# NFW¶

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

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

Parameters
mass

Mass of NFW peak within specified overdensity radius.

concentrationfloat

Concentration of the NFW profile.

redshiftfloat

Redshift of the NFW profile.

massfactor
Mass overdensity factor and type for provided profiles:
Tuple version:

(“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:

“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 Names of the parameters that describe models of this type. 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

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

Names of the parameters that describe models of this type.

The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.

When defining a custom model class the value of this attribute is automatically set by the Parameter attributes defined in the class body.

r_max

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)[source]

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)[source]

Circular velocities of the NFW profile.

Parameters
r

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

Returns
velocity

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)[source]

One dimensional NFW profile function

Parameters
r

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

mass

Mass of NFW peak within specified overdensity radius.

concentrationfloat

Concentration of the NFW profile.

redshiftfloat

Redshift of the NFW profile.

Returns
densityfloat or Quantity [‘density’]

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

Notes

Warning

Output values might contain nan and inf.