Source code for galpy.potential.PseudoIsothermalPotential

###############################################################################
#   PseudoIsothermalPotential.py: class that implements the pseudo-isothermal
#                                 halo potential
###############################################################################
import numpy
from .Potential import Potential, _APY_LOADED
if _APY_LOADED:
    from astropy import units
[docs]class PseudoIsothermalPotential(Potential): """Class that implements the pseudo-isothermal potential .. math:: \\rho(r) = \\frac{\\mathrm{amp}}{4\\,\pi\\, a^3}\\,\\frac{1}{1+(r/a)^2} """
[docs] def __init__(self,amp=1.,a=1.,normalize=False, ro=None,vo=None): """ NAME: __init__ PURPOSE: initialize a pseudo-isothermal potential INPUT: amp - amplitude to be applied to the potential (default: 1); can be a Quantity with units of mass or Gxmass a - core radius (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: 2015-12-04 - Started - Bovy (UofT) """ Potential.__init__(self,amp=amp,ro=ro,vo=vo,amp_units='mass') if _APY_LOADED and isinstance(a,units.Quantity): a= a.to(units.kpc).value/self._ro self.hasC= True self.hasC_dxdv= True self.hasC_dens= True self._a= a self._a2= a**2. self._a3= a**3. if normalize or \ (isinstance(normalize,(int,float)) \ and not isinstance(normalize,bool)): #pragma: no cover self.normalize(normalize) return None
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: 2015-12-04 - Started - Bovy (UofT) """ r2= R**2.+z**2. r= numpy.sqrt(r2) return (0.5*numpy.log(1+r2/self._a2)\ +self._a/r*numpy.arctan(r/self._a))/self._a 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: 2015-12-04 - Started - Bovy (UofT) """ r2= R**2.+z**2. r= numpy.sqrt(r2) return -(1./r-self._a/r2*numpy.arctan(r/self._a))/self._a*R/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: 2015-12-04 - Started - Bovy (UofT) """ r2= R**2.+z**2. r= numpy.sqrt(r2) return -(1./r-self._a/r2*numpy.arctan(r/self._a))/self._a*z/r def _dens(self,R,z,phi=0.,t=0.): """ NAME: _dens PURPOSE: evaluate the density for this potential INPUT: R - Galactocentric cylindrical radius z - vertical height phi - azimuth t - time OUTPUT: the density HISTORY: 2015-12-04 - Started - Bovy (UofT) """ return 1./(1.+(R**2.+z**2.)/self._a2)/4./numpy.pi/self._a3 def _R2deriv(self,R,z,phi=0.,t=0.): """ NAME: _R2deriv 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 (IAS) """ r2= R**2.+z**2. r= numpy.sqrt(r2) return (1./r2*(1.-R**2./r2*(3.*self._a2+2.*r2)/(self._a2+r2))\ +self._a/r2/r*(3.*R**2./r2-1.)*numpy.arctan(r/self._a))\ /self._a 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: 2012-07-25 - Written - Bovy (IAS@MPIA) """ r2= R**2.+z**2. r= numpy.sqrt(r2) return (1./r2*(1.-z**2./r2*(3.*self._a2+2.*r2)/(self._a2+r2))\ +self._a/r2/r*(3.*z**2./r2-1.)*numpy.arctan(r/self._a))\ /self._a def _Rzderiv(self,R,z,phi=0.,t=0.): """ NAME: _Rzderiv PURPOSE: evaluate the mixed R,z derivative for this potential INPUT: R - Galactocentric cylindrical radius z - vertical height phi - azimuth t - time OUTPUT: d2Phi/dR/dz HISTORY: 2013-08-28 - Written - Bovy (IAS) """ r2= R**2.+z**2. r= numpy.sqrt(r2) return (3.*self._a/r2/r2*numpy.arctan(r/self._a)\ -1./r2/r*((3.*self._a2+2.*r2)/(r2+self._a2)))*R*z/r\ /self._a