The 35-day cycle in the X-ray binary HZ Her/Her X-1

We present the results of modelling the 35-day superorbital changes in the B and V lightcurves and X-ray flux of HZ Her/Her X-1. The model is implemented in a computer program written in the C programming language, with a module for parameter optimisation written in Python. The model includes a tilted precessing and warped accretion disc around a freely precessing neutron star. The disc is warped near its inner edge due to interaction with the rotating neutron star magnetosphere. The magnetic torque depends on the precessional phase of the neutron star. The neutron star X-ray emission flux also depends on the free precession phase, which modulates the X-ray illumination of the optical star's atmosphere and the intensity of gas streams. We demonstrate that this model is able to reproduce both the optical observations of HZ Her and the behaviour of the system's 35-day X-ray cycle.