2000AJ....120..110B

We apply the dynamical modeling approach of Statler to 13 elliptical galaxies from the Davies & Birkinshaw sample of radio galaxies to derive constraints on their intrinsic shapes and orientations. We develop an iterative Bayesian algorithm to combine these results to estimate the parent shape distribution from which the sample was drawn, under the assumption that this parent distribution has no preferred orientation. In the process we obtain improved estimates for the shapes of individual objects. The parent shape distribution shows a tendency toward bimodality, with peaks at the oblate and prolate limits. Under minimal assumptions about the galaxies' internal dynamics, 35% of the objects would be strongly triaxial (0.2<T<0.8). However, the parent distribution is sensitive to the assumed orbit populations in the galaxies. Dynamical configurations in which all galaxies rotate purely about either their long or short axes can be ruled out because they would require the sample to have a strong orientation bias. Configurations in which the mean motion about the short or long axis is either ``disklike''–dropping off away from the symmetry planes–or ``spheroid-like''–remaining roughly constant at a given radius–are equally viable. Spheroid-like rotation in the long-axis or short-axis tube orbits significantly lowers the abundance of prolate or oblate galaxies, respectively. If rotation in ellipticals is generally disklike, then triaxiality is rare; if spheroid-like, triaxiality is common.