Magnetic quadri-dipolar stars rotating in vacuum

TL;DR

This paper derives the electromagnetic field and related phenomena for a rotating star with a combined dipole and quadrupole magnetic field, providing insights into neutron star magnetospheres and potential high-velocity kicks.

Contribution

It presents the first exact analytical expressions for the electromagnetic field of a rotating star with combined dipole and quadrupole magnetic fields in vacuum.

Findings

Electromagnetic kick velocities can reach thousands of km/s for high quadrupole components.

Provides a comprehensive formalism for the magnetosphere of neutron stars with complex magnetic fields.

Highlights the significance of multipolar magnetic fields in astrophysical observations.

Abstract

Main sequence stars and compact objects like white dwarfs and neutron stars are usually embedded in magnetic fields that strongly deviate from a pure dipole located right at the stellar centre. An off-centred dipole can sometimes better adjust existing data and offer a simple geometric picture to include multipolar fields. However, such configurations are usually to restrictive, limiting multipolar components to strength less than the underlying dipole. In this paper, we consider the most general lowest order multipolar combination given by a dipole and a quadrupole magnetic field association in vacuum. Following the general formalism for multipolar field computations, we derive the full electromagnetic field outside a rotating quadridipole. Exact analytical expressions for the Poynting flux and the electromagnetic kick are given. Such geometry is useful to study the magnetosphere of neutron stars for which more and more compelling observations reveals hints for at least quadridipolar fields. We also show that for sufficiently high quadrupole components at the stellar surface, the electromagnetic kick imprinted to a neutron star can reach thousands of km/s for a millisecond period at birth.