Chiral plasma instability and inverse cascade from nonequilibrium left-handed neutrinos in core-collapse supernovae

We show that the backreaction of left-handed neutrinos out of equilibrium on the matter sector induces an electric current proportional to a magnetic field even without a chiral imbalance for electrons in core-collapse supernovae. We derive the transport coefficient of this effect based on the recently formulated chiral radiation transport theory for neutrinos. This chiral electric current generates a strong magnetic field via the so-called chiral plasma instability, which could provide a new mechanism for the strong and stable magnetic field of magnetars. We also numerically study the physical origin of the inverse cascade of the magnetic energy in the magnetohydrodynamics including this current. Our results indicate that incorporating the chiral effects of neutrinos would drastically modify the hydrodynamic evolutions of supernovae, which may also be relevant to the explosion dynamics.

Figure 1

Time evolution of $⟨B^2{⟩}^{1/2}$.

Figure 2

Time evolution of normalized helicity in model 1.

Figure 3

Time evolution of 3D visualization of $B_x$ and magnetic field lines in model 1. Panels (a), (b), (c), (d), (e), and (f) correspond to the time $t/{\tau }_{\mathrm{CPI}}=1$, 10, 30, 40, 60, and 100, respectively.

Figure 4

Temporal evolution of 3D visualization of $v_x$ in model 1. Time in each panel is the same as that in Fig. 3.

Figure 5

Time evolution of $⟨{\xi }_B⟩$.

Figure 6

Comparison of the terms in the induction equation at $t=40{\tau }_{\mathrm{CPI}}$ for model 1.