We present new numerical simulations in the thin-disk approximation which characterize the burst mode of protostellar accretion. The burst mode begins upon the formation of a centrifugally balanced disk around a newly formed protostar. It is comprised of prolonged quiescent periods of low accretion rate (typically $\la 10^{-7} \Msun$ yr$^{-1}$) which are punctuated by intense bursts of accretion (typically $\ga 10^{-4} \Msun$ yr$^{-1}$, with duration $\la 100$ yr) during which most of the protostellar mass is accumulated. The accretion bursts are associated with the formation of dense protostellar/protoplanetary embryos, which are later driven onto the protostar by the gravitational torques that develop in the disk. Gravitational instability in the disk, driven by continuing infall from the envelope, is shown to be an effective means of transporting angular momentum outward, and mass inward to the protostar. We show that the disk mass always remains significantly less than the central protostar mass throughout this process. The burst phenomenon is robust enough to occur for a variety of initial values of rotation rate, frozen-in (supercritical) magnetic field, and density-temperature relations. Even in cases where the bursts are nearly entirely suppressed, a moderate increase in cloud size or rotation rate can lead to vigorous burst activity. We conclude that most (if not all) protostars undergo a burst mode of evolution during their early accretion history, as inferred empirically from observations of FU Orionis variables.Comment: 39 pages, 14 figures, aastex; will appear in ApJ 20 Oct 2006; version with higher resolution figures available at http://www.astro.uwo.ca/~basu/pb.ht

We revisit our original papers on the burst mode of accretion by incorporating a detailed energy balance equation into a thin-disk model for the formation and evolution of circumstellar disks around low-mass protostars. Our model includes the effect of radiative cooling, viscous and shock heating, and heating due to stellar and background irradiation. Following the collapse from the prestellar phase allows us to model the early embedded phase of disk formation and evolution. During this time, the disk is susceptible to fragmentation, depending upon the properties of the initial prestellar core. Globally, we find that higher initial core angular momentum and mass content favors more fragmentation, but higher levels of background radiation can moderate the tendency to fragment. A higher rate of mass infall onto the disk than that onto the star is a necessary but not a sufficient condition for disk fragmentation. More locally, both the Toomre Q-parameter needs to be below a critical value and the local cooling time needs to be shorter than a few times the local dynamical time. Fragments that form during the early embedded phase tend to be driven into the inner disk regions and likely trigger mass accretion and luminosity bursts that are similar in magnitude to FU-Orionis-type or EX-Lupi-like events. Disk accretion is shown to be an intrinsically variable process, thanks to disk fragmentation, nonaxisymmetric structure, and the effect of gravitational torques. The additional effect of a generic α-type viscosity acts to reduce burst frequency and accretion variability, and is likely to not be viable for values of α significantly greater than 0.01.

We study numerically the evolution of rotating cloud cores, from the collapse of a magnetically supercritical core to the formation of a protostar and the development of a protostellar disk during the main accretion phase. We find that the disk quickly becomes unstable to the development of a spiral structure similar to that observed recently in AB Aurigae. A continuous infall of matter from the protostellar envelope makes the protostellar disk unstable, leading to spiral arms and the formation of dense protostellar/protoplanetary clumps within them. The growing strength of spiral arms and ensuing redistribution of mass and angular momentum creates a strong centrifugal disbalance in the disk and triggers bursts of mass accretion during which the dense protostellar/protoplanetary clumps fall onto the central protostar. These episodes of clump infall may manifest themselves as episodes of vigorous accretion rate (≥ 10 −4 M ⊙ yr −1 ) as is observed in FU Orionis variables. Between these accretion bursts, the protostar is characterized by a low accretion rate (< 10 −6 M ⊙ yr −1 ). During the phase of episodic accretion, the mass of the protostellar disk remains less than or comparable to the mass of the protostar.

We present the latest development of the disk gravitational instability and fragmentation model, originally introduced by us to explain episodic accretion bursts in the early stages of star formation. Using our numerical hydrodynamics model with improved disk thermal balance and star-disk interaction, we computed the evolution of protostellar disks formed from the gravitational collapse of prestellar cores. In agreement with our previous studies, we find that cores of higher initial mass and angular momentum produce disks that are more favourable to gravitational instability and fragmentation, while a higher background irradiation and magnetic fields moderate the disk tendency to fragment. The protostellar accretion in our models is time-variable, thanks to the nonlinear interaction between different spiral modes in the gravitationally unstable disk, and can undergo episodic bursts when fragments migrate onto the star owing to the gravitational interaction with other fragments or spiral arms. Most bursts occur in the partly embedded Class I phase, with a smaller fraction taking place in the deeply embedded Class 0 phase and a few possible bursts in the optically visible Class II phase. The average burst duration and mean luminosity are found to be in good agreement with those inferred from observations of FU-Orionis-type eruptions. The model predicts the existence of two types of bursts: the isolated ones, showing well-defined luminosity peaks separated with prolonged periods (∼ 10 4 yr) of quiescent accretion, and clustered ones, demonstrating several bursts occurring one after another during just a few hundred years. Finally, we estimate that 40%-70% of the star-forming cores can display bursts after forming a star-disk system.