# Double power-law density triaxial potential¶

class galpy.potential.TwoPowerTriaxialPotential(amp=1.0, a=5.0, alpha=1.5, beta=3.5, b=1.0, c=1.0, zvec=None, pa=None, glorder=50, normalize=False, ro=None, vo=None)[source]

Class that implements triaxial potentials that are derived from two-power density models

$\rho(x,y,z) = \frac{\mathrm{amp}}{4\,\pi\,a^3}\,\frac{1}{(m/a)^\alpha\,(1+m/a)^{\beta-\alpha}}$

with

$m^2 = x'^2 + \frac{y'^2}{b^2}+\frac{z'^2}{c^2}$

and $$(x',y',z')$$ is a rotated frame wrt $$(x,y,z)$$ specified by parameters zvec and pa which specify (a) zvec: the location of the $$z'$$ axis in the $$(x,y,z)$$ frame and (b) pa: the position angle of the $$x'$$ axis wrt the $$\tilde{x}$$ axis, that is, the $$x$$ axis after rotating to zvec.

Note that this general class of potentials does not automatically revert to the special TriaxialNFWPotential, TriaxialHernquistPotential, or TriaxialJaffePotential when using their (alpha,beta) values (like TwoPowerSphericalPotential).

__init__(amp=1.0, a=5.0, alpha=1.5, beta=3.5, b=1.0, c=1.0, zvec=None, pa=None, glorder=50, normalize=False, ro=None, vo=None)[source]

Initialize a triaxial two-power-density potential.

Parameters:
• amp (float or Quantity, optional) – Amplitude to be applied to the potential (default: 1); can be a Quantity with units of mass or Gxmass.

• a (float or Quantity, optional) – Scale radius.

• alpha (float, optional) – Inner power (0 <= alpha < 3).

• beta (float, optional) – Outer power ( beta > 2).

• 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.

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

• 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 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

• 2016-05-30 - Started - Bovy (UofT)

• 2018-08-07 - Re-written using the general EllipsoidalPotential class - Bovy (UofT)