  The X-ray binary Her X-1 consists of an accreting neutron star and the
optical component HZ Her. The 35-day X-ray superorbital variability of this
system is known since its discovery in 1972 by the Uhuru satellite and is
believed to be caused by forced precession of a warped accretion disk tilted to
the orbital plane. We argue that the observed features of the 35-day optical
variability of HZ Her can be explained by free precession of the neutron star
with a period close to that of the forced disk. The model parameters include a)
the X-ray luminosity of the neutron star; b) the optical flux from the
accretion disk; c) the tilt of the inner and outer edges of the accretion disk.
A possible synchronization mechanism based on the coupling between the neutron
star free precession and the dynamical action of non-stationary gas streams is
discussed.
