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We perform general relativistic radiation magnetohydrodynamics (MHD)simulations of super-Eddington accretion flows around a neutron star with adipole magnetic field for modeling the galactic ultra-luminous X-ray source(ULX) exhibiting X-ray pulsations, Swift J0243.6+6124. Our simulations show theaccretion columns near the magnetic poles, the accretion disk outside themagnetosphere, and the outflows from the disk. It is revealed that theeffectively optically thick outflows, consistent with the observed thermalemission at $\sim10^7$ K, are generated if the mass accretion rate is muchhigher than the Eddington rate $\dot{M}_{\rm Edd}$ and the magnetosphericradius is smaller than the spherization radius. In order to explain theblackbody radius ($\sim 100-500$ km) without contradicting the reported spinperiod ($9.8~{\rm s}$) and spin-up rate ($\dot{P}=-2.22\times10^{-8}~{\rms~s^{-1}}$), the mass accretion rate of $(200-1200)\dot{M}_{\rm Edd}$ isrequired. Since the thermal emission was detected in two observations with$\dot{P}$ of $-2.22\times10^{-8}~{\rm s~s^{-1}}$ and $-1.75\times10^{-8}~{\rms~s^{-1}}$ but not in another with $\dot{P}=-6.8 \times10^{-9}~{\rm s~s^{-1}}$,the surface magnetic field strength of the neutron star in Swift J0243.6+6124is estimated to be between $3\times10^{11}~{\rm G}$ and $4\times10^{12}~{\rmG}$. From this restricted range of magnetic field strength, the accretion ratewould be $(200-500)\dot{M}_{\rm Edd}$ when the thermal emission appears and$(60-100)\dot{M}_{\rm Edd}$ when it is not detected. Our results support thehypothesis that the super-Eddington phase in the 2017-2018 giant outburst ofSwift J0243.6+6124 is powered by highly super-Eddington accretion flows onto amagnetized neutron star.

Modeling of Thermal Emission from ULX Pulsar Swift J0243.6+6124 with General Relativistic Radiation MHD simulations