Testing the locality of transport in self-gravitating accretion discs

In this paper we examine the issue of characterizing the transport associated with gravitational instabilities in relatively cold discs, discussing in particular under which condition it can be described within a local, viscous framework. We present the results of global, three-dimensional, SPH simulations of self-gravitating accretion discs, in which the disc is cooled using a simple parameterization for the cooling function. Our simulations show that the disc settles in a ``self-regulated'' state, where the axisymmetric stability parameter $Q\approx 1$ and where transport and energy dissipation are dominated by self-gravity. We have computed the gravitational stress tensor and compared our results with expectations based on a local theory of transport. We find that, for disc masses smaller than $0.25M_{\star}$ and aspect ratio $H/r\lesssim 0.1$, transport is determined locally, thus allowing for a viscous treatment of the disc evolution.