The Physics of Protoneutron Star Winds: Implications for r-Process Nucleosynthesis

We solve the general-relativistic steady-state eigenvalue problem of neutrino-driven protoneutron star winds, which immediately follow core-collapse supernova explosions. We provide velocity, density, temperature, and composition profiles and explore the systematics and structures generic to such a wind for a variety of protoneutron star characteristics. Furthermore, we derive the entropy, dynamical timescale, and neutron-to-seed ratio in the general relativistic framework essential in assessing this site as a candidate for $r$-process nucleosynthesis. Generally, we find that for a given mass outflow rate ($\dot{M}$), the dynamical timescale of the wind is significantly shorter than previously thought. We argue against the existence or viability of a high entropy ($\gtrsim300$ per k$_{\rm B}$ per baryon), long dynamical timescale $r$-process epoch. In support of this conclusion, we model the protoneutron star cooling phase, calculate nucleosynthetic yields in our steady-state profiles, and estimate the integrated mass loss. We find that transonic winds enter a high entropy phase only with very low $\dot{M}$ ($\lesssim1\times10^{-9}$ M$_\odot$ s$^{-1}$) and extremely long dynamical timescale ($\tau_\rho\gtrsim0.2$ seconds). Our results support the possible existence of an early $r$-process epoch at modest entropy ($\sim150$) and very short dynamical timescale, consistent in our calculations with a very massive or very compact protoneutron star that contracts rapidly after the preceding supernova. We explore possible modifications to our models, which might yield significant $r$-process nucleosynthesis generically. Finally, we speculate on the effect of fallback and shocks on both the wind physics and nucleosynthesis.