons

mass_r(r, step_size=<Quantity 0.1 kpc>)

Calculate baryonic halo mass (not total) to a given radius Just a simple sum in steps of step_size

Parameters:

• r (Quantity) – Radius, typically in kpc

• step_size (Quantity, optional) – Step size used for numerical integration (sum)

Returns:

Mr – Enclosed baryonic mass within r Msun units

Return type:

Quantity

class frb.halos.models.MB04(Rc=<Quantity 167. kpc>, log_Mhalo=12.2, c=7.67, f_hot=0.75, **kwargs)

Bases: ModifiedNFW

Halo based on the Maller & Bullock (2004) model of virialized halo gas.

Parameters:

Rc – Quantity cooling radius

__init__(Rc=<Quantity 167. kpc>, log_Mhalo=12.2, c=7.67, f_hot=0.75, **kwargs)

norm_rhoV()

Normalize the density constant from MB04

Returns:

rho_b(xyz)

Baryonic density profile

Parameters:

xyz – ndarray Position array assumed in kpc

Returns:

class frb.halos.models.YF17(log_Mhalo=12.18, c=7.67, f_hot=0.75, **kwargs)

Bases: ModifiedNFW

25. Faerman et al (2017) model of the Milky Way

For the un-normalized density profile, we adopt the average of the warm and hot components in

__init__(log_Mhalo=12.18, c=7.67, f_hot=0.75, **kwargs)

setup_yfdensity()

Normalize the density profile from the input mass

Returns:

Initializes self.rhoN, the density normalization

rho_b(xyz)

Calculate the baryonic density

Parameters:

xyz – ndarray Coordinates in kpc

Returns:

Quantity array

Baryonic mass density (g/cm**3)

Return type:

rho

class frb.halos.models.MB15(log_Mhalo=12.18, c=7.67, f_hot=0.75, **kwargs)

Bases: ModifiedNFW

Encodes the Galactic halo profile from Miller & Bregman 2015, ApJ, 800, 14 https://ui.adsabs.harvard.edu/abs/2015ApJ…800…14M/abstract

The default normalization and beta values are taken from their Table 2, last row. The models presented there do not appear to vary too much.

__init__(log_Mhalo=12.18, c=7.67, f_hot=0.75, **kwargs)

nH(xyz)

Calculate the number density of Hydrogen

Parameters:

xyz – ndarray Coordinates in kpc

Returns:

Number density with units of 1/cm**3

Return type:

ndarray

class frb.halos.models.MilkyWay(log_Mhalo=12.18, c=7.67, f_hot=0.75, alpha=2, y0=2, **kwargs)

Bases: ModifiedNFW

Fiducial model for the Galaxy

Halo mass follows latest constraints

Density profile is similar to Maller & Bullock 2004

__init__(log_Mhalo=12.18, c=7.67, f_hot=0.75, alpha=2, y0=2, **kwargs)

class frb.halos.models.M31(log_Mhalo=12.18, c=7.67, alpha=2, y0=2, f_hot=0.75, **kwargs)

Bases: ModifiedNFW

Preferred model for M31

Taking mass from van der Marel 2012

__init__(log_Mhalo=12.18, c=7.67, alpha=2, y0=2, f_hot=0.75, **kwargs)

DM_from_Galactic(scoord, **kwargs)

Calculate DM through M31’s halo from the Sun given a direction

Parameters:

• scoord – SkyCoord Coordinates of the sightline

• **kwargs – Passed to Ne_Rperp

Returns:

Quantity

Dispersion measure through M31’s halo

Return type:

DM

DM_from_impact_param_b(bimpact, **kwargs)

Calculate DM through M31’s halo from the Sun given an impact parameter

Parameters:

• bimpact – Quantity Ratio of the impact parameter to r200

• **kwargs – Passed to Ne_Rperp

Returns:

Quantity

Dispersion measure through M31’s halo

Return type:

DM

class frb.halos.models.LMC(log_Mhalo=np.float64(11.0), c=12.1, f_hot=0.75, alpha=2, y0=2, **kwargs)

