ON THE PROBABILITY OF MAJOR-AXIS PRECESSION IN TRIAXIAL ELLIPSOIDAL POTENTIALS

Orbits in triaxial ellipsoidal potentials precess about either the maj or or minor axis of the ellipsoid. In standard perturbation theory, it can be shown that a circular orbit will precess about the minor axis if its angular momentum vector lies in a region bounded by two great c ircles that pass through the intermediate axis, and which are inclined with minimum separation i(T) from the minor axis, where i(T)=arctan[( B2 - C2)/(A2 - B2)]1/2, and A, B and C are the axis ratios, A greater- than-or-equal-to B greater-than-or-equal-to C. We test the accuracy of this formula by performing orbit integrations to determine i(S), the simulated turnover angle corresponding to i(T). We reach two principal conclusions: (i) i(S) is usually greater than i(T), by as much as 12- degrees, even for moderate triaxialities A/1.2 < B < C/0.8. This reduc es the expected frequency of polar rings. (ii) i(S) is not a single, w ell-defined number, but can vary by a few degrees, depending upon the initial phase of the orbit. This means that there is a reasonable prob ability for capture of gas on to orbits that precess about both axes. Interactions can then lead to substantial loss of angular momentum and subsequent infall to the Galactic Centre.