R-process heating implementation in hydrodynamic simulations with neural networks

Neutron-rich outflows in neutron-star mergers (NSMs) or other explosive events can be subject to substantial heating through the release of rest-mass energy in the course of the rapid neutron-capture (r-) process. This r-process heating can potentially have a significant impact on the dynamics determining the velocity distribution of the ejecta, but due to the complexity of detailed nuclear networks required to describe the r-process self-consistently, hydrodynamic models of NSMs often neglect r-process heating or include it using crude parametrizations. In this work, we present a conceptually new method, RHINE, for emulating the r-process and concomitant energy release in hydrodynamic simulations via machine-learning algorithms. The method requires the evolution of only a few additional quantities characterizing the composition, of which the nuclear rates of change are obtained at each location and time step from neural networks trained by a large set of trajectories from full nuclear-network calculations. The scheme is tested by comparing spherically symmetric wind simulations and long-term simulations of NSMs using RHINE with post-processing results from nucleosynthesis calculations, showing agreement in the released heating energy to within <10%. In our NSM models on average about 2.3MeV, 0.7MeV, and 2.1MeV are released per baryon in dynamical ejecta, NS-torus ejecta, and black-hole (BH) torus ejecta, respectively. The strongest velocity boost is observed for BH-torus ejecta, which also become 40% more massive with r-process heating. The nucleosynthesis yields are only mildly affected by r-process heating, but the kilonova gets significantly brighter once the BH-torus ejecta become visible. RHINE can be readily implemented in existing hydrodynamics codes using pre-trained machine-learning data and routines for source-term prediction that we provide online.