Bases: ModifiedNFW

Preferred model for LMC

Taking data from D’Onghia & Fox ARAA 2016

Mass updated according to

https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.2685E/abstract

__init__(log_Mhalo=np.float64(11.0), c=12.1, f_hot=0.75, alpha=2, y0=2, **kwargs)

class frb.halos.models.SMC(log_Mhalo=np.float64(9.380211241711606), c=15.0, f_hot=0.75, alpha=2, y0=2, **kwargs)

Bases: ModifiedNFW

Preferred model for SMC

Taking data from D’Onghia & Fox ARAA 2016

__init__(log_Mhalo=np.float64(9.380211241711606), c=15.0, f_hot=0.75, alpha=2, y0=2, **kwargs)

class frb.halos.models.M33(log_Mhalo=np.float64(11.698970004336019), c=8.36, f_hot=0.75, alpha=2, y0=2, **kwargs)

Bases: ModifiedNFW

Preferred model for SMC

Taking data from Corbelli 2006

__init__(log_Mhalo=np.float64(11.698970004336019), c=8.36, f_hot=0.75, alpha=2, y0=2, **kwargs)

class frb.halos.models.ICM(log_Mhalo=np.float64(14.698970004336019), c=5, f_hot=0.7, **kwargs)

Bases: ModifiedNFW

Intracluster medium (ICM) model following the analysis of Vikhilnin et al. 2006

We scale the model to the profile fitted to A907

__init__(log_Mhalo=np.float64(14.698970004336019), c=5, f_hot=0.7, **kwargs)

setup_param(cosmo=None)

Setup key parameters of the model

Parameters:

cosmo – astropy cosmology Cosmology of the universe

scale_profile()

a907_nfw()

Code to regenrate the r200 and c200 values for A907 Now hard-coded

ne(xyz)

Parameters:

xyz (ndarray) – Coordinate(s) in kpc

Returns:

n_e – electron density in cm**-3

Return type:

float or ndarray

nH(xyz)

Scale by He

Parameters:

xyz

Returns:

class frb.halos.models.Virgo(log_Mhalo=np.float64(14.880136251483002), **kwargs)

Bases: ICM

Parameterization of Virgo following the Planck Collaboration paper: A&A 596 A101 (2016)

__init__(log_Mhalo=np.float64(14.880136251483002), **kwargs)

setup_param(cosmo=None)

Setup key parameters of the model

ne(xyz)

Parameters:

xyz (ndarray) – Coordinate(s) in kpc

Returns:

n_e – electron density in cm**-3

Return type:

float or ndarray

frb.halos.models.rad3d2(xyz)

Calculate radius squared to x,y,z inputted Assumes the origin is 0,0,0

Parameters:

xyz (Tuple or ndarray)

Returns:

rad3d

Return type:

float or ndarray

Module for DM halo calculations and galaxy halo models.

Constants

frb.halos.models.m_p = np.float64(1.67262192369e-24)

float64(value=0, /) –

Double-precision floating-point number type, compatible with Python float and C double.

Character code:

'd'

Canonical name:

numpy.double

Alias on this platform (Linux x86_64):

numpy.float64: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa.

Proton mass in CGS units for optimized calculations.

Functions

init_hmf

frb.halos.models.init_hmf()

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:

Initialize the Aemulus Halo Mass Function.

Warning

Uses the original version which codes Tinker+2008. May be refactored to use the more accurate new version.

Returns:

• hmf_emulator - Initialized HMF emulator object

frac_in_halos

frb.halos.models.frac_in_halos(zvals, Mlow, Mhigh, rmax=1.0)

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.

Note

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

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

Warning

This calculation assumes a single concentration for all halos.

stellarmass_from_halomass

frb.halos.models.stellarmass_from_halomass(log_Mhalo, z=0, params=None)

Stellar mass from Halo Mass from Moster+2013 https://doi.org/10.1093/mnras/sts261

Parameters:

• log_Mhalo (float) – log_10 halo mass in solar mass units.

• z (float, optional) – halo redshift. Assumed to be 0 by default.

Returns:

log_10 galaxy stellar mass

in solar mass units.

