Source code for galpy.potential.PowerTriaxialPotential

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#   PowerTriaxialPotential: Potential of a triaxial power-law
#
#                                        amp
#                          rho(x,y,z)= ---------
#                                       m^\alpha
#
#                                 with m^2 = x^2+y^2/b^2+z^2/c^2
#
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import numpy
from ..util import conversion
from .EllipsoidalPotential import EllipsoidalPotential
[docs]class PowerTriaxialPotential(EllipsoidalPotential): """Class that implements triaxial potentials that are derived from power-law density models (including an elliptical power law) .. math:: \\rho(r) = \\frac{\\mathrm{amp}}{r_1^3}\\,\\left(\\frac{r_1}{m}\\right)^{\\alpha} where :math:`m^2 = x^2+y^2/b^2+z^2/c^2`. """
[docs] def __init__(self,amp=1.,alpha=1.,r1=1.,b=1.,c=1., zvec=None,pa=None,glorder=50, normalize=False,ro=None,vo=None): """ NAME: __init__ PURPOSE: initialize a triaxial power-law potential INPUT: amp - amplitude to be applied to the potential (default: 1); can be a Quantity with units of mass or Gxmass alpha - power-law exponent r1= (1.) reference radius for amplitude (can be Quantity) b - y-to-x axis ratio of the density c - z-to-x axis ratio of the density zvec= (None) If set, a unit vector that corresponds to the z axis pa= (None) If set, the position angle of the x axis (rad or Quantity) glorder= (50) if set, compute the relevant force and potential integrals with Gaussian quadrature of this order ro=, vo= distance and velocity scales for translation into internal units (default from configuration file) OUTPUT: (none) HISTORY: 2021-05-07 - Started - Bovy (UofT) """ EllipsoidalPotential.__init__(self,amp=amp,b=b,c=c, zvec=zvec,pa=pa,glorder=glorder, ro=ro,vo=vo,amp_units='mass') r1= conversion.parse_length(r1,ro=self._ro) self.alpha= alpha # Back to old definition if self.alpha != 3.: self._amp*= r1**(self.alpha-3.)*4.*numpy.pi/(3.-self.alpha) # Multiply in constants self._amp*= (3.-self.alpha)/4./numpy.pi if normalize or \ (isinstance(normalize,(int,float)) \ and not isinstance(normalize,bool)): #pragma: no cover self.normalize(normalize) self.hasC= not self._glorder is None self.hasC_dxdv= False self.hasC_dens= self.hasC # works if mdens is defined, necessary for hasC return None
def _psi(self,m): """\psi(m) = -\int_m^\infty d m^2 \rho(m^2)""" return 2./(2.-self.alpha)*m**(2.-self.alpha) def _mdens(self,m): """Density as a function of m""" return m**-self.alpha def _mdens_deriv(self,m): """Derivative of the density as a function of m""" return -self.alpha*m**-(1.+self.alpha)