Constraining the magnetic field geometry of the millisecond pulsar PSR~J0030+0451 from joint radio, thermal X-ray and $\gamma$-ray emission

TL;DR

This study combines multi-wavelength observations of PSR J0030+0451 to constrain its magnetic field geometry, revealing an off-centred dipole configuration consistent across radio, X-ray, and gamma-ray data.

Contribution

It introduces a model of an off-centred dipole based on thermal X-ray hot spots that aligns with radio and gamma-ray pulse profiles, providing new insights into pulsar magnetic geometry.

Findings

Magnetic obliquity approximately 75 degrees.

Line of sight inclination about 54 degrees.

Off-centred dipole model fits multi-wavelength data.

Abstract

With the advent of multi-wavelength electromagnetic observations of neutron stars, spanning many decades in photon energies, from radio wavelengths up to X-rays and $\gamma$-rays, it becomes possible to significantly constrain the geometry and the location of the associated emission regions. In this work, we use results from the modelling of thermal X-ray observations of PSR~J0030+0451 from the NICER mission and phase-aligned radio and $\gamma$-ray pulse profiles to constrain the geometry of an off-centred dipole able to reproduce the light-curves in these respective bands simultaneously. To this aim, we deduce a configuration with a simple dipole off-centred from the location of the centre of the thermal X-ray hot spots and show that the geometry is compatible with independent constraints from radio and $\gamma$-ray pulsations only, leading to a fixed magnetic obliquity of $\alpha \approx 75\deg$ and a line of sight inclination angle of $\zeta \approx 54\deg$. We demonstrate that an off-centred dipole cannot be rejected by accounting for the thermal X-ray pulse profiles. Moreover, the crescent shape of one spot is interpreted as the consequence of a small scale surface dipole on top of the large scale off-centred dipole.