Return type:

log_mstar (float)

Stellar mass from Halo Mass using Moster+2013 relation.

Parameters:

• log_Mhalo : float - log_10 halo mass in solar mass units

• z : float, optional - Halo redshift (default: 0)

• params : list, optional - Custom model parameters

Returns:

• log_mstar : float - log_10 galaxy stellar mass in solar mass units

Reference: https://doi.org/10.1093/mnras/sts261

halomass_from_stellarmass

frb.halos.models.halomass_from_stellarmass(log_mstar, z=0, randomize=False)

Halo mass from Stellar mass (Moster+2013). Inverts the function stellarmass_from_halomass numerically.

Parameters:

• log_mstar (float or numpy.ndarray) – log_10 stellar mass in solar mass units.

• z (float, optional) – galaxy redshift

Returns:

log_10 halo mass

in solar mass units.

Return type:

log_Mhalo (float)

Halo mass from Stellar mass (Moster+2013). Numerically inverts stellarmass_from_halomass.

Parameters:

• log_mstar : float or ndarray - log_10 stellar mass in solar mass units

• z : float, optional - Galaxy redshift (default: 0)

• randomize : bool, optional - Add scatter to the relation

Returns:

• log_Mhalo : float - log_10 halo mass in solar mass units

stellarmass_from_halomass_kravtsov

frb.halos.models.stellarmass_from_halomass_kravtsov(log_mhalo)

Stellar mass from Halo Mass from Kravtsov+2018. https://ui.adsabs.harvard.edu/abs/2018AstL…44….8K/abstract

Caution: This relation is valid for low z (z~0). Higher z values may require a scaled relation. :param log_mhalo: log_10 halo mass :type log_mhalo: float

Returns:

log_10 galaxy

Return type:

log_mstar (float)

Stellar mass from Halo Mass using Kravtsov+2018 relation.

Caution

This relation is valid for low z (z~0). Higher z values may require a scaled relation.

Parameters:

• log_mhalo : float - log_10 halo mass

Returns:

• log_mstar : float - log_10 galaxy stellar mass

Reference: https://ui.adsabs.harvard.edu/abs/2018AstL…44….8K/abstract

halomass_from_stellarmass_kravtsov

frb.halos.models.halomass_from_stellarmass_kravtsov(log_mstar)

Inverts the function frb.halos.models.stellarmass_from_halomass_kravtsov. :param log_mstar: log_10 stellar mass :type log_mstar: float or numpy.ndarray

Returns:

log_10 halo mass

Return type:

log_mhalo (float)

Inverts stellarmass_from_halomass_kravtsov function.

Parameters:

• log_mstar : float or ndarray - log_10 stellar mass

Returns:

• log_mhalo : float - log_10 halo mass

rad3d2

frb.halos.models.rad3d2(xyz)

Calculate radius squared to x,y,z inputted Assumes the origin is 0,0,0

Parameters:

xyz (Tuple or ndarray)

Returns:

rad3d

Return type:

float or ndarray

Calculate radius to x,y,z coordinates. Assumes origin is (0,0,0).

Parameters:

• xyz : tuple or ndarray - 3D coordinates

Returns:

• rad3d : float or ndarray - 3D radius squared

Classes

ModifiedNFW

class frb.halos.models.ModifiedNFW(log_Mhalo=12.2, c=7.67, f_hot: float = None, log_MCGM: float = None, alpha=0.0, y0=1.0, z=0.0, cosmo=FlatLambdaCDM(name='Planck18', H0=<Quantity 67.66 km / (Mpc s)>, Om0=0.30966, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.04897), fb=0.15814118710844152, **kwargs)

Bases: object

Generate a modified NFW model, e.g. Mathews & Prochaska 2017 for the hot, virialized gas.

Parameters:

• log_Mhalo – float, optional log10 of the Halo mass [dark matter + baryons] (solar masses)

• log_MCGM – float, optional log10 of the CGM mass (solar masses) If provided, this sets f_hot [this is its only use]

• c – float, optional concentration of the halo

• f_hot – float, optional Fraction of the total “expected” baryons in this hot (aka CGM) phase Will likely use this for all diffuse gas

• alpha – float, optional Parameter to modify NFW profile power-law

• y0 – float, optional Parameter to modify NFW profile position.

