Ever since Isaac Newton wrote down the law of gravity, scientists (starting with Newton himself) have known that a large gravitating mass may be prone to fragment into a large number of individually collapsing fragments, that then go on to form stars. In recent years, astronomers have realized that the process of gravitational fragmentation is strongly regulated by magnetic forces (as well as magnetic field dissipation - by ambipolar diffusion in the fragmentation stage) and turbulent motions (as well as turbulent dissipation). Work in our group is one of the few in the world that has solved the equations of non-ideal magnetohydrodynamics to calculate the evolution of such processes as they affect gravitational fragmentation. We have published a comprehensive set of papers on the early stages of star formation, as regulated by these processes. A linear analysis of instability in thin layers ( Ciolek & Basu 2006) yielded the result that the preferred fragmentation scale is a sensitive function of the ambient mass-to-flux ratio, as is the time scale for instability. Numerical simulations of the nonlinear evolution (Basu & Ciolek 2004; Basu et al. 2009a; Basu et al. 2009b) yields definitive quantitative predictions for sizes, shapes, and masses of star-forming "cores", as well as infall speeds and overall morphology of clouds. Moreover, these properties are sensitive functions of the ambient magnetic field strength. The addition of highly turbulent initial conditions leads to yet another set of distinct outcomes. For example, infall speeds at core boundaries are highly supersonic in such cases, but only subsonic in the magnetically-dominated models. These are testable differences. Fig. 1 shows the difference in column density and magnetic field morphology by the time of runaway collapse, for either transcritical (left; dimensionless mass-to-flux ratio &mu0 = 1.0, i.e. the critical value for collapse) or supercritical (right; &mu0 = 2.0) clouds. Both models start out with small-amplitude initial perturbations. We propose that magnetic field curvature, as traced by polarization of dust emission, can measure a cloud's ambient mass-to-flux ratio (Basu et al. 2009a). The above work is done in the limit that the self-gravitating layer is geometrically thin and can be treated as a sheet in many respects. Fully three-dimensional non-ideal magnetohydrodynamic simulations ( Kudoh, Basu, Ogata, and Yabe 2007; Kudoh and Basu 2008) have verified that the main results presented above are generic to the fragmentation process.
The Self-Consistent Formation and Evolution of Circumstellar Disks
In a series of papers (Vorobyov & Basu 2005, 2006, 2007, 2008), we modeled the collapse of a rotating prestellar core past the formation of a central point mass (represented by a central sink cell of size 5-10 AU). The subsequent evolution was followed for several Myr, and we were able to study the evolution of the centrifugal circumstellar disk as it was accreting matter from the envelope, as well as transporting matter to the central sink. Our calculations were the first to explicitly demonstrate the phenomenon of envelope-induced gravitational instability, a process that had been speculated upon in the literature much earlier ( Kenyon et al. 1990). The gravitational instabilities led to the formation of clumps which were subsequently accreted to the center, and provided an explanation for the observed FU Ori burst phenomenon. Fig. 2 (right) shows the time evolution of the accretion rate onto the central sink. In addition to a series of rapid accretion bursts in the early evolution, the residual accretion at late times settles down to a value (~ 10-8Msun yr-1) typical of observed T Tauri disk accretion. A further study (Vorobyov & Basu 2008) shows that a range of residual accretion rates, when compiled for models of different starting masses, can nicely explain the observed dM/dt vs M* correlation. While this empirical agreement with observational data is appealing, a deeper theoretical insight that emerges from this work is that mass flow toward the star is driven (even up to the late stages of disk evolution) by the self-gravitational effect of persistent density inhomogeneities in the disk. These nonaxisymmetric fluctuations persist to late times due to the "swing-amplifier" effect, which is enhanced by the presence of a relatively sharp disk edge.
In recent years, we have pushed forward with a study of a large number of models with varying initial conditions. We find that a sequence of increasing mass and/or angular momentum of the initial cloud core leads to increasing probability of the formation of multiple systems. In Vorobyov & Basu (2010a) we found that some models would result in a disk fragment that could clear a gap in the disk and then maintain a stable orbit (see the sequence of images below). We have now added a more detailed treatment of heating and cooling in the disk (including stellar irradiation) and find that the burst mode is robust (Vorobyov & Basu 2010b). The formation of multiple systems and ejection of low mass companions is occurring in some models. The physics of the burst mode and clump formation/migration scenario is very rich indeed and we expect to explore many more consequences in the years ahead.
