The Thermal Regulation of Gravitational Instabilities in Disks Around   Young Stars
  Gravitational instabilities (GIs) are spiral distortions in a self-gravitating disk that appear wherever the local surface density and temperature become favorable for their growth. The restructuring of the disk as it becomes unstable, the thermal processes that sustain the instabilities, and their effect on the long-term evolution of the disk are the studied using 3-D hydrodynamic simulations. These show that the cooling and heating processes balance each other, and as a result the disk asymptotes to quasi-equilibrium within a few orbital periods after the GI onset. The final values of the internal energy and the Toomre Q are independent of cooling time, while the asymptotic mass transport rates are inversely proportional to the cooling time. The formation of dense rings is common in these simulations. GIs fragment into clumps when the cooling time is on the order of the local orbital time, but the clumps are short-lived. External radiation can affect the evolution considerably. GIs are an effective angular momentum and mass transport mechanism, and during their onset, they can reproduce the mass transport rates necessary to trigger FU Ori outbursts. 
Annie C. Mejia