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# NFW

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

  Bases: `Fittable1DModel`

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

  Parameters:
    mass `python:float` or `Quantity` [:ref: ‘mass’]

      Mass of NFW peak within specified overdensity radius.

    concentration `python:float`

      Concentration of the NFW profile.

    redshift `python:float`

      Redshift of the NFW profile.

    massfactor `python:tuple` or `python: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”)

    cosmo `Cosmology`

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

  Other Parameters:
    fixed `a` `python: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.

    tied `python:dict`, 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.

    bounds `python:dict`, 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.

    eqcons `python:list`, optional

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

    ineqcons `python:list`, 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)

    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:
      r `python:float` or `Quantity` [:ref: ‘length’]

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

    Returns:
      velocity `python:float` 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)

    One dimensional NFW profile function

    Parameters:
      r `python:float` or `Quantity` [:ref: ‘length’]

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

      mass `python:float` or `Quantity` [:ref: ‘mass’]

        Mass of NFW peak within specified overdensity radius.

      concentration `python:float`

        Concentration of the NFW profile.

      redshift `python:float`

        Redshift of the NFW profile.

    Returns:
      density `python:float` 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`.