Dynamics and Equation of State Dependencies of Relevance for Nucleosynthesis in Supernovae and Neutron Star Mergers

Neutron stars (NSs) and black holes (BHs) are born when the final collapse of the stellar core terminates the lives of stars more massive than about 9 Msun. This can trigger the powerful ejection of a large fraction of the star's material in a core-collapse supernova (CCSN), whose extreme luminosity is energized by the decay of radioactive isotopes such as 56Ni and 56Co. When evolving in close binary systems, the compact relics of such infernal catastrophes spiral towards each other on orbits gradually decaying by gravitational-wave emission. Ultimately, the violent collision of the two components forms a more massive, rapidly spinning remnant, again accompanied by the ejection of considerable amounts of matter. These merger events can be observed by high-energy bursts of gamma rays with afterglows and electromagnetic transients called kilonovae, which radiate the energy released in radioactive decays of freshly assembled rapid neutron-capture elements. By means of their mass ejection and the nuclear and neutrino reactions taking place in the ejecta, both CCSNe and compact object mergers (COMs) are prominent sites of heavy-element nucleosynthesis and play a central role in the cosmic cycle of matter and the chemical enrichment history of galaxies. The nuclear equation of state (EoS) of NS matter, from neutron-rich to proton-dominated conditions and with temperatures ranging from about zero to ~100 MeV, is a crucial ingredient in these astrophysical phenomena. It determines their dynamical processes, their remnant properties even at the level of deciding between NS or BH, and the properties of the associated emission of neutrinos, whose interactions govern the thermodynamic conditions and the neutron-to-proton ratio for nucleosynthesis reactions in the innermost ejecta. This chapter discusses corresponding EoS dependent effects of relevance in CCSNe as well as COMs. (slightly abridged)