The late Miocene $^{10}$Be anomaly and the possibility of a supernova

Recent measurements of cosmogenic $^{10}$Be in deep-ocean ferromanganese crusts from the Central and Northern Pacific have revealed an anomalous concentration between 11.5 and 9.0 Myr ago, peaking at 10.1 Myr. One possible explanation is a nearby supernova (SN) event. Motivated by this and by the proximity of the Solar System to the Orion star-forming region during that period, we estimate the probability that at least one SN occurred between the onset and peak of the anomaly. Using an open cluster catalog based on Gaia DR3, we trace back the orbits of 2725 clusters and the Sun over the past 20 Myr and compute the expected number of SN events. We find 19 clusters with a probability greater than 1% each of producing at least one SN within 100 pc of the Sun in the time interval 11.5-10.1 Myr ago. The total cumulative probability exceeds zero at 35 pc from the Sun and increases rapidly with distance, reaching 68% near 100 pc. Two young clusters dominate the SN probability: ASCC 20 contributes most within 70 pc, while OCSN 61 becomes more significant beyond that distance. Our results support the plausibility of a SN origin for the $^{10}$Be anomaly and highlight the importance of additional $^{10}$Be records from independent terrestrial archives to determine whether the anomaly is of astrophysical or terrestrial origin.