Radioactive probes of the supernova-contaminated solar nebula: Evidence that the Sun was born in a cluster

We construct a simple model for radioisotopic enrichment of the protosolar nebula by injection from a nearby supernova, based on the inverse square law for ejecta dispersion. In this parameter study, the presolar radioisotopic abundances (i.e., in solar masses) demand a nearby supernova: its distance D can be no larger than 66 times the radius of the protosolar nebula, at a 90% confidence level, assuming 1 M-circle dot of protosolar material. The relevant size of the nebula depends on its state of evolution at the time of radioactivity injection. In one scenario, a collection of low-mass stars, including our Sun, formed in a group or cluster with a high-mass star that ended its life as a supernova while our Sun was still a protostar, a starless core, or perhaps a diffuse cloud. Using recent observations of protostars to estimate the size of the protosolar nebula constrains the distance of the supernova to D similar to 0.02-1.6 pc. This supernova distance limit is consistent with the scales of low-mass star formation around one or more massive stars, but it is closer than expected were the Sun formed in an isolated, solitary state. Consequently, if any presolar radioactivities originated via supernova injection, we must conclude that our Sun was a member of such a group or cluster that has since dispersed; thus, solar system formation should be understood in this context. The temporal choreography from supernova ejecta to meteorites is important, as the modeled timescale is <= 1.8Myr. Finally, the model does not distinguish between progenitor masses from 15 to 25 M-circle dot, although the 20 M-circle dot model is somewhat preferred.