Constraining the magnetic field geometry of the millisecond pulsar PSR~J0030+0451 from joint radio, thermal X-ray and ${\hat{I}}^3$-ray emission

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 ${\hat{I}}^3$-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 ${\hat{I}}^3$-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 ${\hat{I}}^3$-ray pulsations only, leading to a fixed magnetic obliquity of $\hat{I}\pm \approx 75\hat{A}°$ and a line of sight inclination angle of $\hat{I}\P \approx 54\hat{A}°$. 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.

Accepted for publication in A&A