Gravitational instabilities in protostellar discs and the formation of planetesimals

The development of gravitational instabilities in protostellar discs might be the leading process of angular momentum transport in the early phases of star formation. In this paper, we describe some new results that characterise the properties of gravitational perturbations as a function of the gas cooling rate [1, 2]. We show that self-gravitating instabilities can saturate due to thermal effects at an amplitude proportional to 1/root Omega t(cool), where t(cool) is the cooling time and Omega the angular frequency in the disc. Such saturation phenomenon can be simply derived by the condition that spiral density waves efficiently dissipate when their phase velocity with respect to the background flow becomes sonic. We also discuss the conditions under which the transport induced by such structures can be described in terms of a local process. Finally, we describe some simple models of self-regulated protostellar discs, consistent with the above numerical results [3, 4]. We then discuss the relevance of such models in the process of the formation of planetesimals. In particular, we show that planetesimals can form very efficiently early in the evolution of the protostellar disc, but in a spatial region confined to the outermost parts of the disc, roughly coincident with the location of the Kuiper belt in our Solar System. This can have important implications for the dynamics and the observable properties of both protostellar and debris discs.