On the characteristics of fast neutrino flavor instabilities in three-dimensional core-collapse supernova models

We assess the occurrence of fast neutrino flavor instabilities in two three-dimensional state-of-the-art core-collapse supernova simulations performed using a two-moment three-species neutrino transport scheme: one with an exploding $9{\mathrm{M}}_{\odot }$ and one with a nonexploding $20{\mathrm{M}}_{\odot }$ model. Apart from confirming the presence of fast instabilities occurring within the neutrino decoupling and the supernova pre-shock regions, we detect flavor instabilities in the post-shock region for the exploding model. These instabilities are likely to be scattering-induced. In addition, the failure in achieving a successful explosion in the heavier supernova model seems to seriously hinder the occurrence of fast instabilities in the post-shock region. This is a consequence of the large matter densities behind the stalled or retreating shock, which implies high neutrino scattering rates and thus more isotropic distributions of neutrinos and antineutrinos. Our findings suggest that the supernova model properties and the fate of the explosion can remarkably affect the occurrence of fast instabilities. Hence, a larger set of realistic hydrodynamical simulations of the stellar collapse is needed in order to make reliable predictions on the flavor conversion physics.

Figure 1

Shapes of all $\mathcal{F}(\mu )$’s (at different spatial $\mathrm{\Theta }$’s and $\mathrm{\Phi }$’s) that satisfy Eq. (5) for $9{\mathrm{M}}_{\odot }$ model at $t=100\mathrm{ms}$, and at $r=100\mathrm{km}$ (below the shock) and 206 km (above the shock), respectively. Red and blue bands represent cubic and quadratic polynomial functions, respectively. The nature of the crossings changes around the shock, which is at $r\simeq 150\mathrm{km}$.

Figure 2

Aitoff projection of $\alpha$ in the $t=100\mathrm{ms}$ snapshot at $r=100\mathrm{km}$. The shaded zones indicate the angular coordinates for which we find ELN crossings in the range [90, 150] km. Note that the crossings occur where $\alpha$ is maximal. This is a hint in favor of a correlation with the asymmetric PNS convection.

Figure 3

Left and middle panels: Aitoff projection of $\alpha$ and $Y_e$ where the shaded areas represent the SN zones with ELN crossings in the range [50, 150] km. Right panels: The shapes of $\mathcal{F}(\mu )$ that satisfy Eq. (5). All the panels are for the $9{\mathrm{M}}_{\odot }$ model at $r=65\mathrm{km}$, and the upper and lower panels show the data from the $t=400$ and 500 ms snapshots, respectively. Note that the crossings occur at locations where $\alpha$ has nearly its minimal value, in contrast to what we found for forward crossings. The pattern of $\alpha$ (and $Y_e$) is a consequence of LESA [51].

Figure 4

Aitoff projections of ${\tilde{I}}_0/{\tilde{I}}_1$ for ${\nu }_e$ (upper panel) and ${\overline{\nu }}_e$ (lower panel). Note that $({\tilde{I}}_0/{\tilde{I}}_1)$ is larger for ${\overline{\nu }}_e$ at the points where the ELN crossings occur (indicated by shaded areas), suggesting that ${\overline{\nu }}_e$ undergoes more scatterings there.

Figure 5

Aitoff projection of $\alpha$ for the $20{\mathrm{M}}_{\odot }$ model in the $t=400\mathrm{ms}$ snapshot at $r=60\mathrm{km}$. We observe that the average value of $\alpha$ is larger than the one in the $9{\mathrm{M}}_{\odot }$ model.

Figure 6

Aitoff projections of ${\tilde{I}}_0/{\tilde{I}}_1$ for the $20{\mathrm{M}}_{\odot }$ model in the $t=400\mathrm{ms}$ snapshot at $r=60\mathrm{km}$, for ${\nu }_e$ (upper panel) and ${\overline{\nu }}_e$ (lower panel).

Figure 7

Upper panel: growth rate of temporal fast instabilities as functions of the real wave number $K$ of the fast modes propagating in the radial direction. Note that despite the fact that the crossings in the backward direction are very shallow, the growth rates can still be significant for large neutrino number densities. For instance, for $\xi ={10}^4{\mathrm{km}}^{-1}$ and $\delta ={10}^{-4}$, the growth rate can be as high as ${10}^2{\mathrm{km}}^{-1}$. Lower panel: an example of the angular distributions of the eigenvectors of unstable modes, $Q_{\mathbf{v}}$, which is normalized to one here. These distributions correspond to the unstable modes at $K=1.01\xi$, where the growth rates are close to their maxima. Note that the amplitude of $Q_{\mathbf{v}}$ is extremely small in the forward direction where the majority of neutrinos are traveling. In these calculations we assumed that the neutrino gas possesses axial symmetry.