  Providing an accurate modeling of neutrino physics in dense astrophysical
environments such as binary neutron star mergers presents a challenge for
hydrodynamic simulations. Nevertheless, understanding how flavor transformation
can occur and affect the dynamics, the mass ejection, and the nucleosynthesis
will need to be achieved in the future. Computationally expensive, large-scale
simulations frequently evolve the first classical angular moments of the
neutrino distributions. By promoting these quantities to matrices in flavor
space, we develop a linear stability analysis of fast flavor oscillations using
only the first two "quantum" moments, which notably requires generalizing the
classical closure relations that appropriately truncate the hierarchy of moment
equations in order to treat quantum flavor coherence. After showing the
efficiency of this method on a well-understood test situation, we perform a
systematic search of the occurrence of fast flavor instabilities in a neutron
star merger simulation. We discuss the successes and shortcomings of moment
linear stability analysis, as this framework provides a time-efficient way to
design and study better closure prescriptions in the future.
