Gardening on the Moon: An Advection-Diffusion Model to Guide the Search for Supernova Debris in the Lunar Regolith

The vertical redistribution of materials in the lunar regolith-ranging from continuously produced space-weathering products to sporadic pulses of supernova- or kilonova-derived isotopes-remains a fundamental problem in planetary science. We present a unified stochastic model of regolith gardening induced by the impact flux. Treating gardening as a competition between impact-driven advection and diffusion predicts the maturity profiles of Apollo cores over more than 2 orders of magnitude in time (1.4×10^{7} to 4.5×10^{8} yr). This model describes well the depth profiles of live ^{60}Fe in Apollo regolith samples, suggesting that supernova dust capture is independent of native iron abundance, and is consistent with a uniform influx at the latitudes of the Apollo landing sites. We extend our model to predict lunar signals for live r-process species that might originate from supernovae or kilonovae: ^{244}Pu tied to terrestrial detections, and ^{129}I, ^{182}Hf, and ^{247}Cm based on r-process calculations. The ^{244}Pu/^{60}Fe depth profile can probe the origin of ^{244}Pu, motivating searches in Artemis regolith samples down to depths O(100) cm.