Radiation from an off-centred rotating dipole in vacuum

TL;DR

This paper investigates how an off-centred magnetic dipole in a neutron star affects its electromagnetic emission, providing analytical solutions and implications for pulsar observations.

Contribution

It offers the first exact analytical solutions for the electromagnetic field of an off-centred dipole in vacuum, including effects on spin-down luminosity and torque.

Findings

Off-centred dipoles significantly alter electromagnetic emission patterns.

Analytical solutions are derived to any order in the small displacement parameter.

Implications for pulsar braking index and light curves are discussed.

Abstract

When a neutron star forms, after the collapse of its progenitor, a strong magnetic field survives in its interior. This magnetic topology is usually assumed to be well approximated by a dipole located right at the centre of the star. However, there is no particular reason why this dipole should be attached to this very special point. A slight shift from the stellar centre could have strong implications for the surrounding electromagnetic field configuration leading to clear observational signatures. We study the effect of the most general off-centred dipole anchored in the neutron star interior. Exact analytical solutions are given in vacuum outside the star to any order of accuracy in the small parameter $\epsilon = d/R$, where $d$ is the displacement of the dipole from the stellar centre and $R$ the neutron star radius. As a simple diagnostic of this decentred dipole, the spin-down luminosity and the torque exerted on its crust are computed to the lowest leading order in~$\epsilon$. Results are compared to earlier works and a discussion on repercussions on pulsar braking index and multi-wavelength light curves is proposed.