General solution for the vacuum electromagnetic field in the surroundings of a rotating star

¹ LUTH, Observatoire de Paris, CNRS, Université Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France
e-mail: fabrice.mottez@obspm.fr
² Observatoire Astronomique, Université de Strasbourg, 11 rue de l’Université, 67000 Strasbourg, France
e-mail: jean.heyvaerts@astro.unistra.fr

Received: 23 July 2014
Accepted: 10 October 2014

Abstract

Aims. Many recent observations of pulsars and magnetars can be interpreted in terms of neutron stars with multipole electromagnetic fields. As a first approximation, we investigate the multipole magnetic and electric fields in the environment of a rotating star when this environment is deprived of plasma.

Methods. We compute a multipole expansion of the electromagnetic field in vacuum for a given magnetic field on the conducting surface of the rotating star. Then, we consider a few consequences of multipole fields of pulsars.

Results. We provide an explicit form of the solution. For each spherical harmonic of the magnetic field, the expansion contains a finite number of terms. A multipole magnetic field can provide an explanation for the stable sub-structures of pulses, and they offer a solution to the problem of current closure in pulsar magnetospheres.

Conclusions. This computation generalises the widely used model of a rotating star in vacuum with a dipole field. It can be especially useful as a first approximation to the electromagnetic environment of a compact star, for instance a neutron star, with an arbitrarily magnetic field.