###############################################################################
# KuzminDiskPotential.py: class that implements Kuzmin disk potential
#
# - amp
# Phi(R, z)= ---------------------------
# \sqrt{R^2 + (a + |z|)^2}
###############################################################################
import numpy
from .Potential import Potential, _APY_LOADED
if _APY_LOADED:
from astropy import units
[docs]class KuzminDiskPotential(Potential):
"""Class that implements the Kuzmin Disk potential
.. math::
\\Phi(R,z) = -\\frac{\\mathrm{amp}}{\\sqrt{R^2 + (a + |z|)^2}}
with :math:`\\mathrm{amp} = GM` the total mass.
"""
[docs] def __init__(self, amp=1., a=1. ,normalize=False, ro=None,vo=None):
"""
NAME:
__init__
PURPOSE:
initialize a Kuzmin disk Potential
INPUT:
amp - amplitude to be applied to the potential, the total mass (default: 1); can be a Quantity with units of mass density or Gxmass density
a - scale length (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:
KuzminDiskPotential object
HISTORY:
2016-05-09 - Written - Aladdin
"""
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._a = a ## a must be greater or equal to 0.
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)):
self.normalize(normalize)
self.hasC = True
self.hasC_dxdv= True
return None
def _evaluate(self,R,z,phi=0.,t=0.):
"""
NAME:
_evaluate
PURPOSE:
evaluate the potential at (R,z)
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
potential at (R,z)
HISTORY:
2016-05-09 - Written - Aladdin
"""
return -self._denom(R, z)**-0.5
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 = -dphi/dR
HISTORY:
2016-05-09 - Written - Aladdin
"""
return -self._denom(R, z)**-1.5 * R
def _zforce(self, R, z, phi=0., t=0.):
"""
NAME:
_zforce
PURPOSE:
evaluate the vertical force for this potential
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
the vertical force = -dphi/dz
HISTORY:
2016-05-09 - Written - Aladdin
"""
return -numpy.sign(z) * self._denom(R,z)**-1.5 * (self._a + numpy.fabs(z))
def _R2deriv(self,R,z,phi=0.,t=0.):
"""
NAME:
_Rforce
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:
2016-05-13 - Written - Aladdin
"""
return self._denom(R, z)**-1.5 - 3.*R**2 * self._denom(R, z)**-2.5
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:
2016-05-13 - Written - Aladdin
"""
a = self._a
return self._denom(R, z)**-1.5 - 3. * (a + numpy.fabs(z))**2. * self._denom(R, z)**-2.5
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:
2016-05-13 - Written - Aladdin
"""
return -3 * numpy.sign(z) * R * (self._a + numpy.fabs(z)) *self._denom(R, z)**-2.5
def _surfdens(self,R,z,phi=0.,t=0.):
"""
NAME:
_surfdens
PURPOSE:
evaluate the surface density
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
Sigma (R,z)
HISTORY:
2018-08-19 - Written - Bovy (UofT)
"""
return self._a*(R**2+self._a**2)**-1.5/2./numpy.pi
def _denom(self, R, z):
"""
NAME:
_denom
PURPOSE:
evaluate R^2 + (a + |z|)^2 which is used in the denominator
of most equations
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
OUTPUT:
R^2 + (a + |z|)^2
HISTORY:
2016-05-09 - Written - Aladdin
"""
return (R**2. + (self._a + numpy.fabs(z))**2.)