Source code for galpy.df.isotropicHernquistdf
# Class that implements isotropic spherical Hernquist DF
# computed using the Eddington formula
import numpy
from ..util import conversion
from ..potential import evaluatePotentials,HernquistPotential
from .sphericaldf import isotropicsphericaldf
[docs]class isotropicHernquistdf(isotropicsphericaldf):
"""Class that implements isotropic spherical Hernquist DF computed using the Eddington formula"""
[docs] def __init__(self,pot=None,ro=None,vo=None):
"""
NAME:
__init__
PURPOSE:
Initialize an isotropic Hernquist distribution function
INPUT:
pot= (None) Hernquist Potential instance
ro=, vo= galpy unit parameters
OUTPUT:
None
HISTORY:
2020-08-09 - Written - Lane (UofT)
"""
assert isinstance(pot,HernquistPotential),'pot= must be potential.HernquistPotential'
isotropicsphericaldf.__init__(self,pot=pot,ro=ro,vo=vo)
self._psi0= -evaluatePotentials(self._pot,0,0,use_physical=False)
self._GMa = self._psi0*self._pot.a**2.
# first factor = mass to make the DF that of mass density
self._fEnorm= self._psi0*self._pot.a\
/numpy.sqrt(2.)/(2*numpy.pi)**3/self._GMa**1.5
def fE(self,E):
"""
NAME:
fE
PURPOSE
Calculate the energy portion of an isotropic Hernquist distribution function
INPUT:
E - The energy (can be Quantity)
OUTPUT:
fE - The value of the energy portion of the DF
HISTORY:
2020-08-09 - Written - James Lane (UofT)
"""
Etilde= -conversion.parse_energy(E,vo=self._vo)/self._psi0
# Handle E out of bounds
Etilde_out = numpy.where(numpy.logical_or(Etilde<0,Etilde>1))[0]
if len(Etilde_out)>0:
# Set to dummy and 0 later, prevents functions throwing errors?
Etilde[Etilde_out]=0.5
sqrtEtilde= numpy.sqrt(Etilde)
fE= self._fEnorm*sqrtEtilde/(1-Etilde)**2.\
*((1.-2.*Etilde)*(8.*Etilde**2.-8.*Etilde-3.)\
+((3.*numpy.arcsin(sqrtEtilde))\
/numpy.sqrt(Etilde*(1.-Etilde))))
# Fix out of bounds values
if len(Etilde_out) > 0:
fE[Etilde_out] = 0
return fE
def _icmf(self,ms):
'''Analytic expression for the normalized inverse cumulative mass
function. The argument ms is normalized mass fraction [0,1]'''
return self._pot.a*numpy.sqrt(ms)/(1-numpy.sqrt(ms))