Modeling of 35-day superorbital cycle of $B$ and $V$ light curves of IMXB HZ Her/Her X-1

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.