Resonance in forced oscillations of an accretion disk and kilohertz quasi-periodic oscillations

We have performed numerical simulations of a radially perturbed "accretion" torus around a black hole or neutron star and find that the torus performs radial and vertical motions at the appropriate epicyclic frequencies. We find clear evidence that vertical motions are excited in a nonlinear resonance when the applied perturbation is periodic in time. The strongest resonant response occurs when the frequency difference of the two oscillations is equal to one-half the forcing frequency, precisely as recently observed in the accreting pulsar SAX J1808.4 - 3658, where the observed kilohertz quasi-periodic oscillation peak separation is half the spin frequency of 401 Hz.