On the observational appearances of a freely precessing neutron star in Hercules X-1

Evidence for neutron star free precession is discussed, which is often presumed to be responsible for the observed 35-day cycle in Hercules X-1. The precise formula for the period derivative due to free precession is obtained under assumption that the precession period is much longer than that of the neutron star rotation. The optical light curves to be seen from the binary, with freely precessing accretion neutron star are simulated numerically. This simulation takes into account the reflection effect on the surface of the secondary component and on the accretion disk itself for different diagrams of x-ray emission.