Resonant capture, counter-rotating disks, and polar rings

We suggest that polar rings and/or counter-rotating disks in flattened galaxies can be formed from stars captured at the Binney resonance, where the rate of precession of the angular momentum vector of a disk star equals the pattern speed of a triaxial halo. If the halo pattern speed is initially retrograde and slowly decays to zero, stars can be trapped as the Binney resonance sweeps past them, and levitated into polar orbits. If the halo pattern speed is initially retrograde and slowly changes to prograde, trapped stars can evolve from prograde to retrograde disk orbits. The stellar components of polar rings formed by this process should consist of two equal, counter-rotating star streams.