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

TL;DR

This work addresses the uncertain astrophysical origins of the r-process by employing a site-independent, parametric Galactic chemical evolution model and an expansive grid that varies Eu yield per event, event rate, delay time, and progenitor mass range. It uses a multi-objective Pareto-front optimization to fit multiple neutron-capture element trends simultaneously, revealing trade-offs and highlighting the limitations of solar-like scaling for lighter elements. The results indicate that rapid enrichment from relatively low-mass progenitors is favored, and that a single class of r-process events cannot explain both light and heavy neutron-capture elements, requiring at least two components with potentially metallicity-dependent scaling. These findings refine our understanding of r-process sites and have implications for interpreting the chemical evolution history of the Milky Way.

Abstract

The astrophysical site(s) of the r-process are uncertain, with candidates such as neutron star mergers and magneto-rotational supernovae predicting different event rates, delay times, and heavy-element yields. Galactic chemical evolution models constrain these properties by comparing model predictions with observed abundances. We explore, in a systematic and data-driven way, the astrophysical conditions under which r-process enrichment can reproduce the observed trends of multiple neutron-capture elements in the Milky Way. Rather than assuming a fixed site, we adopt a flexible, parametric approach to test whether a common set of r-process parameters can explain the chemical evolution of several heavy elements. We compute a grid of one-infall, homogeneous models varying: Eu yield per event, r-process event rate, enrichment delay time, and progenitor mass range. For each of the $\sim 1.5 \times 10^5$ models, we predict [X/Fe] vs. [Fe/H] trends by scaling Eu yields with the solar r-process pattern. A multi-objective optimisation based on Pareto fronts identifies models that best reproduce the abundance trends. Best-fitting models favour short delay times ($\leq 30\ \rm Myr$), low-mass progenitors ($\sim 20-25\ \rm M_\odot$), and an effective Eu injection of $\sim 2 \times 10^{-7}\ \rm M_\odot$ per event. Stars more massive than $\sim 80\ \rm M_\odot$ are too rare to dominate the enrichment. While heavy elements can be reproduced, lighter ones show stronger conflicts with Eu, reflecting that the solar r-process scaling relation becomes less valid toward lighter elements. No single class of r-process events, under solar-scaled yields, can explain light and heavy neutron-capture elements; at least two components are required: a main r-process consistent with solar and r-rich stars, and a weaker component producing enhanced light r-process elements, similar to that observed in r-poor stars.

Figures (16)

• Figure 1: Lodders2009 total solar abundances of neutron-capture elements (grey dots) with the corresponding r-, s- and p-process fractions (yellow, cyan and magenta diamonds, respectively) from Prantzos2020. Also shown are the chemical evolution model predictions for the s-process component for the subset of elements included in this work (cyan crosses).
• Figure 2: [Eu/Fe] vs. [Fe/H] predicted model curves (left column) for fixed combinations of three out of the four input parameters $(Y_{\rm Eu,\rm r},\ \alpha,\ [M_{\rm l}, M_{\rm u}],\ \tau)$, shown alongside the corresponding $\chi^2_{\rm Eu}$ values as a function of the fourth parameter (right column). In the left column, curve colours indicate the associated $\chi^2_{\rm Eu}$ values.
• Figure 3: Left panel: observed and predicted [Eu/Fe] vs. [Fe/H] trends. Grey circles with error bars show the average observational values in metallicity bins. The solid green curve shows the predicted [Eu/Fe] vs. [Fe/H] trend for the best-fitting model, while the surrounding lighter green lines represents the range spanned by models within the top 100, providing an indication of the model uncertainty. The lower, blue line represents the result of the model in case there is only the s-process contribution. The bottom panel shows the residuals between the binned observations and the model. Right panel: corner plot showing the marginal distributions (diagonal panels) and pairwise correlations (off-diagonal panels) of the parameters $(Y_{\rm Eu,\rm r},\ \alpha,\ [M_{\rm l}, M_{\rm u}],\ \tau)$ for the 100 models with the lowest $\chi^2_{\rm Eu}$. Dashed yellow lines indicate the values of the best-fitting model, with the corresponding numerical values reported above each marginal distribution, and the yellow star marks its position in each correlation plot.
• Figure 4: Observed and predicted [X/Fe] vs. [Fe/H] trends for Sr, Y, Zr and Ba, La, Ce. Solid green curves shows the predicted trend for the best-fitting [Eu/Fe] vs. [Fe/H] trend, while lighter green lines represents that range spanned by models within the top 100. The lower, light blue lines represent the results of the model in case there is only the s-process contribution. Symbols for the observational data are the same as in Figure \ref{['fig: best models EuFe vs FeH']}.
• Figure 5: Reduced $\chi^2$ values for [Eu/Fe] vs. [Fe/H] and [Zr/Fe] vs. [Fe/H]. Grey points show all computed models, while magenta points highlight the Pareto-optimal solutions for the Eu–Zr pair, corresponding to the lower-left boundary of the objective space. The zoomed plot shows the low–$\chi^2$ region, where the optimal compromise between $\chi^2_{\mathrm{Eu}}$ and $\chi^2_{\mathrm{Zr}}$ is located (yellow star).