Source code for galpy.potential.TriaxialGaussianPotential

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#   TriaxialGaussianPotential.py: Potential of a triaxial Gaussian stratified
#                                 on similar ellipsoids
#
#                                 \rho(x,y,z) ~ exp(-m^2/[2\sigma^2])
#
#                                 with m^2 = x^2+y^2/b^2+z^2/c^2
#
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import numpy
from scipy import special
from ..util import conversion
from .EllipsoidalPotential import EllipsoidalPotential
[docs]class TriaxialGaussianPotential(EllipsoidalPotential): """Potential of a triaxial Gaussian (`Emsellem et al. 1994 <https://ui.adsabs.harvard.edu/abs/1994A%26A...285..723E/abstract>`__): .. math:: \\rho(x,y,z) = \\frac{\\mathrm{amp}}{(2\\pi\\,\\sigma)^{3/2}\\,b\\,c}\,e^{-\\frac{m^2}{2\\sigma^2}} where :math:`\\mathrm{amp} = GM` is the total mass and :math:`m^2 = x^2+y^2/b^2+z^2/c^2`. """
[docs] def __init__(self,amp=1.,sigma=5.,b=1.,c=1., zvec=None,pa=None,glorder=50, normalize=False,ro=None,vo=None): """ NAME: __init__ PURPOSE: initialize a Gaussian potential INPUT: amp - amplitude to be applied to the potential (default: 1); can be a Quantity with units of mass or Gxmass sigma - Gaussian dispersion scale (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: 2020-08-18 - 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') sigma= conversion.parse_length(sigma,ro=self._ro) self._sigma= sigma self._twosigma2= 2.*self._sigma**2 self._scale= self._sigma # Adjust amp self._amp/= (2.*numpy.pi)**1.5*self._sigma**3.*self._b*self._c 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 -self._twosigma2*numpy.exp(-m**2./self._twosigma2) def _mdens(self,m): """Density as a function of m""" return numpy.exp(-m**2/self._twosigma2) def _mdens_deriv(self,m): """Derivative of the density as a function of m""" return -2.*m*numpy.exp(-m**2/self._twosigma2)/self._twosigma2 def _mass(self,R,z=None,t=0.): """ NAME: _mass PURPOSE: evaluate the mass within R (and z) for this potential; if z=None, integrate to ellipsoidal boundary INPUT: R - Galactocentric cylindrical radius z - vertical height t - time OUTPUT: the mass enclosed HISTORY: 2021-03-09 - Written - Bovy (UofT) """ if not z is None: raise AttributeError # Hack to fall back to general return numpy.pi*self._b*self._c*self._twosigma2*self._sigma\ *(numpy.sqrt(2.*numpy.pi)*special.erf(R/self._sigma/numpy.sqrt(2.)) -2.*R/self._sigma*numpy.exp(-R**2./self._twosigma2))