The Multipolar Magnetic Field of Millisecond Pulsar PSR J0030+0451

TL;DR

This study models the complex magnetic field configurations of the millisecond pulsar PSR J0030+0451 using advanced magnetic field models and observational data, revealing diverse configurations consistent with X-ray and gamma-ray observations.

Contribution

It introduces a detailed analysis of non-dipolar magnetic fields in pulsars using combined X-ray and gamma-ray data, employing MCMC techniques to explore magnetic field degeneracies.

Findings

Multiple magnetic field configurations can reproduce NICER X-ray waveforms.

Force-free magnetosphere models align with observed gamma-ray light curves.

Degeneracies in magnetic field structures highlight the complexity of pulsar magnetic topology.

Abstract

Modeling of the NICER X-ray waveform of the pulsar PSR J0030+0451, aimed to constrain the neutron star mass and radius, has inferred surface hot-spots (the magnetic polar caps) that imply significantly non-dipolar magnetic fields. To this end, we investigate magnetic field configurations that comprise offset dipole plus quadrupole components using static vacuum field and force-free global magnetosphere models. Taking into account the compactness and observer angle values provided by Miller et al. (2019) and Riley et al. (2019), we compute geodesics from the observer plane to the polar caps to compute the resulting X-ray light curve. We explore, through Markov chain Monte Carlo techniques, the detailed magnetic field configurations that can reproduce the observed X-ray light curve and have discovered degeneracies, i.e., diverse field configurations, which can provide sufficient descriptions to the NICER X-ray waveforms. Having obtained the force-free field structures, we then compute the corresponding synchronous gamma-ray light curves following Kalapotharakos et al. (2014) these we compare to those obtained by Fermi-LAT, to provide models consistent with both the X-ray and the gamma-ray data, thereby restricting further the multipole field parameters. An essential aspect of this approach is the proper computation of the relative phase between the synchronous X- and gamma-ray light curves. We conclude with a discussion of the broader implications of our study.