The stability of "perfect elliptic disks." II. A minimal streaming case

Two-dimensional realizations of self-consistent models for the "perfect ell iptic disks" were tested for global stability by gravitational N-body integ ration. The family, of perfect elliptic disk potentials have two isolating integrals; time-independent distribution functions f(E, I-2), which self-co nsistently reproduce the density distribution, can be found numerically, us ing a modified marching scheme to compute the relative contributions of eac h member in a library of orbits. The possible solutions are not unique; for a given ellipticity, the models can have a range of angular momenta. Here results are presented for cases with minimal angular momentum, hence maxima l random motion. As in previous work, N-body realizations were constructed using a modified quiet start technique to place particles on these orbits u niformly in action-angle space, making the initial conditions as smooth as possible. The most elliptical models initially showed bending instabilities ; by the end of the run they had become slightly rounder. The most nearly a xisymmetric models tended to become more elongated, reminiscent of the radi al orbit instability in spherical systems. Between these extremes, there is a range of axial ratios 0.305 less than or similar to b/a less than or sim ilar to 0.570 for which the minimum streaming models appear to be stable.