Mixing and Transport in the Solar Nebula
Boss & Vanhala (2000, 2001) prepared reviews of triggered collapse and injection models, using Prudence Foster's finite differences code at very high spatial resolution (440 x 1440 cells) to demonstrate the convergence of the R-T fingers in triggered injection models. A two dimensional hydrodynamical calculation with unprecedentedly high spatial resolution (960 x 2880 zones, or almost 3 million grid points) demonstrated that it suitable shock front can both trigger the collapse of an otherwise stable presolar cloud, and inject shock front particles into the collapsing cloud through the formation of what become Rayleigh-Taylor fingers of compressed fluid layers falling into the gravitational potential well of the growing protostar. These calculations suggest that heterogeneity derived from these R-T fingers will persist down to the scale of their injection onto the surface of the solar nebula. Haghighipour developed a numerical code capable of calculating the orbital evolution of dust grains of varied sizes in a gaseous nebula, subject to Epstein and Stokes drag as well as the self-gravity of the disk. In collaboration with the PI and George W. Wetherill, Haghighipour has been involved in development of a new idea on the possibility of rapid formation of ice giant planets via the disk instability mechanism. Haghighipour studied the stability of a five-body system consisting of the Sun and four protoplanets by numerically integrating their equations of motions. Using Levison and Duncan s SWIFT integrator, Haghighipour showed that, depending on the orbital parameters of the bodies, such a system can be stable for 0.1-10 Myr. Time periods of 1 Myr or more are long enough to be consistent with the time scale proposed for the formation of giant planets by the disk instability mechanism and the photoevaporation of the gaseous envelopes of the outermost protoplanets by a nearby OB star, resulting in the formation of ice giant planets. The PI has used his three dimensional models of marginally gravitationally unstable disks to study the preservation of isotopic heterogeneity in evolving protoplanetary disks. Such heterogeneity might arise from the infall onto the disk s surface of solids processed in the X-wind region of the disk, or derived from stellar nucleosynthesis and injected by R-T fingers. The technique used consists of solving a color equation, identical to the gas continuity equation, which follows the time evolution in three space dimensions of an arbitrarily placed initial color field, i.e., a dye inserted the disk. The models show that significant concentrations of color could persist for time periods of about a thousand years or more, even in the most dynamically active region of such a disk. Such a time period might be long enough for solids to coagulate and grow to significant sizes while retaining the isotopic signature of their birth region in the nebula.