Vincent Duez

ON THE STABILITY OF NON-FORCE-FREE MAGNETIC EQUILIBRIA IN STARS

The existence of stable magnetic configurations in white dwarfs, neutron stars, and various non-convective stellar regions is now well recognized. It has recently been shown numerically that various families of equilibria, including axisymmetric mixed poloidal-toroidal configurations, are stable. Here we test the stability of an analytically derived non-force-free magnetic equilibrium resulting from an initial relaxation (self-organization) process, using three-dimensional magnetohydrodynamic simulations: the obtained mixed configuration is compared with the dynamical evolution of its purely poloidal and purely toroidal components, both known to be unstable. The mixed equilibrium shows no sign of instability under white noise perturbations. This configuration therefore provides a good description of magnetic equilibrium topology inside non-convective stellar objects and will be useful to initialize magneto-rotational transport in stellar evolution codes and in multi-dimensional magnetohydrodynamic simulations.

The dynamics of the radiative zone of the Sun

Helioseismology puts strong constraints on the internal sound speed and on the rotation profile in the radiative zone. Young stars of solar type are more active and faster rotators than the Sun. So we begin to build models which include different rotation histories and compare the results with all the solar observations. The profiles of the rotation we get have interesting consequence for the introduction of magnetic field in the radiative zone. We discuss also the impact of mass loss deduced from measured flux of young stars. We deduce from these comparisons some quantitative effect of the dynamical processes (rotation, magnetic field and mass loss) of these early stages on the present sound speed and density. We show finally how we can improve our present knowledge of the radiative zone with PICARD and GOLFNG.

A family of stable configurations to model magnetic fields in stellar radiation zones

We conduct 3D magneto-hydrodynamic (MHD) simulations in order to test the stability of the magnetic equilibrium configuration described by Duez & Mathis (2010). This analytically-derived configuration describes the lowest energy state for a given helicity in a stellar radiation zone. The necessity of taking into account the non force-free property of the large-scale, global field is here emphasized. We then show that this configuration is stable. It therefore provides a useful model to initialize the magnetic topology in upcoming MHD simulations and stellar evolution codes taking into account magneto-rotational transport processes.

A first model of stable magnetic configuration in stellar radiation zones

We test the stability of a magnetic equilibrium configuration using numerical simulations and semi-analytical tools. The tested configuration is, as described by Duez & Mathis (2010), the lowest energy state for a given helicity in a stellar radiation zone. We show using 3D magneto-hydrodynamic (MHD) simulations that the present configuration is stable with respect to all submitted perturbations, that would lead to the development of kink-type instabilities in the case of purely poloidal or toroidal fields, both well known to be unstable. We also discuss, using semi-analytic work, the stabilizing influence of one component on the other and show that the found configuration actually lies in the stability domain predicted by a linear analysis of resonant modes.

MHD relaxation of fossil magnetic fields in stellar interiors

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 Taylors 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.