# Logarithmic halo potential¶

class galpy.potential.LogarithmicHaloPotential(amp=1.0, core=1e-08, q=1.0, b=None, normalize=False, ro=None, vo=None)[source]

Class that implements the logarithmic potential

$\Phi(R,z) = \frac{\mathrm{amp}}{2}\,\ln\left[R^2+\left(\frac{z}{q}\right)^2+\mathrm{core}^2\right]$

Alternatively, the potential can be made triaxial by adding a parameter $$b$$

$\Phi(x,y,z) = \frac{\mathrm{amp}}{2}\,\ln\left[x^2+\left(\frac{y}{b}\right)^2+\left(\frac{z}{q}\right)^2+\mathrm{core}^2\right]$

With these definitions, $$\sqrt{\mathrm{amp}}$$ is the circular velocity at $$r \gg \mathrm{core}$$ at $$(y,z) = (0,0)$$.

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

Initialize a logarithmic potential.

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

• core (float or Quantity, optional) – Core radius at which the logarithm is cut.

• q (float) – Potential flattening (z/q)**2.

• b (float, optional) – Shape parameter in y-direction (y –> y/b; see definition).

• 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.

• 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).

Notes

• 2010-04-02 - Started - Bovy (NYU)