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 $10^\circ$. 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 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 $10\mathrm{-}13^\circ$ implies a highly super-critical flow and boosting factors at the order of $\mathcal{B}=60\mathrm{-}90$ that would yield a fairly low surface magnetic field strength of $2\times 10^{10}\,$Gauss.