On the orbital phase dependence of the turn-on times of Hercules X-1

The present investigation is concerned with the dynamics of tilted accretion disks in binary systems. It is shown that the expected motion of a ring of matter in an accretion disk is more complicated than simple precession at a uniform rate. The motion is found to be better described by a vector normal to the plane of the ring of matter whose tip periodically traces out a small ellipse centered on the tip of a uniformly precessing vector. It is also demonstrated that this 'wobble' can be utilized to explain why the turn-ons of Hercules X-1 preferentially occur around orbital phases 0.2 and 0.7. If an accretion disk in a binary system is tilted with respect to the binary orbital plane, then it must undergo forced precession with the corresponding 'wobble'. This 'wobble' may be, at least, partially responsible for the phase dependence of the distribution of X-ray turn-on times of Hercules X-1.