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, similar to 75-100 M-circle dot. Such massive stars are found only in clusters with greater than or similar to 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 less than or similar to 1%. If the presence of shortlived 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 2 orders of magnitude greater than Orion, where multiple supernovae impacted many disks in a short period of time.