Spheroidal force-free neutron star magnetospheres

Abstract

Context. Fast rotating and self-gravitating astrophysical objects suffer strong deformations from centrifugal forces. If, moreover, they are magnetised, they generate an electromagnetic wave that is perturbed accordingly. When stellar objects are also surrounded by an ideal plasma, a magnetosphere is formed. For neutron stars, a relativistic magnetised wind is launched, efficiently extracting rotational kinetic energy flowing into particle creation and radiation. Aims. We study the electromagnetic configuration of a force-free magnetosphere encompassing an ideal spheroidal rotating conductor as an inner boundary. We put special emphasis on millisecond period neutron star magnetospheres, that is those showing a significant oblate shape. For completeness, we also investigate the effect of prolate stars. Methods. Force-free solutions were computed by numerical integration of the time-dependent Maxwell equations in spheroidal coordinates using pseudo-spectral techniques. Relevant quantities such as the magnetic field structure, the spin-down luminosity, the polar cap rims, and the current density are shown and compared to the force-free spherical star results. Results. We find that the force-free magnetic field produced by spheroidal stars remains very similar to their spherical counterpart. However, the spin-down luminosity slightly decreases with increasing oblateness or prolateness. Moreover, the polar cap area increases and, for the most part, always encompasses the equivalent spherical star polar cap rims. The polar cap current density is also drastically affected. Conclusions. Neutron stars are significantly distorted by either rotational effects such as millisecond pulsars or by magnetic pressure such as magnetars and high magnetic field pulsars. An observational interpretation of and fitting a thermal X-ray pulsation will greatly benefit from an accurate and quantitative analysis similar to the one presented in this paper. However, even for the fastest possible rotation, the effect would certainly be unobservable, in the sense that we cannot predict what feature of the light curve would supposedly reveal the neutron star deformation due to fast rotation.