# 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)