The neutrino fast flavor instability: solving the mean-field equations with angular moments

Multi-Messenger-Astrophysics (MMA) events produce a wealth of data. These enormous datasets will reveal new insights into the physics of core collapse supernovae, neutron star mergers, and other objects where it is actually possible, if not probable, that new physics is in operation. To tease out these intriguing possibilities, we will need to analyze signals from photons, gravitational waves, chemical elements, and neutrinos. This task is made all the more difficult when it is necessary to evolve the neutrino component of the radiation field and associated quantum-mechanical property of flavor in order to model the astrophysical system of interest --- a numerical challenge at the forefront of MMA. We take a step in this direction by adopting the technique of angular-integrated moments with a truncated tower of dynamical equations and a closure, convolving the flavor-transformation with spatial transport to evolve the neutrino radiation quantum field. Using the FLASH hydrodynamics code, we show that our moment scheme captures the dynamical features of fast flavor instabilities in a variety of systems, although our technique is by no means a universal blueprint for solving fast flavor transformation. We highlight the success and challenges of our method, while proposing improvements for future work.