On self-sustained dynamo cycles in accretion discs

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK e-mail: g.lesur@damtp.cam.ac.uk

Received: 7 May 2008
Accepted: 6 July 2008

Abstract

Context. MHD turbulence is known to exist in shearing boxes with either zero or nonzero net magnetic flux. However, the way turbulence survives in the zero-net-flux case is not explained by linear theory and appears as a purely numerical result that is not well understood. This type of turbulence is also related to the possibility of having a dynamo action in accretion discs, which may help to generate the large-scale magnetic field required by ejection processes.

Aims. We look for a nonlinear mechanism able to explain the persistence of MHD turbulence in shearing boxes with zero net magnetic flux, and potentially leading to large-scale dynamo action.

Methods. Spectral nonlinear simulations of the magnetorotational instability are shown to exhibit a large-scale axisymmetric magnetic field, maintained for a few orbits. The generation process of this field is investigated using the results of the simulations and an inhomogeneous linear approach. We show that quasilinear nonaxisymmetric waves may provide a positive back-reaction on the large-scale field when a weak inhomogeneous azimuthal field is present, explaining the behaviour of the simulations. We finally reproduce the dynamo cycles using a simple closure model summarising our linear results.

Results. The mechanism by which turbulence is sustained in zero-net-flux shearing boxes is shown to be related to the existence of a large-scale azimuthal field, surviving for several orbits. In particular, it is shown that MHD turbulence in shearing boxes can be seen as a dynamo process coupled to a magnetorotational-type instability.