The force-free twisted magnetosphere of a neutron star

TL;DR

This paper models twisted, force-free magnetospheres of neutron stars, revealing how currents influence magnetic properties and energy, with implications for understanding magnetar behavior and evolution.

Contribution

It introduces a detailed force-free magnetosphere model that matches vacuum solutions externally and explores the impact of magnetospheric currents on magnetic field strength and energy.

Findings

Magnetic dipole moment can increase by up to 40% due to currents.

Total energy increases by up to 25% compared to vacuum models.

Existence of a critical twist angle (~1.5 rad) beyond which solutions do not exist.

Abstract

We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to $40\%$ with respect to a vacuum model with the same surface magnetic field, due to the contribution of magnetospheric currents to the global magnetic field. Thus, estimates of the surface magnetic field based on the large-scale dipolar braking torque are slightly overestimating the surface value by the same amount. Consistently, there is a moderate increase in the total energy of the model with respect to the vacuum solution of up to $25\%$, which would be the available energy budget in the event of a fast, global magnetospheric reorganization commonly associated with magnetar flares. We have also found the interesting result of the existence of a critical twist ($\varphi_{\rm max} \lesssim 1.5$ rad), beyond which we cannot find any more numerical solutions. Combining the models considered in this paper with the evolution of the interior of neutron stars will allow us to study the influence of the magnetosphere on the long-term magnetic, thermal, and rotational evolution.