Residence Times of Particles in Diffusive Protoplanetary Disk Environments II. Radial Motions and Applications to Dust Annealing

The origin of crystalline grains in comets and the outer regions of protoplanetary disks remains a mystery. It has been suggested that such grains form via annealing of amorphous precursors in the hot, inner region of a protoplanetary disk, where the temperatures needed for such transformations were found, and were then transported outward by some dynamical means. Here we develop a means of tracking the paths that dust grains would have taken through a diffusive protoplanetary disk and examine the types and ranges of environments that particles would have seen over a 10$^{6}$ year time period in the dynamic disk. We then combine this model with three annealing laws to examine how the dynamic evolution of amorphous grains would have led to their physical restructuring and their delivery to various regions of the disk. It is found that "sibling particles"-- those particles that reside at the same location at a given period of time--take a wide range of unique and independent paths through the disk to arrive there. While high temperatures can persist in the disk for very long time periods, we find that those grains which are delivered to the cold outer regions of the disk are largely annealed in the first few $\times10^{5}$ yrs of disk history. This suggests that the crystallinity of grains in the outer disk would be determined early and remain unchanged for much of disk history, in agreement with recent astronomical observations.