Abstract

--- - Context. 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 has become possible to significantly constrain the geometry and the location of the associated emission regions. - Aims. In this work, we use results from the modelling of thermal X-ray observations of PSR J0030+0451 from the Neutron Star Interior Composition Explorer (NICER) mission and phase-aligned radio and gamma-ray pulse profiles to constrain the geometry of an off-centred dipole that is able to reproduce the light curves in these respective bands simultaneously. - Methods. To this aim, we deduced a configuration with a simple dipole off-centred from the location of the centre of the thermal X-ray hot spots. We show that the geometry is compatible with independent constraints from radio and gamma-ray pulsations only, leading to a fixed magnetic obliquity of alpha approximate to 75 degrees and a line-of-sight inclination angle of zeta approximate to 54 degrees. - Results. 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.