On the likelihood of supernova enrichment of protoplanetary disks

We estimate the likelihood of direct injection of supernova ejecta into protoplanetary disks using a model in which the number of stars with disks decreases linearly with time, and clusters expand linearly with time such that their surface density is independent of stellar number. The similarity of disk dissipation and main sequence lifetimes implies that the typical supernova progenitor is very massive, ~ 75-100 Msun. Such massive stars are found only in clusters with > 10^4 members. Moreover, there is only a small region around a supernova within which disks can survive the blast yet be enriched to the level observed in the Solar System. These two factors limit the overall likelihood of supernova enrichment of a protoplanetary disk to < 1%. If the presence of short lived radionucleides in meteorites is to be explained in this way, however, the Solar System most likely formed in one of the largest clusters in the Galaxy, more than two orders of magnitude greater than Orion, where multiple supernovae impacted many disks in a short period of time.