Oblate Staeckel wrapper potential

class galpy.potential.OblateStaeckelWrapperPotential(*args, **kwargs)

Potential wrapper class that approximates a given axisymmetric potential as an oblate Staeckel potential by defining (see Binney 2012; Bovy 2026)

\begin{align} U(u) & = \cosh^2 u \,\Phi\left(u,{\pi\over 2}\right)\,,\\ V(v) & = \cosh^2 u_0 \,\Phi\left(u_0,{\pi\over 2}\right)-\left(\sinh^2 u_0+\sin^2 v\right)\,\Phi\left(u_0,v\right)\,. \end{align}

in the prolate spheroidal coordinate system defined by the focal length \(\Delta\). Here \(u_0\) is a reference value of \(u\) at which the potential is split. The potential is then given by

\begin{align} \Phi(u,v) & = {U(u)-V(v)\over \sinh^2 u + \sin^2 v}\,. \end{align}

__init__(amp=1.0, pot=None, delta=0.5, u0=0.0, ro=None, vo=None)

Initialize an OblateStaeckelWrapper Potential.

Parameters:

• amp (float, optional) – Amplitude to be applied to the potential. Default is 1.0.

• pot (Potential or a combined potential formed using addition (pot1+pot2+…)) – Potential instance or a combined potential formed using addition (pot1+pot2+…); this potential is made into an oblate Staeckel potential.

• delta (float or Quantity, optional) – The focal length. Default is 0.5.

• u0 (float or tuple or tuple of Quantity) – Reference u value; if a tuple is given, this is assumed to be a (R,z) value to be converted to u.

• 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

• 2017-12-15 - Started - Bovy (UofT)