The combined X-ray and $\gamma$-ray modeling of millisecond pulsars PSR J0030+0451 in the dissipative magnetospheres

TL;DR

This study models the X-ray and gamma-ray emissions of millisecond pulsar PSR J0030+0451 using dissipative magnetosphere models with combined dipole and quadrupole fields, successfully matching observations from NICER and Fermi.

Contribution

It introduces a novel 3D pseudo-spectral method to solve dissipative magnetospheres with combined dipole and off-centred quadrupole fields, improving emission modeling accuracy.

Findings

Model accurately reproduces NICER X-ray light curves.

Model successfully matches Fermi gamma-ray observations.

Demonstrates importance of non-dipole magnetic fields in pulsar emission.

Abstract

Modeling of the NICER X-ray light curves of millisecond pulsars PSR J0030+0451 provides a strong evidence for the existence of non-dipole magnetic fields. We study the X-ray and $\gamma$-ray emission of PSR J0030+0451 in the dissipative dipole plus off-centred quadrupole magnetospheres. The dissipative FF+AE dipole magnetospheres by combining force-free (FF) and Aristotelian electrodynamics (AE) are solved by a 3D pseudo-spectral 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 $\gamma$-ray emission from PSR J0030+0451 are simultaneously computed by using a ray-tracing method and a particle trajectory method. The modelled X-ray and $\gamma$-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 $\gamma$-ray emission for PSR J0030+0451.