Source code for galpy.potential.MiyamotoNagaiPotential

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#   MiyamotoNagaiPotential.py: class that implements the Miyamoto-Nagai 
#                              potential
#                                                           GM
#                              phi(R,z) = -  ---------------------------------
#                                             \sqrt(R^2+(a+\sqrt(z^2+b^2))^2)
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import numpy
from .Potential import Potential, kms_to_kpcGyrDecorator, _APY_LOADED
if _APY_LOADED:
    from astropy import units
[docs]class MiyamotoNagaiPotential(Potential): """Class that implements the Miyamoto-Nagai potential .. math:: \\Phi(R,z) = -\\frac{\\mathrm{amp}}{\\sqrt{R^2+(a+\\sqrt{z^2+b^2})^2}} with :math:`\\mathrm{amp} = GM` the total mass. """
[docs] def __init__(self,amp=1.,a=1.,b=0.1,normalize=False, ro=None,vo=None): """ NAME: __init__ PURPOSE: initialize a Miyamoto-Nagai potential INPUT: amp - amplitude to be applied to the potential, the total mass (default: 1); can be a Quantity with units of mass or Gxmass a - scale length (can be Quantity) b - scale height (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: 2010-07-09 - Started - Bovy (NYU) """ 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 if _APY_LOADED and isinstance(b,units.Quantity): b= b.to(units.kpc).value/self._ro self._a= a self._scale= self._a self._b= b self._b2= self._b**2. if normalize or \ (isinstance(normalize,(int,float)) \ and not isinstance(normalize,bool)): self.normalize(normalize) self.hasC= True self.hasC_dxdv= True self.hasC_dens= True self._nemo_accname= 'MiyamotoNagai'
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: 2010-07-09 - Started - Bovy (NYU) """ return -1./numpy.sqrt(R**2.+(self._a+numpy.sqrt(z**2.+self._b2))**2.) 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: 2010-07-09 - Written - Bovy (NYU) """ return -R/(R**2.+(self._a+numpy.sqrt(z**2.+self._b2))**2.)**(3./2.) 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: 2010-07-09 - Written - Bovy (NYU) """ sqrtbz= numpy.sqrt(self._b2+z**2.) asqrtbz= self._a+sqrtbz if isinstance(R,float) and sqrtbz == asqrtbz: return (-z/ (R**2.+(self._a+numpy.sqrt(z**2.+self._b2))**2.)**(3./2.)) else: return (-z*asqrtbz/sqrtbz/ (R**2.+(self._a+numpy.sqrt(z**2.+self._b2))**2.)**(3./2.)) 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: 2010-08-08 - Written - Bovy (NYU) """ sqrtbz= numpy.sqrt(self._b2+z**2.) asqrtbz= self._a+sqrtbz if isinstance(R,float) and sqrtbz == asqrtbz: return 3./\ (R**2.+sqrtbz**2.)**2.5/4./numpy.pi*self._b2 else: return (self._a*R**2.+(self._a+3.*sqrtbz)*asqrtbz**2.)/\ (R**2.+asqrtbz**2.)**2.5/sqrtbz**3./4./numpy.pi*self._b2 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) """ return 1./(R**2.+(self._a+numpy.sqrt(z**2.+self._b2))**2.)**1.5 \ -3.*R**2./(R**2.+(self._a+numpy.sqrt(z**2.+self._b2))**2.)**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: 2012-07-25 - Written - Bovy (IAS@MPIA) """ sqrtbz= numpy.sqrt(self._b2+z**2.) asqrtbz= self._a+sqrtbz if isinstance(R,float) and sqrtbz == asqrtbz: return (self._b2+R**2.-2.*z**2.)*(self._b2+R**2.+z**2.)**-2.5 else: return ((self._a**3.*self._b2 + self._a**2.*(3.*self._b2 - 2.* z**2.) *numpy.sqrt(self._b2 + z**2.) + (self._b2 + R**2. - 2.*z**2.)*(self._b2 + z**2.)**1.5 +self._a* (3.*self._b2**2. - 4.*z**4. + self._b2*(R**2. - z**2.)))/ ((self._b2 + z**2.)**1.5* (R**2. + asqrtbz**2.)**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: 2013-08-28 - Written - Bovy (IAS) """ sqrtbz= numpy.sqrt(self._b2+z**2.) asqrtbz= self._a+sqrtbz if isinstance(R,float) and sqrtbz == asqrtbz: return -(3.*R*z/(R**2.+asqrtbz**2.)**2.5) else: return -(3.*R*z*asqrtbz /sqrtbz/(R**2.+asqrtbz**2.)**2.5) @kms_to_kpcGyrDecorator def _nemo_accpars(self,vo,ro): """ NAME: _nemo_accpars PURPOSE: return the accpars potential parameters for use of this potential with NEMO INPUT: vo - velocity unit in km/s ro - length unit in kpc OUTPUT: accpars string HISTORY: 2014-12-18 - Written - Bovy (IAS) """ ampl= self._amp*vo**2.*ro return "0,%s,%s,%s" % (ampl,self._a*ro,self._b*ro)