Collisional and fast neutrino flavor instabilities in two-dimensional core-collapse supernova simulation with Boltzmann neutrino transport

We present a comprehensive study on the occurrences of the collisional flavor instability (CFI) and the fast flavor instability (FFI) of neutrinos based on a 2D core-collapse supernova simulation performed with a Boltzmann radiation hydrodynamics code. We find that CFI occurs in a region with the baryon-mass density of ${10}^{10}\lesssim \rho \lesssim {10}^{12}\mathrm{g}{\mathrm{cm}}^{-3}$, which is similar to the previous results in 1D core-collapse supernova models. In contrast to 1D, however, the CFI region varies with time vigorously in the 2D model, whereas it had a quiescent structure in 1D. This is attributed to the fact that the turbulent flows advected from a gain region account for the temporal variations. Another noticeable difference from the 1D models is the appearance of resonancelike CFI where number densities of ${\nu }_e$, ${\overline{\nu }}_e$ nearly coincide each other. The CFI growth rate there is enhanced and can reach $\sim {10}^8{\mathrm{s}}^{-1}$. As for FFI, on the other hand, it appears in three different regions: (1) the region overlapped with the resonancelike CFI, (2) neutrino decoupling regions where ${\overline{\nu }}_e\mathrm{s}$ are strongly emitted, and (3) optically thin regions where neutral-current scatterings dominate over charged-current reactions. Although overall properties for FFI are consistent with previous studies, we find that the number of electron-neutrinos lepton number crossing temporarily becomes multiple, which can be assessed accurately only by multiangle treatments in neutrino transport. We find that the growth rate of FFI is always higher than CFI if both of them occur, which suggests that the former is dominant for the linear evolution.

Figure 1

Time-radius map of the growth rate of CFI (top) and FFI (bottom) for the angle $\theta =45°$ and 90°. White broken lines, from top to bottom, denote the radius for the density ${10}^{10}$, ${10}^{11}$, ${10}^{12}$, and ${10}^{13}\mathrm{g}{\mathrm{cm}}^{-3}$, respectively. Red broken line denote the shock radius.

Figure 2

Meridian map of CFI growth rate (left), FFI growth rate (middle), and the dominant instability (right) at $t=404\mathrm{ms}$ after bounce.

Figure 3

From top to bottom, radial profiles of (1) the growth rates of CFI and FFI, (2) ratios $G/A$ and $\alpha /\gamma$, (3) number densities and $G$, $|A|$, and (4) collision rates for each species of neutrinos and $\gamma$, $\alpha$. Left and right panels are for the angle $\theta =45°$ and $\theta =90°$, respectively. The snapshot is at $t=404\mathrm{ms}$ after bounce.

Figure 4

Radial profiles of collision rates for individual neutrino interactions (top) and $Y_e$ (bottom). The angles and the time snapshot is same as Fig. 3. The abbreviations of neutrino interactions are as follows: electron capture (ecp), antielectron capture (aecp), neutrino pair production (pap), and the nucleon bremsstrahlung (nbr).

Figure 5

Radial profiles of the FFI growth rate (top) and $G_{\mathrm{in}/\mathrm{out}}$, ${\overline{G}}_{\mathrm{in}/\mathrm{out}}$ (middle) and the differences between $G_{\mathrm{in}/\mathrm{out}}$ and ${\overline{G}}_{\mathrm{in}/\mathrm{out}}$ (bottom) at $t=404\mathrm{ms}$ after bounce.

Figure 6

Angular distribution of the distribution function of 16.5 MeV neutrinos at 74 km (top), 35 km (middle), 55 km (bottom). The angle is $\theta =90°$ and the snapshot time is $t=404\mathrm{ms}$ after bounce.

Figure 7

Radial profiles of the CFI and FFI growth rates for $\theta =45°$ (top) and $\theta =90°$ (bottom) at $t=404\mathrm{ms}$ after bounce.