BurkertDensityProfile

class profiles.density.BurkertDensityProfile(**kwargs)

Burkert Density Profile.

This profile describes dark matter halos with a flat density core, often used to fit rotation curves of dwarf galaxies [1].

\[\rho(r) = \frac{\rho_0}{\left(1 + \frac{r}{r_s}\right) \left(1 + \left(\frac{r}{r_s}\right)^2\right)}\]

where:

• \(\rho_0\) is the central density.

• \(r_s\) is the scale radius.

Parameters

Parameters for BurkertDensityProfile

Name	Symbol	Description
rho_0	\(\rho_0\)	Central density
r_s	\(r_s\)	Scale radius

Expressions

Expressions for BurkertDensityProfile

Name	Symbol	Notes
ellipsoidal_psi	\(\psi(r) = 2\int_{0}^{r}\!\xi\,\rho(\xi)\,d\xi\)	Inherited from base

References

[1]

A. Burkert. The Structure of Dark Matter Halos in Dwarf Galaxies. \apjl , 447:L25–L28, July 1995. arXiv:astro-ph/9504041, doi:10.1086/309560.

Example

>>> import matplotlib.pyplot as plt
>>> from pisces.profiles.density import (
...     BurkertDensityProfile,
... )

>>> r = np.linspace(0.1, 10, 100)
>>> profile = BurkertDensityProfile(
...     rho_0=1.0, r_s=1.0
... )
>>> rho = profile(r)

>>> _ = plt.loglog(
...     r, rho, "k-", label="Burkert Profile"
... )
>>> _ = plt.xlabel("Radius (r)")
>>> _ = plt.ylabel("Density (rho)")
>>> _ = plt.legend()
>>> plt.show()

(Source code, png, hires.png, pdf)

See also

NFWDensityProfile, CoredNFWDensityProfile, KingDensityProfile

Methods

__init__(**kwargs)	Initialize a profile instance with specific parameter values.
compute_circular_velocity(r[, units, G])	Compute the circular velocity at radius \(r\).
compute_cosmological_overdensity_profile(z, R)	Compute the spherical overdensity profile relative to the critical density at redshift \(z\).
compute_cosmological_overdensity_radius(z, ...)	Find the radius enclosing a target overdensity relative to the critical density at redshift \(z\).
compute_deflection_angle(R[, mode, units, ...])	Compute the gravitational lensing deflection angle at projected radius \(R\).
compute_einstein_radius(z_lens, z_source[, ...])	Compute the Einstein ring angular radius \(\\theta_E\) for a perfectly aligned source-lens system.
compute_enclosed_mass(r[, units])	Numerically compute the enclosed mass \(M(r)\) within radius \(r\).
compute_escape_velocity(r[, units, G])	Compute the escape velocity at radius \(r\).
compute_fractional_mass_radius(rmin, rmax[, ...])	Find the radius enclosing a given fraction of the total mass.
compute_gravitational_field(r[, units, G])	Numerically compute the gravitational field \(g(r)\) at radius \(r\).
compute_gravitational_potential(r[, units, G])	Numerically compute the gravitational potential \(\Phi(r)\).
compute_lensing_convergence(R, z_lens, z_source)	Compute the lensing convergence \(\kappa(R)\) at projected radius \(R\).
compute_surface_density(R[, units])	Numerically compute the projected surface density at radius R from the origin.
compute_total_mass([units])	Numerically compute the total mass of the profile by integrating to infinity.
from_dict(data)	Reconstruct a profile instance from a dictionary.
from_hdf5(h5obj[, name])	Reconstruct a profile from HDF5 attributes.
from_json(filepath)	Reconstruct a profile from a JSON file.
from_yaml(filepath)	Reconstruct a profile from a YAML file.
get_derived_profile(profile_name, **kwargs)	Access and instantiate a derived profile by name.
get_expression_latex([substitute])	Return the LaTeX representation of the profile's symbolic expression.
get_output_units(*argu)	Determine the output units of the operation given some set of input units.
get_parameters_latex()	Return a LaTeX table of the profile parameters.
lambdify_expression(expression)	Convert a symbolic expression into a callable function.
list_derived_profiles()	List all available derived profiles for this instance.
substitute_expression(expression)	Replace symbolic parameters with numerical values in an expression.
to_dict()	Serialize this profile to a minimal dictionary representation.
to_hdf5(h5obj[, name])	Store profile metadata into an HDF5 object as attributes.
to_json(filepath, **kwargs)	Serialize the profile to a JSON file.
to_yaml(filepath, **kwargs)	Serialize the profile to a YAML file.

Attributes

derived_profile_classes	Get the available derived profile classes for this instance.
parameter_symbols	Get the symbolic representations of the coordinate system parameters.
parameters	The parameters of this coordinate system.
variable_symbols	The symbols representing each of the coordinate axes in this coordinate system.
variables	The axes names present in this coordinate system.