Neutrino flavor instabilities in neutron star mergers with moment transport: slow, fast, and collisional modes

TL;DR

This work extends a moment-based linear stability analysis to multi-energy neutrino systems in neutron star mergers, incorporating vacuum and collision terms to capture slow, collisional, and fast flavor instabilities. By applying the framework to a 7 ms post-merger NSM snapshot from the M1-NuLib simulation, the authors compare full multi-energy results with energy-averaged methods (two schemes: A for gapped modes and B for gapless modes), finding that NSM environments admit both gapped and gapless CFIs and that energy-averaged descriptions can be accurate when used with the appropriate mode classification and a combined estimate. Including anisotropies reveals that fast instabilities often dominate near the HMNS, but collisional and slow modes become relevant in tidal arms and at large distances, with slow modes enhanced by anisotropies; many-body corrections and scattering have modest impact on the instability landscape. The study provides practical guidance for incorporating flavor instabilities in large-scale NSM simulations, showing when monochromatic closures are reliable and highlighting the need for nonlocal closures and self-consistent evolution to capture the full nonlinear outcome.

Abstract

Determining where, when, and how neutrino flavor oscillations must be included in large-scale simulations of hot and dense astrophysical environments is an enduring challenge that must be tackled to obtain accurate predictions. Using an angular moment-based linear stability analysis framework, we examine the different kinds of flavor instabilities that can take place in the context of the post-processing of a neutron star merger simulation, with a particular focus on the collisional flavor instability and a careful assessment of several commonly used approximations. First, neglecting anisotropies of the neutrino field, we investigate the extent to which commonly used monoenergetic growth rates reproduce the results obtained from a full multi-energy treatment. Contrary to the large discrepancies found in core-collapse supernova environments, we propose a simple combination of energy-averaged estimates that reproduces the multi-energy growth rates in our representative simulation snapshot. We then quantify the impact of additional physical effects, including nuclear many-body corrections, scattering opacities, and the inclusion of the vacuum term in the neutrino Hamiltonian. Finally, we include the neutrino distribution anisotropies, which allows us to explore, for the first time in a multi-energy setting, the interplay between collisional, fast, and slow modes in a moment-based neutron star merger simulation. We find that despite a dominance of the fast instability in most of the simulation volume, certain regions only exhibit a collisional instability, while others, especially at large distances, exhibit a slow instability that is largely underestimated if anisotropic effects are neglected.

Figures (16)

• Figure 1: Data from the transverse slice at $Y = 0$ in the $7 \, \mathrm{ms}$ postmerger snapshot of the "M1-NuLib" simulation in Foucart:2024npn. Top left: ratio of $\nu_e$ and $\bar{\nu}_e$ number densities. Bottom left: ratio of $\nu_x$ and $\nu_e$ number densities. Top right: ratio of the effective temperatures (i.e., average energies) of $\nu_x$ and $\nu_e$, with matter density contours shown in blue (from the innermost to the outermost: $\{10^{14},10^{12},10^{11},10^{10}\} \, \mathrm{g \, cm^{-3}}$). Bottom right: comparison of the energy-averaged absorption rates defined in Eq. \ref{['eq:methodB']}, showing the higher interaction rates of neutrinos over antineutrinos.
• Figure 2: Result of the multi-energy homogeneous and isotropic LSA, without the vacuum term in the QKEs. Top: growth rate of the instability. Bottom: real part of the eigenfrequency of the fastest growing mode, enabling the identification of regions of gapless and gapped CFI. The point marked with an orange star, in the middle of the gapless region, is studied in Appendix \ref{['app:compareWang']} and Sec. \ref{['subsec:examples']}.
• Figure 3: Comparison of various determination of the isotropic and homogeneous CFI growth rate: multi-energy analysis (top left), single-energy analysis with averaged collision rates via method A (top right) and method B (bottom right). Two colormaps are used for the gapped (blue) and gapless (orange) modes. On the bottom left panel, the combination of monochromatic results \ref{['eq:combination_minusA_plusB']} shows excellent agreement with the multi-energy results.
• Figure 4: Sign of the sum of the energy-averaged damping rates $\langle \Gamma \rangle_\mathrm{A} + \langle \overline{\Gamma} \rangle_\mathrm{A}$ for the same slice as Fig. \ref{['fig:isotropic_CFI_allmethods']}.
• Figure 5: Cumulative distribution function of the relative difference between the CFI growth rates obtained with method A (evaluated on gapped modes) or method B (evaluated on gapless modes), and the multi-energy result.