pynbody.analysis.theoretical_profiles.NFWProfile

class pynbody.analysis.theoretical_profiles.NFWProfile(density_scale_radius=None, scale_radius=None, halo_radius=None, concentration=None, halo_mass=None)

Bases: AbstractBaseProfile

Represents a Navarro-Frenk-White (NFW) profile.

Methods

__call__(radius)	Call self as a function.
enclosed_mass(radius)	Return the mass, M(r), enclosed within a given radius
fit(radial_data, profile_data[, ...])	Fit the given profile using a least-squares method.
keys()	Return the keys of the profile parameters
logarithmic_slope(radius)	Return the logarithmic slope of the profile, d ln rho / d ln r, at a given radius
parameter_bounds(r_values, rho_values)	Return bounds on the parameter values for the profile fit

jacobian

__init__(density_scale_radius=None, scale_radius=None, halo_radius=None, concentration=None, halo_mass=None)

Represents a Navarro-Frenk-White (NFW) profile.

The profile can then be initialised through one of the following combination of parameters:

• scale_radius, density_scale_radius and optionally halo_radius;

• halo_radius, concentration and density_scale_radius;

• halo_radius, concentration and halo_mass.

From one mode of initialisation, the derived parameters of the others are calculated, e.g. if you initialise with halo_mass + concentration, the scale_radius and central density will be derived. The exception is if you initialise with scale_radius + density_scale_radius without halo_radius.

Units may be passed into the parameters by using scalar arrays.

Parameters:

• scale_radius (float | array-like, optional) – The radius at which the slope is equal to -2

• density_scale_radius (float | array-like, optional) – 1/4 of density at r=rs (normalisation).

• halo_mass (float | array-like, optional) – The mass enclosed inside the outer halo radius

• halo_radius (float | array-like) – The outer boundary of the halo (r200m, r200c, rvir … depending on definitions)

• concentration (float | array-like, optional) – The outer_radius / scale_radius

enclosed_mass(radius)

Return the mass, M(r), enclosed within a given radius

classmethod fit(radial_data, profile_data, profile_err=None, use_analytical_jac=True, guess=None, verbose=0, return_profile=True)

Fit the given profile using a least-squares method.

Parameters:

• radial_data (array_like) – The central radius of the bins in which the profile data is measured

• profile_data (array_like) – The profile density values

• profile_err (array_like, optional) – The error on the profile data

• use_analytical_jac (bool) – Whether to use the analytical jacobian of the profile function. If False, finite differencing is used.

• guess (array_like, optional) – An initial guess for the parameters of the profile. If None, the initial guess is taken to be all ones, according to the underlying scipy.optimize.curve_fit function.

• verbose (int) – The verbosity level to pass to the underlying scipy.optimize.curve_fit function.

• return_profile (bool) – Whether to return the profile object or just the parameters

Returns:

• fitted_profile (array_like | AbstractBaseProfile) – If return_profile is True, the fitted profile object. Otherwise, the fitted parameters.

• cov (array_like) – The covariance matrix of the fit. The diagonal elements are the variance of the parameters.

keys()

Return the keys of the profile parameters

logarithmic_slope(radius)

Return the logarithmic slope of the profile, d ln rho / d ln r, at a given radius

classmethod parameter_bounds(r_values, rho_values)

Return bounds on the parameter values for the profile fit

Parameters:

• r_values (array_like) – The radii at which the profile is measured

• rho_values (array_like) – The density values of the profile

Returns:

bounds – A 2-tuple containing lower and upper bounds respectively for the parameters of the profile

Return type:

tuple[array_like]