Non-linear simple relativistic Alfvén waves in astrophysical plasmas

¹ LUTH, Observatoire de Paris, CNRS, Unversité Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France
e-mail: thierry.lehner@obspm.fr; 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: 12 December 2011
Accepted: 7 April 2012

Abstract

Aims. Large amplitude MHD perturbations are generated in magnetized tenuous relativistically moving plasmas, such as winds emitted by compact stellar objects or galactic nuclei, when a rapid change occurs at their boundaries or when an obstacle is present in them. These perturbations may involve relativistic motions in the rest-frame of the unperturbed plasma. In this paper, we calculate the characteristics and the structure of relativistic non-linear Alfvén waves.

Methods. We establish these properties for special-relativistic perturbations occurring in a particular type of non-linear waves, the simple waves.

Results. We derive the conditions applicable to Alfvénic perturbations in a cold flow. We calculate the characteristics of these perturbations and the structure of wave trains of finite extent in the propagation direction of these characteristics, as observed in the unperturbed fluid proper frame. We determine the velocity of the characteristics with respect to any observer. This velocity is found to be a first integral, constant in time and space. This implies that relativistic Alfvénic perturbations are channeled, in the unperturbed fluid proper frame, by the unperturbed magnetic field and travel along this field neither steepening nor breaking into shocks. For finite wave trains, the Lorentz factor is found to be limited by some maximum value that we calculate and that depends on the ratio of proper magnetic energy density to material energy density in the unperturbed fluid.