Propagation of the gravo-magneto disc instability

Discs that contain dead zones are subject to the gravo-magneto instability which arises when the turbulence shifts from gravitational to magnetic. We have previously described this instability through a local analysis at some radius in the disc in terms of a limit cycle. A disc may be locally unstable over a radial interval. In this paper, we consider how the local instability model can describe global disc outbursts. The outburst is triggered near the middle of the range of locally unstable radii. The sudden increase in turbulence within high surface density material causes a snowplough of density that propagates both inwards and outwards. All radii inside the trigger radius become unstable, as well as locally unstable radii outside the trigger radius. In addition, a locally stable region outside the trigger radius may also become unstable as the gravitational instability is enhanced by the snowplough. For the circumstellar disc model we consider, we find that a quarter of the disc mass is accreted on to the central object during the outburst. The radius out to which the disc is globally unstable is twice that for which it is locally unstable.