Studying magnetic fields of ultraluminous X-ray pulsars using different accretion torques

Abstract

The magnetic field of ultraluminous X-ray (ULX) pulsars is the key parameter to understand the nature and accretion physics. However, the typical magnetic field values in these ULX pulsars are still under debate. We used six different torque models to study the magnetic fields of ULX pulsars, to see how derived magnetic fields change with different models, and to determine which models are more suitable for ULX pulsars. We took the currently available period, period derivative, and flux data of 7 confirmed ULX pulsars, M82 X-2, ULX NGC 7793 P13, ULX NGC 5907, NGC 300 ULX1, NGC 1313 X-2, M51 ULX-7, Swift J0243.6+6124, plus one potential ULX pulsars, SMC X-3. The magnetic fields of these ULX pulsars were constrained from two physical conditions: the spin-up process and near equilibrium. We checked possible dependence of the magnetic field estimations on the different torque models. The calculations suggest the accretion torque models by Ghosh and Lamb (1979), Wang (1995), Kluźniak and Rappaport (2007) and Campbell (2012) are more likely to support magnetar models for ULX pulsars, while Lovelace et al. (1995)'s model generally predicts the magnetic field in normal neutron stars. Implications of our results combined with other independent methods are also discussed, which will help us to understand the nature and rotational behavior of these ULX pulsars.