Arbitrary Eddington-inversion DF

class galpy.df.eddingtondf(pot=None, denspot=None, rmax=10000.0, scale=None, ro=None, vo=None)[source]

Class that implements isotropic spherical DFs computed using the Eddington formula

\[f(\mathcal{E}) = \frac{1}{\sqrt{8}\,\pi^2}\,\left[\int_0^\mathcal{E}\mathrm{d}\Psi\,\frac{1}{\sqrt{\mathcal{E}-\Psi}}\,\frac{\mathrm{d}^2\rho}{\mathrm{d}\Psi^2} +\frac{1}{\sqrt{\mathcal{E}}}\,\frac{\mathrm{d}\rho}{\mathrm{d}\Psi}\Bigg|_{\Psi=0}\right]\,,\]

where \(\Psi = -\Phi+\Phi(\infty)\) is the relative potential, \(\mathcal{E} = \Psi-v^2/2\) is the relative (binding) energy, and \(\rho\) is the density of the tracer population (not necessarily the density corresponding to \(\Psi\) according to the Poisson equation). Note that the second term on the right-hand side is currently assumed to be zero in the code.

__init__(pot=None, denspot=None, rmax=10000.0, scale=None, ro=None, vo=None)[source]

Initialize an isotropic distribution function computed using the Eddington inversion.

Parameters:

  • pot (Potential instance or list thereof) – Represents the gravitational potential (assumed to be spherical).

  • denspot (Potential instance or list thereof, optional) – Represents the density of the tracers (assumed to be spherical; if None, set equal to pot).

  • rmax (float or Quantity, optional) – Maximum radius to consider. DF is cut off at E = Phi(rmax).

  • scale (float or Quantity, optional) – Characteristic scale radius to aid sampling calculations. Optional and will also be overridden by value from pot if available.

  • 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

  • 2021-02-04 - Written - Bovy (UofT)