Interpolated spherical potential¶
The interpSphericalPotential
class provides a general interface to
generate interpolated instances of spherical potentials or lists of
such potentials. This interpolated potential can be used in any
function where other threedimensional galpy potentials can be
used. This includes functions that use C
to speed up
calculations.
The interpSphericalPotential
interpolates the radial force of a
spherical potential and determines the potential and its second
derivative from the base radialforce interpolation object. To set up
an interpSphericalPotential
instance, either provide it with a
function that returns the radial force and the grid to interpolate it
on, as for example,
>>> from galpy import potential
>>> ip= potential.interpSphericalPotential(rforce=lambda r: 1./r,
rgrid=numpy.geomspace(0.01,20,101),Phi0=0.)
which sets up an interpSphericalPotential
instance that has the
same radial force as the spherical LogarithmicHaloPotential
. If
you have a function that gives the enclosed mass within a given
radius, simply pass it divided by \(r^2\) to set up a
interpSphericalPotential
instance for this enclosedmass profile.
Alternatively, you can specify a galpy
potential or list of
potentials and (again) the radial interpolation grid, as for example,
>>> lp= LogarithmicHaloPotential(normalize=1.)
>>> ip= potential.interpSphericalPotential(rforce=lp,
rgrid=numpy.geomspace(0.01,20,101))
Note that, because the potential is defined through integration of the
(negative) radial force, we need to specify the potential at the
smallest grid point, which is done through the Phi0=
keyword in
the first example. When using a galpy
potential (or list), this
value is automatically determined.
Also note that the density of the potential is assumed to be zero outside of the final radial grid point. That is, the potential outside of the final grid point is \(GM/r\) where \(M\) is the mass within the final grid point. If during an orbit integration, the orbit strays outside of the interpolation grid, a warning is issued.
Warning
The density of a interpSphericalPotential
instance is assumed to be zero outside of the largest radial grid point.

class
galpy.potential.
interpSphericalPotential
(self, rforce=None, rgrid=numpy.geomspace(0.01, 20, 101), Phi0=None, ro=None, vo=None)[source]¶ Class that interpolates a spherical potential on a grid

__init__
(self, rforce=None, rgrid=numpy.geomspace(0.01, 20, 101), Phi0=None, ro=None, vo=None)[source]¶ NAME:
__init__PURPOSE:
initialize an interpolated, spherical potentialINPUT:
rforce= (None) Either a) function that gives the radial force as a function of r or b) a galpy Potential instance or list thereof
rgrid= (numpy.geomspace(0.01,20,101)) radial grid on which to evaluate the potential for interpolation (note that beyond rgrid[1], the potential is extrapolated as GM(<rgrid[1])/r)
Phi0= (0.) value of the potential at rgrid[0] (only necessary when rforce is a function, for galpy potentials automatically determined)
ro=, vo= distance and velocity scales for translation into internal units (default from configuration file)
OUTPUT:
(none)HISTORY:
20200713  Written  Bovy (UofT)
