Constraining supernova equations of state with equilibrium constants from heavy-ion collisions

Cluster formation is a fundamental aspect of the equation of state (EOS) of warm and dense nuclear matter such as can be found in supernovae (SNe). Similar matter can be studied in heavy-ion collisions (HICs). We use the experimental data of Qin et al. [Phys. Rev. Lett. 108, 172701 (2012)] to test calculations of cluster formation and the role of in-medium modifications of cluster properties in SN EOSs. For the comparison between theory and experiment we use chemical equilibrium constants as the main observables. This reduces some of the systematic uncertainties and allows deviations from ideal gas behavior to be identified clearly. In the analysis, we carefully account for the differences between matter in SNe and HICs. We find that, at the lowest densities, the experiment and all theoretical models are consistent with the ideal gas behavior. At higher densities ideal behavior is clearly ruled out and interaction effects have to be considered. The contributions of continuum correlations are of relevance in the virial expansion and remain a difficult problem to solve at higher densities. We conclude that at the densities and temperatures discussed mean-field interactions of nucleons, inclusion of all relevant light clusters, and a suppression mechanism of clusters at high densities have to be incorporated in the SN EOS.