The Gravitational Instability and its Role in the Evolution of Protoplanetary and Protostellar Discs

In this thesis I present numerical simulations of massive, cold, non-ionised self-gravitating accretion discs about a central massive object, and then use them to investigate structure formation and energy/angular momentum transport, the effects of different cooling regimes on the likelihood of bound condensates forming through direct gravitational fragmentation, and the potential for resolved sub-mm imaging of such systems. I also present a review of current theories of viscous and wave transport in astrophysical discs, observed properties of protostellar and protoplanetary discs and a numerical scheme suitable for conducting computational experiments on fluid discs. I find that the structures excited in self-gravitating fluid discs self-regulate in such a manner that the density waves formed are very weak shocks, with the amplitude of the density perturbations forming the waves determined by the cooling regime. This self-regulation process ensures that for discs of \lesssim 10% of the central object mass the transport properties are determined principally by local effects, representing a crucial difference between collisional (fluid) and collisionless (stellar) discs as the latter cannot form shocks. I further find that the effects of an opacity-based cooling function makes self-gravitating protoplanetary discs significantly more susceptible to fragment formation in certain opacity regimes at relatively high (10−5 − 10−3 M⊙ yr−1) accretion rates due to the dependence on temperature perturbations. Furthermore I find that fragment formation due to direct gravitational collapse is feasible in such discs only at radii \gtrsim 50 AU, and this radius increases with decreasing temperature if the background temperature falls below approximately 10K. Finally I have used simple disc models in conjuction with a realistic telescope model to demonstrate that resolved images of spiral structure in massive, self-gravitating protostellar discs should be readily observable with ALMA, out to distances representative of local star-forming complexes.