Modeling 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 longterm, well sampled Swift light curve of the recently confirmed ULX pulsar NGC 5907 X-1 with an established period of 78 days. 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 super-critical flow and boosting factors at the order of B = 60–90 that would yield a fairly low surface magnetic field strength of 2× 10 Gauss.