Periodic Orbits in Triaxial Galaxies with Weak Cusps

Abstract

The orbital structure of triaxial models with weak central density cusps, $\ddot{I}\propto r^{-{\hat{I}}^3},gamma<1$, is investigated. The stability of the $x$- (long-) axis orbit -- and hence the existence of box orbits -- depends sensitively on ${\hat{I}}^3$; the range of model shapes for which the $x$-axis orbit is stable becomes progressively smaller as ${\hat{I}}^3$ approaches one. The banana and fish boxlets in the $x-z$ (long axis-short axis) plane are stable over a wide range of model parameters. The boxlets in the $x-y$ and $y-z$ planes are generally vertically unstable.

14 Latex pages, 12 Postscript figures, uses aastex, epsf.sty. Submitted to The Astronomical Journal, May 1997