• z – float, optional Redshift of the halo

• cosmo – astropy cosmology, optional Cosmology of the universe.

H0

Quantity; Hubble constant

fb

float; Cosmic fraction of baryons (stars+dust+gas) in the entire halo Default to 0.16

r200

Quantity Virial radius

rho0

Quantity Density normalization

M_b

Quantity Mass in baryons of the

Generate a modified NFW model for hot, virialized gas (e.g. Mathews & Prochaska 2017).

Parameters:

• log_Mhalo : float, optional - log10 of halo mass in solar masses (default: 12.2)

• c : float, optional - Concentration of the halo (default: 7.67)

• f_hot : float, optional - Fraction of baryons in hot phase (default: 0.75)

• alpha : float, optional - Parameter to modify NFW profile power-law (default: 0)

• y0 : float, optional - Parameter to modify NFW profile position (default: 1)

• z : float, optional - Redshift of the halo (default: 0)

• cosmo : astropy cosmology, optional - Cosmology of the universe

Key Attributes:

• H0 : Quantity - Hubble constant

• fb : float - Cosmic fraction of baryons (default: 0.16)

• r200 : Quantity - Virial radius

• rho0 : Quantity - Density normalization

• M_b : Quantity - Mass in baryons

Methods:

setup_param(cosmo)

Setup key parameters of the model

Parameters:

cosmo – astropy cosmology Cosmology of the universe

Setup key parameters of the model.

Ne_Rperp(Rperp, step_size=<Quantity 0.1 kpc>, rmax=1.0, add_units=True, cumul=False)

Calculate N_e at an input impact parameter Rperp Just a simple sum in steps of step_size

This integrates through the entire halo. Use half if this is for the host

Parameters:

• Rperp (Quantity) – Impact parameter, typically in kpc

• step_size (Quantity, optional) – Step size used for numerical integration (sum)

• rmax (float, optional) – Maximum radius for integration in units of r200

• add_units (bool, optional) – Speed up calculations by avoiding units

• cumul (bool, optional)

Returns:

• if cumul –

  zval: ndarray (kpc)

  z-values where z=0 is the midplane

  Ne_cumul: ndarray

  Cumulative Ne values (pc cm**-3)

• else –

  Ne: Quantity

  Column density of total electrons

Calculate column density along a perpendicular path through the halo.

__init__(log_Mhalo=12.2, c=7.67, f_hot: float = None, log_MCGM: float = None, alpha=0.0, y0=1.0, z=0.0, cosmo=FlatLambdaCDM(name='Planck18', H0=<Quantity 67.66 km / (Mpc s)>, Om0=0.30966, Tcmb0=<Quantity 2.7255 K>, Neff=3.046, m_nu=<Quantity [0., 0., 0.06] eV>, Ob0=0.04897), fb=0.15814118710844152, **kwargs)

setup_param(cosmo)

Setup key parameters of the model

Parameters:

cosmo – astropy cosmology Cosmology of the universe

fy_dm(y)

Enclosed mass function for the Dark Matter NFW Assumes the NFW profile

Parameters:

y (float or ndarray) – y = c(r/r200)

Returns:

f_y

Return type:

float or ndarray

fy_b(y)

Enclosed mass function for the baryons

Parameters

y: float or ndarray

Returns:

f_y – Enclosed mass

Return type:

float or ndarray

ne(xyz)

Calculate n_e from n_H with a correction for Helium Assume 25% mass is Helium and both electrons have been stripped

Parameters:

xyz (ndarray (3, npoints)) – Coordinate(s) in kpc

Returns:

n_e – electron density in cm**-3

Return type:

float or ndarray

nH(xyz)

Calculate the Hydrogen number density Includes a correction for Helium

Parameters:

xyz (ndarray) – Coordinate(s) in kpc

Returns:

nH – Density in cm**-3

Return type:

float or ndarray

rho_b(xyz)

Mass density in baryons in the halo; modified

Parameters:

xyz (ndarray) – Position (assumes kpc)

