Annu. Rev. Astron. Astrophys. 1991. 29: 239-274 Copyright © 1991 by Annual Reviews. All rights reserved

2.5 Figure Rotation

Relatively little work has been done on the construction of triaxial galaxy models with figure rotation. A few special analytic models exist, but these do not have realistic density profiles (127, 128, 129, 160, 161, 345, 346, 347, 350).

As is well-known from the study of flat barred galaxy models (e.g., 65, 151, 274, 316, 327), figure rotation has significant consequences for the orbital structure (42). The available three-dimensional studies have concentrated mostly on tumbling around the short axis (37, 79, 154, 223, 225, 227, 257, 258, 273). For slow tumbling rates most orbits are regular. However, the directional non-uniqueness of stationary triaxial systems (Section 2.2.2) disappears in models with a rotating figure. The Coriolis force distinguishes between the clockwise and counterclockwise branch of an orbit, so that these have different shapes. Box orbits acquire a net angular momentum around the rotation axis (356), while long-axis tubes tip out of the plane containing the intermediate and short axis, with the two branches tipping in opposite directions, so that they have non-zero angular momentum about both the long and the short axis (306).

Schwarzschild was able to reproduce the density distribution of a slowly tumbling triaxial mass model with different combinations of orbits, thus establishing the non-uniqueness of such equilibrium models (306). This is not surprising, as there now are no less than seven different major orbit families (boxes, and three pairs of tubes). In order to obtain a symmetric figure, Schwarzschild had to populate the two branches of the two families of long-axis tubes in equal numbers, so that the total angular momentum points along the short axis. Conversely, this result implies that net streaming around the long axis is expected to give measurable asymmetries (intrinsic twists) if the figure is rotating. This may provide a way to put an upper limit on the figure rotation of long-axis rotators (Section 3.4.1).

Rotating models have been produced also by N-body simulations (371). Van Albada (341) took the non-rotating triaxial endproduct of a simulation, applied a torque on the individual particles for a finite period of time, and found that he could generate stationary models with internal streaming, or tumbling models with internal streaming always in the direction of the tumbling. It seems likely, however, that a larger variety of internal dynamics is possible. In the inner regions of the few self-consistent rotating models that have been constructed by Schwarzschild's method (306, 354), the mean streaming motions are retrograde in a corotating frame. Under favorable circumstances an external, stationary, observer may measure retrograde streaming, but only in the inner few core radii (355). Such counterrotation has been observed in a number of elliptical galaxies (Section 3.3.1).