NFW#

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

Bases: Fittable1DModel

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

Parameters:

massfloat or Quantity [:ref: ‘mass’]

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:

fixeddict, 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

`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')#

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#: 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)[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:

rfloat or Quantity [:ref: ‘length’]: Radial position of velocity to be calculated for the NFW profile.

Returns:

velocityfloat or Quantity [:ref: ‘speed’]: 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:

rfloat or Quantity [:ref: ‘length’]: Radial position of density to be calculated for the NFW profile.
massfloat or Quantity [:ref: ‘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.