Pulse profiles of tall accretion columns in X-ray pulsars

Accreting X-ray pulsars (XRPs) are strongly magnetized neutron stars (NSs) distinguished by a periodic variability pattern related to the rotation of their magnetospheres (pulsations). Many of these objects show complex asymmetric pulse profiles that are difficult to explain in the framework of existing models. We calculate the pulsations of X-ray radiation from a magnetized NS in the regime of supercritical accretion, when the radiation shock wave is high above the NS surface, and the observed radiation comes from two optically thick accretion columns located downstream of the shocks. We show that the accretion column beam pattern calculated from the first principles has a potential of reproducing the variety of XRP pulse shapes. The surfaces of the columns are assumed to radiate locally as blackbodies with the temperature distribution following the solution of Basko and Sunyaev (1976). The adopted geometry of the field is an inclined dipole. It is taken into account that the two accretion flows above the shocks attenuate and scatter the radiation of the accretion columns. Using the ray-tracing technique, we obtain a vast variety of pulse shapes controlled by the mass accretion rate, magnetic angle, the direction towards the observer, and the parameters that determine the particular set of magnetic field lines being loaded with accreting matter. We propose a universal dimensionless parameter describing the asymmetry of a pulse quantitatively. The model naturally produces asymmetric pulse profiles observed in many XRPs. Its applicability, however, is limited to the brightest objects like pulsating ultraluminous Xray sources and strong flares of Galactic XRPs.