Convective-reactive proton-¹²C combustion in Sakurai's object (V4334 Sagittarii) and implications for the evolution and yields from the first generations of stars

Depending on mass and metallicity as well as evolutionary phase, stars occasionally experience convective-reactive nucleosynthesis episodes. We specifically investigate the situation when nucleosynthetically unprocessed, H-rich material is convectively mixed with an He-burning zone, for example in a convectively unstable shell on top of electron-degenerate cores in asymptotic giant branch stars, young white dwarfs, or X-ray bursting neutron stars. Such episodes are frequently encountered in stellar evolution models of stars of extremely low or zero metal content, such as the first stars. We have carried out detailed nucleosynthesis simulations based on stellar evolution models and informed by hydrodynamic simulations. We focus on the convective-reactive episode in the very late thermal pulse star Sakurai's object (V4334 Sagittarii). Asplund et al. determined the abundances of 28 elements, many of which are highly non-solar, ranging from H, He, and Li all the way to Ba and La, plus the C isotopic ratio. Our simulations show that the mixing evolution according to standard, one-dimensional stellar evolution models implies neutron densities in the He intershell (≤ few 10¹¹ cm^-3) that are too low to obtain a significant neutron capture nucleosynthesis on the heavy elements. We have carried out three-dimensional hydrodynamic He-shell flash convection simulations in 4π geometry to study the entrainment of H-rich material. Guided by these simulations we assume that the ingestion process of H into the He-shell convection zone leads only after some delay time to a sufficient entropy barrier that splits the convection zone into the original one driven by He burning and a new one driven by the rapid burning of ingested H. By making such mixing assumptions that are motivated by our hydrodynamic simulations we obtain significantly higher neutron densities (∼ few 10¹⁵ cm ^-3) and reproduce the key observed abundance trends found in Sakurai's object. These include an overproduction of Rb, Sr, and Y by about two orders of magnitude higher than the overproduction of Ba and La. Such a peculiar nucleosynthesis signature is impossible to obtain with the mixing predictions in our one-dimensional stellar evolution models. The simulated Li abundance and the isotopic ratio ¹²C/¹³C are as well in agreement with observations. Details of the observed heavy element abundances can be used as a sensitive diagnostic tool for the neutron density, for the neutron exposure and, in general, for the physics of the convective-reactive phases in stellar evolution. For example, the high elemental ratio Sc/Ca and the high Sc production indicate high neutron densities. The diagnostic value of such abundance markers depends on uncertain nuclear physics input. We determine how our results depend on uncertainties of nuclear reaction rates, for example for the ¹³C(α, n)¹⁶O reaction.