NFW

class astropy.modeling.physical_models.NFW(mass=<Quantity 1. solMass>, concentration=1.0, redshift=0.0, massfactor=('critical', 200), cosmo=None, **kwargs)

Bases: astropy.modeling.Fittable1DModel

Navarro–Frenk–White (NFW) profile - model for radial distribution of dark matter.

Parameters

massfloat or Quantity

Mass of NFW peak within specified overdensity radius.

concentrationfloat

Concentration of the NFW profile.

redshiftfloat

Redshift of the NFW profile.

massfactortuple or str

Mass overdensity factor and type for provided profiles:

Tuple version:

(“virial”,) : virial radius

(“critical”, N) : radius where density is N times that of the critical density

(“mean”, N) : radius where density is N times that of the mean density

String version:

“virial” : virial radius

“Nc” : radius where density is N times that of the critical density (e.g. “200c”)

“Nm” : radius where density is N times that of the mean density (e.g. “500m”)

cosmoCosmology

Background cosmology for density calculation. If None, the default cosmology will be used.

Other Parameters

fixeda dict, optional

A dictionary {parameter_name: boolean} of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively the fixed property of a parameter may be used.

tieddict, optional

A dictionary {parameter_name: callable} of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship. Alternatively the tied property of a parameter may be used.

boundsdict, optional

A dictionary {parameter_name: value} of lower and upper bounds of parameters. Keys are parameter names. Values are a list or a tuple of length 2 giving the desired range for the parameter. Alternatively, the min and max properties of a parameter may be used.

eqconslist, optional

A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem.

ineqconslist, optional

A list of functions of length n such that ieqcons[j](x0,*args) >= 0.0 is a successfully optimized problem.

Notes

Model formula:

\[\rho(r)=\frac{\delta_c\rho_{c}}{r/r_s(1+r/r_s)^2}\]

References

1

https://arxiv.org/pdf/astro-ph/9508025

2

https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile

3

https://en.wikipedia.org/wiki/Virial_mass

Attributes Summary

concentration
input_units	This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted).
mass
param_names
r_max	Radius of maximum circular velocity.
r_s	Scale radius of the NFW profile.
r_virial	Mass factor defined virial radius of the NFW profile (R200c for M200c, Rvir for Mvir, etc.).
redshift
return_units	This property is used to indicate what units or sets of units the output of evaluate should be in, and returns a dictionary mapping outputs to units (or None if any units are accepted).
rho_scale	Scale density of the NFW profile.
v_max	Maximum circular velocity.

Methods Summary

A_NFW(y)	Dimensionless volume integral of the NFW profile, used as an intermediate step in some calculations for this model.
circular_velocity(r)	Circular velocities of the NFW profile.
evaluate(r, mass, concentration, redshift)	One dimensional NFW profile function

Attributes Documentation

concentration = Parameter('concentration', value=1.0, bounds=(1.0, None))

input_units

mass = Parameter('mass', value=1.0, unit=solMass, bounds=(1.0, None))

param_names = ('mass', 'concentration', 'redshift')

r_max

Radius of maximum circular velocity.

r_s

Scale radius of the NFW profile.

r_virial

Mass factor defined virial radius of the NFW profile (R200c for M200c, Rvir for Mvir, etc.).

redshift = Parameter('redshift', value=0.0, bounds=(0.0, None))

return_units

rho_scale

Scale density of the NFW profile. Often written in the literature as \(\rho_s\)

v_max

Maximum circular velocity.

Methods Documentation

static A_NFW(y)

Dimensionless volume integral of the NFW profile, used as an intermediate step in some calculations for this model.

Notes

Model formula:

\[A_{NFW} = [\ln(1+y) - \frac{y}{1+y}]\]

circular_velocity(r)

Circular velocities of the NFW profile.

Parameters

rfloat or Quantity

Radial position of velocity to be calculated for the NFW profile.

Returns

velocityfloat or Quantity

NFW profile circular velocity at location r. The velocity units are: [km / s]

Notes

Model formula:

\[v_{circ}(r)^2 = \frac{1}{x}\frac{\ln(1+cx)-(cx)/(1+cx)}{\ln(1+c)-c/(1+c)}\]

\[x = r/r_s\]

Warning

Output values might contain nan and inf.

evaluate(r, mass, concentration, redshift)

One dimensional NFW profile function

Parameters

rfloat or Quantity

Radial position of density to be calculated for the NFW profile.

massfloat or Quantity

Mass of NFW peak within specified overdensity radius.

concentrationfloat

Concentration of the NFW profile.

redshiftfloat

Redshift of the NFW profile.

Returns

densityfloat or Quantity

NFW profile mass density at location r. The density units are: [mass / r ^3]

Notes

Warning

Output values might contain nan and inf.