Constraining r-process nucleosynthesis with multi-objective Galactic chemical evolution models

The astrophysical site(s) of the rapid neutron-capture process (r-process) remains uncertain, with competing scenarios such as neutron star mergers and magneto-rotational supernovae offering different predictions for the timing, frequency, and yield for heavy elements pollution. Galactic chemical evolution models provide an important tool to constrain these properties by comparing model predictions to the observed abundance of neutron-capture elements across different metallicities. Our aim is to explore, in a systematic and data-driven manner, the range of astrophysical conditions under which the r-process enrichment can reproduce the observed trends of multiple neutron-capture elements in the Milky Way. Rather than assuming a fixed physical site, we adopted a flexible parametric approach to assess whether a common set of r-process parameters can simultaneously explain the chemical evolution of several heavy elements of interest. We constructed a grid of one-infall homogeneous Galactic chemical evolution models varying four key parameters: the Eu r-process yield per event, the rate of r-process-producing events, the delay time before enrichment, and the progenitor star mass range. For each of the ∼ 1.5 versus 10^5 models, we computed the predicted X/Fe Fe/H trends for several neutron-capture elements, obtained by scaling Eu yields with the solar r-process pattern, and we evaluated the model performance using ̧hi^2 statistics. A multi-objective optimisation approach based on Pareto front analysis was used to identify models that best reproduce the observed abundance trends across multiple neutron-capture elements simultaneously. The best models consistently favour short delay times (łeq 30 ̊m Myr), low-mass progenitors (∼ 20-25 ̊m M_⊙), and an effective Eu injection rate of ∼ 2 10^ -7 ̊m M_⊙ per event. Stars more massive than ∼ 80 ̊m M_⊙ are too rare to account for the observed r-process enrichment alone, and therefore they cannot be the only source. While heavier neutron-capture elements (Ba, La, Ce) can be simultaneously reproduced within the Pareto-optimal set, the lighter ones (Sr, Y, Zr) present stronger conflicts with Eu, leading to systematically larger distances from the ideal solution. This tension reflects the fact that the solar r-process scaling relation, used to extend Eu yields to other elements, becomes progressively less valid towards lighter neutron-capture elements. Our results suggest that no single class of r-process events under solar-scaled yields can simultaneously account for the chemical evolution of both light and heavy neutron-capture elements. Instead, at least two distinct scaling components appear necessary: one corresponding to the main r-process, similar to the solar and r-process rich star patterns, and another weak component with enhanced production of lighter r-process elements, similar to that observed in r-process poor stars.