The Combined X-Ray and γ -Ray Modeling of Millisecond Pulsar PSR J0030+0451 in the Dissipative Magnetospheres

Abstract Modeling of the Neutron Star Interior Composition Explorer (NICER) X-ray light curves of millisecond pulsar PSR J0030+0451 provides strong evidence for the existence of nondipole magnetic fields. We study the X-ray and γ -ray emission of PSR J0030+0451 in the dissipative dipole plus off-centred quadrupole magnetospheres. The dissipative force-free (FF) + Aristotelian electrodynamics (AE) dipole magnetospheres by combining FF and AE are solved by a 3D pseudospectral method in the rotating coordinate system. We use the FF+AE dipole plus off-centred quadrupole fields with minimum free parameters to reproduce two hotspot configurations found by the NICER observations. The X-ray and γ -ray emission from PSR J0030+0451 are simultaneously computed by using a ray-tracing method and a particle trajectory method. The modeled X-ray and γ -ray emission is then directly compared with those of PSR J0030+0451 from the NICER and Fermi observations. Our results can well reproduce the observed trends of the NICER X-ray and Fermi γ -ray emission for PSR J0030+0451.