Astrophysical dynamics – from stars to galaxies Proceedings IAU Symposium No. 271, 2010 N. H. Brummell, A. S. Brun. M. S. Miesch & Y. Ponty, eds. c  International Astronomical Union 2011 doi:10.1017/S1743921311017698 MHD relaxation of fossil magnetic fields in stellar interiors St´ ephane Mathis 1,2 , Vincent Duez 3 & Jonathan Braithwaite 3 1 Laboratoire AIM, CEA/DSM-CNRS-Universit´ e Paris Diderot, IRFU/SAp Centre de Saclay, F-91191 Gif-sur-Yvette, France email: stephane.mathis@cea.fr 2 Observatoire de Paris-LESIA 5, place Jules Janssen, F-92195 Meudon Cedex 3 Argelander Institut f¨ ur Astronomie, Universit¨ at Bonn, Auf dem H¨ ugel 71, D-53111 Bonn, Germany email: vduez@astro.uni-bonn.de;jonathan@astro.uni-bonn.de Abstract. The understanding of fossil fields origin, topology, and stability is one of the corner stones of the stellar magnetism theory. On one hand, since they survive on secular time scales, they may modify the structure and the evolution of their host stars. On the other hand, they must have a complex stable structure since it has been demonstrated that the simplest purely poloidal or toroidal fields are unstable on dynamical time scales. In this context, the only stable stellar configurations found today are those resulting from numerical simulations by Braithwaite and collaborators who studied the evolution of an initial stochastic magnetic field, which relaxes with a selective decay of magnetic helicity and energy, on mixed stable configurations (poloidal and toroidal) that seem to be in equilibrium and then diffuse. In this talk, we report the semi- analytical investigation of such an equilibrium field in the axisymmetric case. We use variational methods, which describe selective decay of magnetic helicity and energy during MHD relaxation, and we identify a supplementary invariant due to the stable stratification of stellar radiation zones. This leads to states that generalize force-free Taylor’s relaxation states studied in plasma laboratory experiments that become non force-free in the stellar case. Moreover, astrophysical applications are presented and the stability of obtained configurations is studied. Keywords. magnetohydrodynamics (MHD), plasmas, stars: magnetic field 1. Introduction Magnetic fields are now detected more and more often at the surface of main-sequence (and pre main-sequence) intermediate mass and massive stars, which have an external radiative envelope. Indeed, strong fields (300 G to 30 kG) are observed in some fraction of Herbig stars (Alecian et al. 2008), A stars (the Ap stars, see Auri` ere et al. 2007), as well as in B stars and in a handful of O stars (Grunhut et al. 2009). Furthermore, we cannot dismiss the possibility of a large-scale magnetic field being responsible for the quasi-uniform rotation of the bulk of the solar radiation zone, as revealed by p-modes helioseismology (Eff-Darwich et al. 2008). Finally, non convective compact objects display fields strength of 10 4 − 10 9 G for white dwarfs and of 10 8 − 10 15 G for neutron stars. Magnetic fields in stably stratified non convective stellar regions will thus be able to deeply modify our vision of stars evolution since their formation (Commer¸ con et al. 2010) to their late stages, for example for gravitational supernovae. Indeed, they will modify stellar internal dynamics, for example the transport of angular momentum and the resulting rotation history, and chemicals mixing (see Mathis & Zahn 2005). The large-scale, ordered nature (often approximately dipolar) of such magnetic fields and the scaling of their strengths as a function of their host properties (according to the 270 https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921311017698 Downloaded from https://www.cambridge.org/core. IP address: 54.87.9.134, on 13 Dec 2021 at 03:22:36, subject to the Cambridge Core terms of use, available at