Supernova enrichment of planetary systems in low-mass star clusters

The presence and abundance of short lived radioisotopes (SLRs) $^{26}$Al and $^{60}$Fe in chondritic meteorites implies that the Sun formed in the vicinity of one or more massive stars that exploded as supernovae (SNe). Massive stars are more likely to form in massive star clusters ($>$1000 M$_{\odot}$) than lower mass clusters. However, photoevaporation of protoplanetary discs from massive stars and dynamical interactions with passing stars can inhibit planet formation in clusters with radii of $\sim$1 pc. We investigate whether low-mass (50 - 200 M$_{\odot}$) star clusters containing one or two massive stars are a more likely avenue for early Solar system enrichment as they are more dynamically quiescent. We analyse $N$-body simulations of the evolution of these low-mass clusters and find that a similar fraction of stars experience supernova enrichment than in high mass clusters, despite their lower densities. This is due to two-body relaxation, which causes a significant expansion before the first supernova even in clusters with relatively low (100 stars pc$^{-3}$) initial densities. However, because of the high number of low mass clusters containing one or two massive stars, the absolute number of enriched stars is the same, if not higher than for more populous clusters. Our results show that direct enrichment of protoplanetary discs from supernovae occurs as frequently in low mass clusters containing one or two massive stars (>20 M$_{\odot}$) as in more populous star clusters (1000 M$_\odot$). This relaxes the constraints on the direct enrichment scenario and therefore the birth environment of the Solar System.