2013MNRAS.435.1147P

Accretion of matter on to the surface of a freely precessing neutron star (NS) with a complex non-dipole magnetic field can explain the change of X-ray pulse profiles of Her X-1 observed by RXTE with the phase of the 35-d cycle. We demonstrate this using all available measurements of X-ray pulse profiles in the 9-13keV energy range obtained with the RXTE/Proportional Counter Array (PCA). The measured profiles guided the elaboration of a geometrical model and the definition of locations of emitting poles, arcs and spots on the NS surface which satisfactorily reproduce the observed pulse profiles and their dependence on free precession phase. We have found that the observed trend of the times of the 35-d turn-ons on the O-C diagram, which can be approximated by a collection of consecutive linear segments around the mean value, can be described by our model by assuming a variable free precession period, with a fractional period change of about a few per cent. Under this assumption and using our model, we have found that the times of phase zero of the NS free precession (which we identify with the maximum separation of the brightest spot on the NS surface with the NS spin axis) occur about 1.6d after the mean turn-on times inside each `stable' epoch, producing a linear trend on the O-C diagram with the same slope as the observed times of turn-ons. We propose that the 2.5 percent changes in the free precession period that occur on time scales of several to tens of 35-d cycles can be related to wandering of the principal inertia axis of the NS body due to variations in the patterns of accretion on to the NS surface. The closeness of periods of the disc precession and the NS free precession can be explained by the presence of a synchronization mechanism in the system, which modulates the dynamical interaction of the gas streams and the accretion disc with the NS free precession period.