Streamlines of the Mean Stellar Motions in Elliptical Galaxies
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**Session 51 -- Galaxies**
*Oral presentation, Thursday, June 15, 1995, 10:00am - 11:30am*

## [51.04] Streamlines of the Mean Stellar Motions in Elliptical Galaxies

*R. F. Anderson, T. S. Statler (U. of North Carolina)*

The stellar velocity fields of elliptical galaxies are important diagnostics
of their intrinsic shapes, which in turn hold clues to their origin and
evolution. The construction of dynamical velocity field models is a complex
task, but is greatly simplified if one has a geometrical approximation for
the streamlines of the mean stellar motions. In the special class of
St\"ackel potentials, a single confocal ellipsoidal coordinate system
gives a set of streamlines that precisely fit the mean motions of all orbits
in a given potential. Unfortunately, the St\"ackel potentials are not
realistic models for ellipticals; but confocal streamlines may nonetheless
be a valid approximation for the mean motions in realistic triaxial systems.
Here we test this conjecture, by fitting confocal streamlines to the mean
velocities of individual orbits in realistic potentials.

We numerically integrate orbits in Schwarzschild's (1993)
logarithmic potential and find the average velocity vector in each of
$\sim 2000$ spatial cells. Integrations are performed over
typically $\sim 50000$ orbital periods in each case. Six sets of axis ratios
are used; in each, $\sim 50$ orbits, comprising short-axis and
long-axis tubes, as well as the circulating resonant families, are integrated.
Confocal streamlines are compared to the orbital velocity vectors by
finding the RMS magnitude of the cross product between the
true velocity and streamline unit vectors. Minimizing this quantity yields
a best fit confocal system for each orbit. Initial results for non-rotating
potentials indicate that the parameters of the fitted coordinate system do
not vary much among different orbits in the same potential; thus confocal
streamlines will be a good approximation to the total mean velocity field.
Results for rotating potentials will also be presented.

\noindent
REFERENCE

\noindent
Schwarzschild, M. 1993, ApJ, 409, 563.

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