Protostellar disks are the ubiquitous corollary outcome of the angular momentum conserving, gravitational collapse of molecular cloud cores into stars. Disks are an essential component of the star formation process, mediating the accretion of material onto the protostar, and for redistributing excess angular momentum during the collapse. We present a model to explain the observed correlation between mass accretion rates and stellar mass that has been inferred from observations of intermediate to upper mass T Tauri stars. We explain this correlation within the framework of gravitationally driven torques parameterized in terms of Toomre’s Q criterion. Our models reproduce both the observed correlation and spread in the accretion rate--protostellar mass relation, as has been observed for protostars with masses of 0.2 \u3c M \u3c 3.0 solar masses, such as those found in the Rho Ophiuchus and Taurus star forming regions.
We also examine the formation and long-term evolution of primordial protostellar disks harbored by the first stars (Population III stars), using 2+1D numerical hydrodynamics simulations in the thin-disk limit. The disks that form in the primordial environment are very massive and subject to vigorous fragmentation. Fragments torqued inward due to gravitational inter- actions with sub-structure within the disk give rise to accretion and luminosity bursts several orders of magnitude above the mean rate---the first evidence for the burst mode of accretion among Population III stars. By considering the cosmological landscape in this epoch, we argue from the Jeans criterion for the existence of clusters of Population III stars. A simultaneity of burst mode accretion events among several cluster members results in fluctuations that are nearly 1000 times greater than the mean cluster luminosity, approaching 109 solar luminosity. This phenomenon arises solely as a result of the gravitational-instability--driven episodic fragmentation and accretion that characterizes this early stage of protostellar evolution. We speculate as to how these extrema may provide a window through which next-generation telescopes will be able to gather observational evidence for the existence of the first stars