Source code for galpy.potential.FlattenedPowerPotential

###############################################################################
#   FlattenedPowerPotential.py: Power-law potential that is flattened in the 
#                               potential (NOT the density)
#
#                                     amp
#                          phi(R,z)= --------- ; m^2 = R^2 + z^2/q^2
#                                   m^\alpha
###############################################################################
import numpy
from ..util import conversion
from .Potential import Potential
_CORE=10**-8
[docs]class FlattenedPowerPotential(Potential): """Class that implements a power-law potential that is flattened in the potential (NOT the density) .. math:: \\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 :math:`\\alpha=0` See Figure 1 in `Evans (1994) <http://adsabs.harvard.edu/abs/1994MNRAS.267..333E>`_ for combinations of alpha and q that correspond to positive densities """
[docs] def __init__(self,amp=1.,alpha=0.5,q=0.9,core=_CORE,normalize=False,r1=1., ro=None,vo=None): """ NAME: __init__ PURPOSE: initialize a flattened power-law potential INPUT: amp - amplitude to be applied to the potential (default: 1); can be a Quantity with units of velocity-squared alpha - power q - flattening core - core radius (can be Quantity) r1= (1.) reference radius for amplitude (can be Quantity) normalize - 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=, vo= distance and velocity scales for translation into internal units (default from configuration file) OUTPUT: (none) HISTORY: 2013-01-09 - Written - Bovy (IAS) """ Potential.__init__(self,amp=amp,ro=ro,vo=vo,amp_units='velocity2') core= conversion.parse_length(core,ro=self._ro) r1= conversion.parse_length(r1,ro=self._ro) self.alpha= alpha self.q2= q**2. self.core2= core**2. # Back to old definition self._amp*= r1**self.alpha if normalize or \ (isinstance(normalize,(int,float)) \ and not isinstance(normalize,bool)): #pragma: no cover self.normalize(normalize) self.hasC= True self.hasC_dxdv= True self.hasC_dens= True
def _evaluate(self,R,z,phi=0.,t=0.): """ NAME: _evaluate PURPOSE: evaluate the potential at R,z INPUT: R - Galactocentric cylindrical radius z - vertical height phi - azimuth t - time OUTPUT: Phi(R,z) HISTORY: 2013-01-09 - Started - Bovy (IAS) """ if self.alpha == 0.: return 1./2.*numpy.log(R**2.+z**2./self.q2+self.core2) else: m2= self.core2+R**2.+z**2./self.q2 return -m2**(-self.alpha/2.)/self.alpha def _Rforce(self,R,z,phi=0.,t=0.): """ NAME: _Rforce PURPOSE: evaluate the radial force for this potential INPUT: R - Galactocentric cylindrical radius z - vertical height phi - azimuth t - time OUTPUT: the radial force HISTORY: 2010-07-10 - Written - Bovy (NYU) """ if self.alpha == 0.: return -R/(R**2.+z**2./self.q2+self.core2) else: m2= self.core2+R**2.+z**2./self.q2 return -m2**(-self.alpha/2.-1.)*R def _zforce(self,R,z,phi=0.,t=0.): """ NAME: _zforce PURPOSE: evaluate the vertical force for this potential INPUT: R - Galactocentric cylindrical radius z - vertical height phi - azimuth t - time OUTPUT: the vertical force HISTORY: 2010-07-10 - Written - Bovy (NYU) """ if self.alpha == 0.: return -z/self.q2/(R**2.+z**2./self.q2+self.core2) else: m2= self.core2+R**2.+z**2./self.q2 return -m2**(-self.alpha/2.-1.)*z/self.q2 def _R2deriv(self,R,z,phi=0.,t=0.): """ NAME: _Rderiv PURPOSE: evaluate the second radial derivative for this potential INPUT: R - Galactocentric cylindrical radius z - vertical height phi - azimuth t - time OUTPUT: the second radial derivative HISTORY: 2011-10-09 - Written - Bovy (NYU) """ if self.alpha == 0.: denom= 1./(R**2.+z**2./self.q2+self.core2) return denom-2.*R**2.*denom**2. else: m2= self.core2+R**2.+z**2./self.q2 return -m2**(-self.alpha/2.-1.)*((self.alpha+2)*R**2./m2-1.) def _z2deriv(self,R,z,phi=0.,t=0.): """ NAME: _z2deriv PURPOSE: evaluate the second vertical derivative for this potential INPUT: R - Galactocentric cylindrical radius z - vertical height phi - azimuth t- time OUTPUT: the second vertical derivative HISTORY: 2012-07-26 - Written - Bovy (IAS@MPIA) """ if self.alpha == 0.: denom= 1./(R**2.+z**2./self.q2+self.core2) return denom/self.q2-2.*z**2.*denom**2./self.q2**2. else: m2= self.core2+R**2.+z**2./self.q2 return -1./self.q2*m2**(-self.alpha/2.-1.)*((self.alpha+2)*z**2./m2/self.q2-1.) def _dens(self,R,z,phi=0.,t=0.): """ NAME: _dens PURPOSE: evaluate the density force for this potential INPUT: R - Galactocentric cylindrical radius z - vertical height phi - azimuth t - time OUTPUT: the density HISTORY: 2013-01-09 - Written - Bovy (IAS) """ if self.alpha == 0.: return 1./4./numpy.pi/self.q2*((2.*self.q2+1.)*self.core2+R**2.\ +(2.-1./self.q2)*z**2.)/\ (R**2.+z**2./self.q2+self.core2)**2. else: m2= self.core2+R**2.+z**2./self.q2 return 1./self.q2*(self.core2*(1.+2.*self.q2)+R**2.*(1.-self.alpha*self.q2)+z**2.*(2.-(1.+self.alpha)/self.q2))*m2**(-self.alpha/2.-2.)/4./numpy.pi