Returns:

rho – Density in g / cm**-3

Return type:

Quantity

Ne_Rperp(Rperp, step_size=<Quantity 0.1 kpc>, rmax=1.0, add_units=True, cumul=False)

Calculate N_e at an input impact parameter Rperp Just a simple sum in steps of step_size

This integrates through the entire halo. Use half if this is for the host

Parameters:

• Rperp (Quantity) – Impact parameter, typically in kpc

• step_size (Quantity, optional) – Step size used for numerical integration (sum)

• rmax (float, optional) – Maximum radius for integration in units of r200

• add_units (bool, optional) – Speed up calculations by avoiding units

• cumul (bool, optional)

Returns:

• if cumul –

  zval: ndarray (kpc)

  z-values where z=0 is the midplane

  Ne_cumul: ndarray

  Cumulative Ne values (pc cm**-3)

• else –

  Ne: Quantity

  Column density of total electrons

RM_Rperp(Rperp, Bparallel, step_size=<Quantity 0.1 kpc>, rmax=1.0, add_units=True, cumul=False, zmax=None)

Calculate RM at an input impact parameter Rperp Just a simple sum in steps of step_size Assumes a constant Magnetic field

Parameters:

• Rperp (Quantity) – Impact parameter, typically in kpc

• (Quantity) (Bparallel) – Magnetic field

• step_size (Quantity, optional) – Step size used for numerical integration (sum)

• rmax (float, optional) – Maximum radius for integration in units of r200

• add_units (bool, optional) – Speed up calculations by avoiding units

• cumul (bool, optional)

• zmax (float, optional) – Maximum distance along the sightline to integrate. Default is rmax*rvir

Returns:

• if cumul –

  zval: ndarray (kpc)

  z-values where z=0 is the midplane

  Ne_cumul: ndarray

  Cumulative Ne values (pc cm**-3)

• else –

  RM: Quantity

  Column density of total electrons

mass_r(r, step_size=<Quantity 0.1 kpc>)

Calculate baryonic halo mass (not total) to a given radius Just a simple sum in steps of step_size

Parameters:

• r (Quantity) – Radius, typically in kpc

• step_size (Quantity, optional) – Step size used for numerical integration (sum)

Returns:

Mr – Enclosed baryonic mass within r Msun units

Return type:

Quantity

ICM

class frb.halos.models.ICM(log_Mhalo=np.float64(14.698970004336019), c=5, f_hot=0.7, **kwargs)

Bases: ModifiedNFW

Intracluster medium (ICM) model following the analysis of Vikhilnin et al. 2006

We scale the model to the profile fitted to A907

Intracluster Medium model, child of ModifiedNFW.

Implements the Miller & Bregman 2015 ICM model for galaxy clusters.

Methods:

nH(xyz)

Scale by He

Parameters:

xyz

Returns:

Calculate the number density of Hydrogen.

Parameters:

• xyz : ndarray - Coordinates in kpc

Returns:

• ndarray - Number density in units of 1/cm³

__init__(log_Mhalo=np.float64(14.698970004336019), c=5, f_hot=0.7, **kwargs)

setup_param(cosmo=None)

Setup key parameters of the model

Parameters:

cosmo – astropy cosmology Cosmology of the universe

scale_profile()

a907_nfw()

Code to regenrate the r200 and c200 values for A907 Now hard-coded

ne(xyz)

Parameters:

xyz (ndarray) – Coordinate(s) in kpc

Returns:

n_e – electron density in cm**-3

Return type:

float or ndarray

nH(xyz)

Scale by He

Parameters:

xyz

Returns:

MilkyWay

class frb.halos.models.MilkyWay(log_Mhalo=12.18, c=7.67, f_hot=0.75, alpha=2, y0=2, **kwargs)

Bases: ModifiedNFW

Fiducial model for the Galaxy

Halo mass follows latest constraints

Density profile is similar to Maller & Bullock 2004

Fiducial model for the Galaxy. Halo mass follows latest constraints.

Density profile is similar to Maller & Bullock 2004.

