# Flattened Power-law potential¶

Flattening is in the potential as in Evans (1994) rather than in the density

class galpy.potential.FlattenedPowerPotential(amp=1.0, alpha=0.5, q=0.9, core=1e-08, normalize=False, r1=1.0, ro=None, vo=None)[source]

Class that implements a power-law potential that is flattened in the potential (NOT the density)

$\Phi(R,z) = -\frac{\mathrm{amp}\,r_1^\alpha}{\alpha\,\left(R^2+(z/q)^2+\mathrm{core}^2\right)^{\alpha/2}}$

and the same as LogarithmicHaloPotential for $$\alpha=0$$

See Figure 1 in Evans (1994) for combinations of alpha and q that correspond to positive densities

__init__(amp=1.0, alpha=0.5, q=0.9, core=1e-08, normalize=False, r1=1.0, ro=None, vo=None)[source]

Initialize a flattened power-law potential.

Parameters:
• amp (float or Quantity, optional) – Amplitude to be applied to the potential. Can be a Quantity with units of velocity squared.

• alpha (float, optional) – Power-law exponent.

• q (float, optional) – Flattening parameter.

• core (float or Quantity, optional) – Core radius.

• normalize (bool or float, optional) – If True, normalize such that vc(1.,0.)=1., or, if given as a number, such that the force is this fraction of the force necessary to make vc(1.,0.)=1.

• r1 (float or Quantity, optional) – Reference radius for amplitude.

• 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

• 2013-01-09 - Written - Bovy (IAS)