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 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 \alpha-type viscosity acts to reduce burst frequency and accretion variability, and is likely to not be viable for values of \alpha 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 (\ge 10^{-4} M_sun/yr) as is observed in FU Orionis variables. Between these accretion bursts, the protostar is characterized by a low accretion rate (< 10^{-6} M_sun/yr). During the phase of episodic accretion, the mass of the protostellar disk remains less than or comparable to the mass of the protostar.

We determine the observational signatures of protostellar cores by coupling two-dimensional radiative transfer calculations with numerical hydrodynamical simulations that predict accretion rates that both decline with time and feature short-term variability and episodic bursts caused by disk gravitational instability and fragmentation. We calculate the radiative transfer of the collapsing cores throughout the full duration of the collapse, using as inputs the core, disk, protostellar masses, radii, and mass accretion rates predicted by the hydrodynamical simulations. From the resulting spectral energy distributions, we calculate standard observational signatures (L _bol, T _bol, L _bol/L _smm) to directly compare to observations. We show that the accretion process predicted by these models reproduces the full spread of observed protostars in both L _bol-T _bol and L _bol-M _core space, including very low luminosity objects, provides a reasonable match to the observed protostellar luminosity distribution, and resolves the long-standing luminosity problem. These models predict an embedded phase duration shorter than recent observationally determined estimates (0.12 Myr versus 0.44 Myr), and a fraction of total time spent in Stage 0 of 23%, consistent with the range of values determined by observations. On average, the models spend 1.3% of their total time in accretion bursts, during which 5.3% of the final stellar mass accretes, with maximum values being 11.8% and 35.5% for the total time and accreted stellar mass, respectively. Time-averaged models that filter out the accretion variability and bursts do not provide as good of a match to the observed luminosity problem, suggesting that the bursts are required.

In the last twenty years, the topic of episodic accretion has gained significant interest in the star formation community. It is now viewed as a common, though still poorly understood, phenomenon in low-mass star formation. The FU Orionis objects (FUors) are long-studied examples of this phenomenon. FUors are believed to undergo accretion outbursts during which the accretion rate rapidly increases from typically $10^{-7}$ to a few $10^{-4}$ $M_\odot$ yr$^{-1}$, and remains elevated over several decades or more. EXors, a loosely defined class of pre-main sequence stars, exhibit shorter and repetitive outbursts, associated with lower accretion rates. The relationship between the two classes, and their connection to the standard pre-main sequence evolutionary sequence, is an open question: do they represent two distinct classes, are they triggered by the same physical mechanism, and do they occur in the same evolutionary phases? Over the past couple of decades, many theoretical and numerical models have been developed to explain the origin of FUor and EXor outbursts. In parallel, such accretion bursts have been detected at an increasing rate, and as observing techniques improve each individual outburst is studied in increasing detail. We summarize key observations of pre-main sequence star outbursts, and review the latest thinking on outburst triggering mechanisms, the propagation of outbursts from star/disk to disk/jet systems, the relation between classical EXors and FUors, and newly discovered outbursting sources -- all of which shed new light on episodic accretion. We finally highlight some of the most promising directions for this field in the near- and long-term.Comment: 24 pages, 8 figures. Accepted for publication as a review chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Hennin