__init__(log_Mhalo=12.18, c=7.67, f_hot=0.75, alpha=2, y0=2, **kwargs)

M31

class frb.halos.models.M31(log_Mhalo=12.18, c=7.67, alpha=2, y0=2, f_hot=0.75, **kwargs)

Bases: ModifiedNFW

Preferred model for M31

Taking mass from van der Marel 2012

Preferred model for M31. Mass from van der Marel 2012.

Attributes:

• distance : Quantity - Distance from Sun (752 kpc)

• coord : SkyCoord - Coordinates of M31

Methods:

DM_from_Galactic(scoord, **kwargs)

Calculate DM through M31’s halo from the Sun given a direction

Parameters:

• scoord – SkyCoord Coordinates of the sightline

• **kwargs – Passed to Ne_Rperp

Returns:

Quantity

Dispersion measure through M31’s halo

Return type:

DM

Calculate DM through M31’s halo from the Sun given a direction.

Parameters:

• scoord : SkyCoord - Coordinates of the sightline

Returns:

• DM : Quantity - Dispersion measure through M31’s halo

__init__(log_Mhalo=12.18, c=7.67, alpha=2, y0=2, f_hot=0.75, **kwargs)

DM_from_Galactic(scoord, **kwargs)

Calculate DM through M31’s halo from the Sun given a direction

Parameters:

• scoord – SkyCoord Coordinates of the sightline

• **kwargs – Passed to Ne_Rperp

Returns:

Quantity

Dispersion measure through M31’s halo

Return type:

DM

DM_from_impact_param_b(bimpact, **kwargs)

Calculate DM through M31’s halo from the Sun given an impact parameter

Parameters:

• bimpact – Quantity Ratio of the impact parameter to r200

• **kwargs – Passed to Ne_Rperp

Returns:

Quantity

Dispersion measure through M31’s halo

Return type:

DM

Examples

Basic halo model usage:

from frb.halos.models import ModifiedNFW, halomass_from_stellarmass
from astropy import units as u

# Create a halo model
halo = ModifiedNFW(log_Mhalo=12.5, z=0.3, f_hot=0.6)

# Calculate DM at 100 kpc offset
offset = 100 * u.kpc
dm_contribution = halo.Ne_Rperp(offset)
print(f"DM contribution: {dm_contribution}")

Stellar-halo mass relations:

from frb.halos.models import stellarmass_from_halomass, halomass_from_stellarmass

# Convert halo mass to stellar mass
log_mhalo = 12.0  # log solar masses
log_mstar = stellarmass_from_halomass(log_mhalo, z=0.5)

# Invert the relation
log_mhalo_recovered = halomass_from_stellarmass(log_mstar, z=0.5)

print(f"Halo mass: {log_mhalo}")
print(f"Stellar mass: {log_mstar:.2f}")
print(f"Recovered halo mass: {log_mhalo_recovered:.2f}")

Galaxy-specific models:

from frb.halos.models import MilkyWay, M31
from astropy.coordinates import SkyCoord
from astropy import units as u

# Milky Way model
mw = MilkyWay(log_Mhalo=12.1, f_hot=0.7)

# M31 model with DM calculation
m31 = M31(log_Mhalo=12.2)
target_coord = SkyCoord('01h33m51s', '+30d39m37s')
dm_m31 = m31.DM_from_Galactic(target_coord)
print(f"DM through M31: {dm_m31}")

Halo mass function calculations:

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

# Calculate matter fraction in halos
redshifts = np.array([0.1, 0.5, 1.0])
mass_min = 1e11  # Solar masses
mass_max = 1e15

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 halos")

Advanced usage with scatter:

# Include scatter in stellar-halo mass relation
log_mstar = 10.5
z = 0.3

# Multiple realizations with scatter
log_mhalos = []
for i in range(100):
    log_mhalo = halomass_from_stellarmass(log_mstar, z=z, randomize=True)
    log_mhalos.append(log_mhalo)

mean_mhalo = np.mean(log_mhalos)
std_mhalo = np.std(log_mhalos)
print(f"Mean log(Mhalo): {mean_mhalo:.2f} ± {std_mhalo:.2f}")