Constraining the Delay Time Distribution of the r- and s-Process from Stellar Ages at Solar Metallicity

We present a new approach to constraining the delay time distribution (DTD) governing r- and s-process element production. Rather than using metallicity as a proxy for time, we work directly with stellar ages at solar metallicity, where chemical equilibrium models are most applicable. We analyze two complementary samples: more than 10,000 red clump (RC) thin disk stars at solar metallicity from LAMOST, and solar twins with high-precision abundances; both have well-determined stellar ages τ. We fit chemical-equilibrium models with power-law DTDs to the evolution of [Eu/Mg] (τ) and [Ba/Mg] (τ) in each sample, taking europium as a canonical r-process element and barium as an s-process element, each referenced to magnesium as a near-instantaneous, CCSNe-dominated element. To validate the method, we first apply it to [Fe/Mg] (τ) and recover that about!70% of Fe comes from a delayed channel with a declining DTD proportional to t-1.2, in agreement with well-established results for iron production in thermonuclear supernovae. It also shows that about 60% of Eu and Ba forming today originate from strongly-delayed processes, and the inferred delayed-production rates of both Eu and Ba rise with delay time, opposite to that of thermonuclear supernovae. These results provide direct temporal constraints on r- and s-process enrichment, complementary to metallicity-based chemical-evolution studies. Because we model abundance referenced to Mg, and the same trend is recovered across stars of different guiding-center radii, this appears unaffected by radial migration and chemical evolution varying with Galactocentric radius. If confirmed, it points to delayed neutron-capture production beyond NS--NS mergers.