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.

In this work are presented the results of modelling of 35 d superorbital changes of B and V lightcurves and X-ray flux of HZ Her/Her X-1. The model implemented in the new code written in C programming language, with 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 X-ray emission flux from the neutron star also depends on the free precession phase which modulates the X-ray illumination of the optical star atmosphere and the intensity of gas streams. We demonstrate that this model is able to well reproduce both optical observations of HZ Her and the behaviour of the 35-day X-ray cycle.

Nikolay Shakura∗1,2, Dmitry Kolesnikov1, Konstantin Postnov1,2, Igor Volkov1,3, Ilfan Bikmaev2, Tatiana Irsmambetova1, Rüdiger Staubert4, Joern Wilms5, Eldar Irtuganov2, Pavel Shurygin2, Polina Golysheva1, Sergey Shugarov1,6, Igor Nikolenko3, Eugene Trunkovsky1, Gabriele Schönherr8, Axel Schwope8, Dmitry Klochkov4 1Sternberg Astronomical Institute, Moscow State University, 119234, Moscow, Russia 2Kazan Federal University, Kazan, Russia 3Institute of Astronomy RAS, Moscow, Russia 4Institute for Astronomy and Astrophysics, Tubingen, Germany, 5Astronomical Institute of the University of Erlangen-Nuremberg, Bamberg, Germany, 6Astronomical Institute of the Slovak Academy of Scienses, Tatranska Lomnica, Slovakia 7Crimean Astrophysical Observatory, Nauchny, Russia 8Leibniz Institute for Astrophysics, Potsdam, Germany E-mail: nikolai.shakura@gmail.com, kolesnikovkda@gmail.com

Accretion onto magnetized neutron stars is considered using as a case study long-term X-ray and optical observations of HZ Her/Her X-1, an X-ray binary system with a 1.7-day orbital period where disc accretion occurs from the optical donor star (HZ Her) onto a neutron star (Her X-1). On top of orbital variability and pulsating X-ray emission from the neutron star rotating with a period of about one second, a 35-day X-ray modulation of emission is observed. The 35-day variability is due to a tilted precessing accretion disc that periodically screens X-ray emission from the neutron star. The disc precession that occurs in the direction opposite to the orbital motion is determined by the joint action of the tidal torque from the donor and dynamical torque from the gas streams. Several dozen thousand broadband UBV photometric observations of HZ Her have been obtained since 1972. The shape of the orbital light curves of HZ Her also changes with the 35-day cycle phase. The orbital variability can be reproduced in a model that includes a precessing tilted 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 X-ray emission flux from the neutron star also depends on the free precession phase that modulates the heating of the optical-star atmosphere and the intensity of gas streams. We show that this model reproduces well both optical observations of HZ Her and the behavior of the 35-day X-ray cycle.

The X-ray binary Her X-1 consists of an accreting neutron star and the optical component HZ Her. The 35-day X-ray 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 the warped accretion disk tilted to the orbital plane. We argue that the observed features of the 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 precession. The model parameters include a) the intensity (power) of the stream of matter flowing out of the optical star; b) the X-ray luminosity of the neutron star; c) the optical flux of the accretion disk; d) the X-ray irradiation pattern on the donor star; e) the tilt of the inner and outer edge 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.