# Ellipsoidal potentials¶

class galpy.potential.EllipsoidalPotential.EllipsoidalPotential(amp=1.0, b=1.0, c=1.0, zvec=None, pa=None, glorder=50, ro=None, vo=None, amp_units=None)[source]

Base class for potentials corresponding to density profiles that are stratified on ellipsoids:

$\rho(x,y,z) \equiv \rho(m^2)$

where $$m^2 = x^2+y^2/b^2+z^2/c^2$$. Note that $$b$$ and $$c$$ are defined to be the axis ratios (rather than using $$m^2 = x^2/a^2+y^2/b^2+z^2/c^2$$ as is common).

Implement a specific density distribution with this form by inheriting from this class and defining functions _mdens(self,m) (the density as a function of m), _mdens_deriv(self,m) (the derivative of the density as a function of m), and _psi(self,m), which is:

$\psi(m) = -\int_{m^2}^\infty d m^2 \rho(m^2)$

See PerfectEllipsoidPotential for an example and Merritt & Fridman (1996) for the formalism.

__init__(amp=1.0, b=1.0, c=1.0, zvec=None, pa=None, glorder=50, ro=None, vo=None, amp_units=None)[source]

Initialize an ellipsoidal potential.

Parameters:
• amp (float or Quantity, optional) – Amplitude to be applied to the potential (default: 1); can be a Quantity with units that depend on the specific spheroidal potential.

• b (float, optional) – y-to-x axis ratio of the density.

• c (float, optional) – z-to-x axis ratio of the density.

• zvec (numpy.ndarray, optional) – If set, a unit vector that corresponds to the z axis.

• pa (float or Quantity, optional) – If set, the position angle of the x axis (rad or Quantity).

• glorder (int, optional) – If set, compute the relevant force and potential integrals with Gaussian quadrature of this order.

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

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

• amp_units (str, optional) – Type of units that amp should have if it has units (passed to Potential.__init__).

Notes

• 2018-08-06 - Started - Bovy (UofT)