On the Magnetic Fields of Ultraluminous X-ray Pulsars.

So far quite a few ultraluminous X-ray (ULX) pulsars have been discovered. In this work, we construct a super-Eddington, magnetic accretion disk model to estimate the dipole magnetic field of eight ULX pulsars based on their observed spin-up variations and luminosities. We obtain two branches of dipole magnetic field solutions. They are distributed in the range of $B\sim (0.16-64.5)\times 10^{10}\,{\rm G}$ and $\sim (0.275-79.0)\times 10^{13}\,{\rm G}$ corresponding to the low- and high-$B$ solutions respectively. The low magnetic field solutions correspond to the state that the neutron stars are far away from the spin equilibrium, and the high magnetic field solutions are close to the spin equilibrium. The ultra-strong magnetic fields derived in Be-type ULX pulsars imply that the accretion mode in Be-type ULX pulsars could be more complicated than in the persistent ULX pulsars and may not be accounted for by the magnetized accretion disk model. We suggest that the transition between the accretor and the propeller regimes may be used to distinguish between the low- and high-$B$ magnetic field solutions in addition to the detection of the cyclotron resonance scattering features.