Code comparison for fast flavor instability simulations

The fast flavor instability (FFI) is expected to be ubiquitous in core-collapse supernovae and neutron star mergers. It rapidly shuffles neutrino flavor in a way that could impact the explosion mechanism, neutrino signals, mass outflows, and nucleosynthesis. The variety of initial conditions and simulation methods employed in simulations of the FFI prevent an apples-to-apples comparison of the results. We simulate a standardized test problem using five independent codes and verify that they are all faithfully simulating the underlying quantum kinetic equations under the assumptions of axial symmetry and homogeneity in two directions. We quantify the amount of numerical error in each method and demonstrate that each method is superior in at least one metric of this error. We make the results publicly available to serve as a benchmark.

Figure 1

Domain-integrated survival property (top panel) and transition probability (bottom panel) as a function of time. The initial perturbations grow exponentially until the instability saturates at $t\approx 1300{\mu }^{-1}$. All simulations show the same instability growth rate, saturation time, saturation amplitude, and late-time equilibrium.

Figure 2

Space-integrated polarization vector components as a function of direction at $t=5000{\mu }^{-1}$. The vertical dashed line at $u=0.786$ shows the location of the ELN crossing in the initial distribution. All simulations agree on the distribution of neutrino flavor to the left of the crossing and show near complete mixing to the right of the crossing. All simulations agree on the magnitude of the flavor off-diagonal components at the end of the simulation.

Figure 3

Fourier power spectrum of the flavor-coherent off-diagonal component of the neutrino number density $n_{ex}$ at $t=0$ (dotted) and $t=5000$ (solid). All simulations are seeded with the same spectrum of perturbations but with random phases, and all simulations agree on the location of the peak and the slope of the exponential tails at late times. The horizontal bands are a result of numerical error.

Figure 4

Deviation of the domain-integrated electron lepton number from its initial value, as defined in Eq. (12). The SU(2) symmetry of the Hamiltonian guarantees that this remains at zero, so nonzero values reflect numerical error. All codes exhibit excellent ELN conservation to better than one part in ${10}^6$.

Figure 5

Maximum deviation of the flavor vector length from unity. The Hermitian nature of the Hamiltonian guarantees that this remains at zero. Nonzero values reflect numerical error, especially in the advection terms. There are few emu data points, resulting from infrequent output of the storage-intensive particle data.