SIMBAD references

We improve on our previous treatments of the long-term evolution of protostellar disks by explicitly solving disk self-gravity in two dimensions. The current model is an extension of the one-dimensional layered accretion disk model of Bae et al. We find that gravitational instability (GI)-induced spiral density waves heat disks via compressional heating (i.e., PdV work), and can trigger accretion outbursts by activating the magnetorotational instability (MRI) in the magnetically inert disk dead zone. The GI-induced spiral waves propagate well inside of the gravitationally unstable region before they trigger outbursts at R ≲ 1 AU where GI cannot be sustained. This long-range propagation of waves cannot be reproduced with the previously used local α treatments for GI. In our standard model where zero dead-zone residual viscosity (α_rd) is assumed, the GI-induced stress measured at the onset of outbursts is locally as large as 0.01 in terms of the generic α parameter. However, as suggested in our previous one-dimensional calculations, we confirm that the presence of a small but finite α_rd triggers thermally driven bursts of accretion instead of the GI + MRI-driven outbursts that are observed when α_rd= 0. The inclusion of non-zero residual viscosity in the dead zone decreases the importance of GI soon after mass feeding from the envelope cloud ceases. During the infall phase while the central protostar is still embedded, our models stay in a "quiescent" accretion phase with {dot}M_acc ∼ 10^–8 - 10^–7 M_☉/yr over 60% of the time and spend less than 15% of the infall phase in accretion outbursts. While our models indicate that episodic mass accretion during protostellar evolution can qualitatively help explain the low accretion luminosities seen in most low-mass protostars, detailed tests of the mechanism will require model calculations for a range of protostellar masses with some constraint on the initial core angular momentum, which affects the length of time spent in a quasi-steady disk accretion phase.