$\nu p$-process in Core-Collapse Supernovae: Imprints of General Relativistic Effects

The origin of a number of proton-rich isotopes in the solar system has been a long-standing puzzle. A promising explanation is the $\nu p$-process, which is posited to operate in the neutrino-driven outflows that form inside core-collapse supernovae after shock revival. While recent studies have analyzed several relevant physical effects that influence the efficiency of this process, the impact of General Relativity (GR) on it remains unexplored. We perform a comparative analysis of the time-integrated $\nu p$-process yields in Newtonian and fully GR calculations, using detailed models of time-evolving outflow profiles. The GR effects are seen to suppress the production of seed nuclei, significantly boosting the resulting $p$-nuclide abundances. Our reference GR model, with an 18~$M_\odot$ progenitor, reproduces both the relative and absolute solar system abundances of the entire set of the $p$ nuclides in the mass range $74\leq A\leq102$. The yields are suboptimal in our 12.75~$M_\odot$ GR model, where the outflow transitions to the supersonic regime several seconds into the explosion, suppressing further $p$-nuclide production. In both models, most of the production of the crucial $^{92,94}{\rm Mo}$ and $^{96,98}{\rm Ru}$ $p$ isotopes occurs relatively early, 1--3 seconds after shock revival. In contrast, a large fraction of the shielded isotope $^{92}{\rm Nb}$ is produced in the subsequent ejecta. The impact of GR on this isotope is especially large, with its final abundance boosted by a factor of 25 compared to a Newtonian calculation. In summary, with the GR effects taken into account, the $\nu p$-process in a sufficiently massive progenitor can provide a unifying explanation for the origin of all $p$ nuclei in the solar system up to $^{102}$Pd.