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

TL;DR

This paper introduces a new model for the light curve modulations of ultraluminous X-ray sources, incorporating physics of electron scatterings and geometrical beaming, applied to a specific ULX pulsar to infer wind and magnetic field properties.

Contribution

The paper develops a Monte Carlo-based XSPEC model that accounts for electron scatterings and geometrical beaming in ULX outflows, providing a new tool for analyzing their light curves.

Findings

Geometrical beaming can amplify emission by over 100 times for narrow outflow angles.

The model successfully fits the light curve of NGC 5907 X-1 with a wind precession scenario.

Estimated magnetic field strength of the pulsar is around 2×10^{10} Gauss.

Abstract

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.