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Although ultraluminous X-ray pulsars (ULXPs) are believed to be powered by super-Eddington accretion onto a magnetized neutron star (NS), the detailed structures of the inflow-outflow and magnetic fields are still not well understood. We perform general relativistic radiation magnetohydrodynamics (GR-RMHD) simulations of super-Eddington accretion flows onto a magnetized NS with dipole and/or quadrupole magnetic fields. Our results show that an accretion disk and optically thick outflows form outside the magnetospheric radius, while inflows aligned with magnetic field lines appear inside. When the dipole field is more prominent than the quadrupole field at the magnetospheric radius, accretion columns form near the magnetic poles, whereas a quadrupole magnetic field stronger than the dipole field results in the formation of a belt-like accretion flow near the equatorial plane. The NS spins up as the angular momentum of the accreting gas is converted into the angular momentum of the electromagnetic field, which then flows into the NS. Even if an accretion column forms near one of the magnetic poles, the observed luminosity is almost the same on both sides with the accretion column and the side without it because the radiation energy is transported to both sides through scattering. Our model suggests that galactic ULXP, Swift J0243.6+6124, has a quadrupole magnetic field of $2\times10^{13}~{\rm G}$ and a dipole magnetic field of less than $4\times10^{12}~{\rm G}$., Comment: 22 pages, 12 figures, accepted for publication in ApJ

A phase-resolved analysis on the X-ray spectrum of Ultra-Luminous X-ray Pulsar (ULXP) NGC 300 ULX-1 is performed with data taken with XMM-Newton and NuSTAR on 2016 December 16th. In addition to the classical phase-restricting analysis, a method developed in active galactic nuclei studies is newly employed for ULXP. It has revealed that the pulsation cycle of the source can be divided into two intervals in terms of X-ray variability. This suggests the rotating flow consists of at least two representative emission regions. Furthermore, the new method successfully decomposed the spectrum into an independent pair in each interval. One is an unchanging-component spectrum that can be reproduced by a standard disk model with a $720^{+220}_{-120}$ km inner radius and a $0.25\pm0.03$ keV peak temperature. The other is the spectrum of the component that coincides with the pulsation. This was explained with a Comptonization of a $0.22^{+0.2}_{-0.1}$ keV blackbody and exhibited a harder photon index in the brighter phase interval of two. The results are consistent with a picture that the pulsating emission originates from a funnel-like flow formed within the magnetosphere, and the inner flow exhibiting a harder continuum is observed exclusively when the opening cone points to the observer., Comment: 27 pages, 15 figures, accepted for publication in ApJ

We perform general relativistic radiation magnetohydrodynamics (MHD) simulations of super-Eddington accretion flows around a neutron star with a dipole magnetic field for modeling the galactic ultra-luminous X-ray source (ULX) exhibiting X-ray pulsations, Swift J0243.6+6124. Our simulations show the accretion columns near the magnetic poles, the accretion disk outside the magnetosphere, and the outflows from the disk. It is revealed that the effectively optically thick outflows, consistent with the observed thermal emission at $\sim10^7$ K, are generated if the mass accretion rate is much higher than the Eddington rate $\dot{M}_{\rm Edd}$ and the magnetospheric radius is smaller than the spherization radius. In order to explain the blackbody radius ($\sim 100-500$ km) without contradicting the reported spin period ($9.8~{\rm s}$) and spin-up rate ($\dot{P}=-2.22\times10^{-8}~{\rm s~s^{-1}}$), the mass accretion rate of $(200-1200)\dot{M}_{\rm Edd}$ is required. Since the thermal emission was detected in two observations with $\dot{P}$ of $-2.22\times10^{-8}~{\rm s~s^{-1}}$ and $-1.75\times10^{-8}~{\rm s~s^{-1}}$ 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+6124 is estimated to be between $3\times10^{11}~{\rm G}$ and $4\times10^{12}~{\rm G}$. From this restricted range of magnetic field strength, the accretion rate would 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 the hypothesis that the super-Eddington phase in the 2017-2018 giant outburst of Swift J0243.6+6124 is powered by highly super-Eddington accretion flows onto a magnetized neutron star., Comment: 24 pages, 9 figures, 2 tables, accepted for publication in ApJ

We calculate the pulsed fraction (PF) of the super-critical column accretion flows onto magnetized neutron stars (NSs), of which the magnetic axis is misaligned with the rotation axis, based on the simulation results by Kawashima et al.(2016, PASJ, 68, 83). Here, we solve the geodesic equation for light in the Schwarzschild spacetime in order to take into account the light bending effect. The gravitational redshift and the relativistic doppler effect from gas motions of the accretion columns are also incorporated. The pulsed emission appears since the observed luminosity, which exceeds the Eddington luminosity for the stellar-mass black holes, periodically changes via precession of the column caused by the rotation of the NS. The PF tends to increase as $\theta_{\rm obs}$ approaching to $\theta_{\rm B}$, where $\theta_{\rm obs}$ and $\theta_{\rm B}$ are the observer's viewing angle and the polar angle of the magnetic axis measured from the rotation axis. The maximum PF is around 50 %. Also, we find that the PF becomes less than 5 % for $\theta_{\rm obs} \lesssim 5^\circ$ or for $\theta_{\rm B} \lesssim 5^\circ$. Our results are consistent with observations of ultraluminous X-ray pulsars (ULXPs) with few exceptions, since the ULXPs mostly exhibit the PF of $\lesssim$ 50 %. Our present study supports the hypothesis that the ULXPs are powered by the super-critical column accretion onto NSs., Comment: 10 pages, 8 figures, accepted for publication in PASJ