Modelling the light curves of ultraluminous X-ray sources as precession

We present a freely available xspec model for the modulations seen in the long-term light curves of multiple ultraluminous X-ray sources (ULXs). By incorporating the physics of multiple electron scatterings (ray traced with a Monte Carlo routine), we go beyond analytical predictions and show that the geometrical beaming of radiation in the conical outflow can be more than a factor of 100 for opening angles smaller than 10°. We apply our new model to the long-term, well-sampled Swift light curve of the recently confirmed ULX pulsar NGC 5907 X-1 with an established period of 78 d. Our results suggest that geometrical beaming together with a slight precession of the conical wind can describe the light curve with a consistent set of parameters for the wind. The small opening angle of roughly |10∘ -13^∘| implies a highly supercritical flow and boosting factors of the order of |B=60|–90 that would yield a fairly low surface magnetic field strength of 2 × 1010 G.