Constant-anisotropy Power-Law DF

class galpy.df.constantbetaPowerLawdf(pot=None, denspot=None, beta=0, rmax=10000.0, rmin=None, ro=None, vo=None)[source]

Class that implements the anisotropic spherical distribution function with constant \(\beta\) for a power-law tracer density \(\nu(r) = \nu_0\,r^{-\gamma}\) in a power-law potential \(\Phi(r) = -\Psi_0\,r^{2-\alpha}\) generated by \(\rho(r) \propto r^{-\alpha}\) with \(\alpha > 2\), where \(\Psi_0 = -\Phi(1)\) and \(\nu_0 = \nu(1)\).

The distribution function is

\[f(E,L) = L^{-2\beta}\,\frac{\nu_0\,2^\beta\,\Gamma(p+1)}{(2\pi)^{3/2}\,\Gamma(1-\beta)\,\Gamma(p+\beta-\tfrac{1}{2})\,\Psi_0^{p}}\,\mathcal{E}^{p+\beta-3/2}\]

where \(\mathcal{E} = -E \geq 0\) is the relative energy and \(p = (\gamma - 2\beta)/(\alpha - 2)\).

__init__(pot=None, denspot=None, beta=0, rmax=10000.0, rmin=None, ro=None, vo=None)[source]

Initialize a constant-anisotropy power-law distribution function.

Parameters:

  • pot (PowerSphericalPotential) – Power-law potential with alpha > 2.

  • denspot (PowerSphericalPotential, optional) – Power-law potential representing the tracer density. If None, self-consistent (tracer = potential-generating density).

  • beta (float, optional) – Anisotropy parameter. Must be < 1. Default: 0.

  • rmax (float or Quantity, optional) – Maximum radius for sampling. Default: 1e4.

  • rmin (float or Quantity, optional) – Minimum radius. Auto-detected for divergent potentials if not specified.

  • ro (float or Quantity, optional) – Distance scale for translation into internal units (default from configuration file).

  • vo (float or Quantity, optional) – Velocity scale for translation into internal units (default from configuration file).

Notes

  • 2025-03-27 - Written - Bovy (UofT)