On magnetic instabilities and dynamo action in stellar radiation zones

Context. We examine the MHD instabilities arising in the radiation zone of a differentially rotating star, in which a poloidal field of fossil origin is sheared into a toroidal field. Aims. We focus on the non-axisymmetric instability that affects the toroidal magnetic field in a rotating star, which was first studied by Pitts and Tayler in the non-dissipative limit. If such an instability were able to mix the stellar material, it could have an impact on the evolution of the star. According to Spruit, it could also drive a dynamo. Methods. We compare the numerical solutions built with the 3-dimensional ASH code with the predictions drawn from an analytical study of the Pitts & Tayler instability. Results. The Pitts & Tayler instability is manifestly present in our simulations, with its conspicuous m = 1 dependence in azimuth. But its analytic treatment used so far is too simplified to be applied to the real stellar situation. Although the instability generated field reaches an energy comparable to that of the mean poloidal field, that field seems unaffected by the instability: it undergoes Ohmic decline, and is neither eroded nor regenerated by the instability. The toroidal field is produced by shearing the poloidal field and it draws its energy from the differential rotation. The small scale motions behave as Alfvén waves; they cause negligible eddy-diffusivity and contribute little to the net transport of angular momentum. Conclusions. In our simulations we observe no sign of dynamo action, of either mean field or fluctuation type, up to a magnetic Reynolds number of 105. However the Pitts & Tayler instability is sustained as long as the differential rotation acting on the poloidal field is able to generate a toroidal field of sufficient strength. But in the Sun such a poloidal field of fossil origin is ruled out by the nearly uniform rotation of the deep interior.