Production of Mo and Ru isotopes in neutrino-driven winds: implications for solar abundances and presolar grains

The origin of the so-called $p$-isotopes $^{92,94}\mathrm{Mo}$ and $^{96,98}\mathrm{Ru}$ in the solar system remains a mystery as several astrophysical scenarios fail to account for them. In addition, data on presolar silicon carbide grains of type X (SiC X) exhibit peculiar Mo patterns, especially for $^{95,97}\mathrm{Mo}$. We examine production of Mo and Ru isotopes in neutrino-driven winds associated with core-collapse supernovae (CCSNe) over a wide range of conditions. We find that proton-rich winds can make dominant contributions to the solar abundance of $^{98}\mathrm{Ru}$, significant contributions to those of $^{96}$Ru ($\lesssim 40\%$) and $^{92}$Mo ($\lesssim 27\%$), and relatively minor contributions to that of $^{94}$Mo ($\lesssim 14\%$). In contrast, neutron-rich winds make negligible contributions to the solar abundances of $^{92,94}$Mo and cannot produce $^{96,98}$Ru. However, we show that some neutron-rich winds can account for the peculiar Mo patterns in SiC X grains. Our results can be generalized if conditions similar to those studied here are also obtained for other types of ejecta in either CCSNe or neutron star mergers.