Evaluating Approximate Flavor Instability Metrics in Neutron Star Mergers

Neutrinos can rapidly change flavor in the inner dense regions of core-collapse supernovae and neutron star mergers due to the neutrino fast flavor instability. If the amount of flavor transformation is significant, the FFI could significantly affect how supernovae explode and how supernovae and mergers enrich the universe with heavy elements. Since many state of the art supernova and merger simulations rely on neutrino transport algorithms based on angular moments of the radiation field, there is incomplete information with which to determine if the distributions are unstable to the FFI. In this work we test the performance of several proposed moment-based instability tests in the literature. We perform time-independent general relativistic neutrino transport on a snapshot of a 3D neutron star merger simulation to generate reasonable neutrino distributions and check where each of these criteria correctly predict instability. In addition, we offer a new ``maximum entropy'' instability test that is somewhat more complex, but offers more detailed (though still approximate) estimates of ELN crossing width and depth. We find that this maximum entropy test and the resonant trajectory test are particularly accurate at predicting instability in this snapshot, though all tests predict instability where significant flavor transformation is most likely.