Coupling of neutrino beam-driven MHD waves and resonant instabilities in rotating magnetoplasmas with neutrino two-flavor oscillations

TL;DR

This work shows that in a rotating, magnetized plasma interacting with a neutrino beam and two-flavor oscillations, the Coriolis force couples shear Alfvén and oblique magnetosonic waves, creating new mixed modes and resonant instabilities. The authors derive a general dispersion relation incorporating neutrino beam effects, flavor oscillations, and rotation, and then compute growth rates for both magnetosonic and Alfvén instabilities. The growth rates are enhanced by the Coriolis-induced coupling, with distinct angular dependences and parameter sensitivities (notably $\lambda$, $n_0$, and $B_0$), suggesting a potentially important role in the dynamics of core-collapse supernovae. The results extend prior NMHD analyses by revealing neutrino-driven perturbations in Alfvén waves and their coupling to magnetosonic modes, offering new insights into energy transport and explosion mechanisms in extreme astrophysical settings.

Abstract

We present an analysis of neutrino-driven magnetohydrodynamic (MHD) waves and instabilities in a rotating magnetoplasma with weak neutrino interactions. We show, for the first time, that neutrino-driven shear Alfv{é}n and oblique magnetosonic waves can be coupled by the Coriolis force, forming new wave modes affected by this force, as well as neutrino beam and two neutrino flavor oscillations. Our work extends previous theories by demonstrating that shear Alfv{é}n waves are influenced by neutrino effects and by identifying instabilities resulting from resonant interactions with both a streaming neutrino beam and flavor oscillations. We find that the Coriolis force, as well as plasma density and magnetic field strength, have a significant impact on the profiles of the instability growth rates. Our findings may shed new light on the physical mechanisms underlying core-collapse supernovae.

Figures (5)

• Figure 1: A schematic diagram showing the geometry of the magnetic field, rotational motion, and the wave vector.
• Figure 2: Instability growth rates corresponding to fast [with a plus sign; subplots (a) and (c)] and slow [with a minus sign; subplots (b) and (d)] magnetosonic waves are shown against the propagation angle $\theta$. The blue solid ($\gamma_\nu^{\pm}$), red dashed ($\gamma_{\nu o}^{\pm}$) and black dashed-dotted ($\gamma_{\nu oc}^{\pm}$) lines correspond to the instability growth rates when (i) only the neutrino beam effects are present, (ii) only the neutrino beam and two-flavor effects are present, and (iii) the neutrino beam, two-flavor effects, and the effects of coupling with the Alfvén modes in the presence of the Coriolis force are present, respectively. The magnetic field strength for subplots (a) and (b) [subplots (c) and (d)] is $B_0=5\times 10^{6}$ T ($B_0=2\times 10^{7}$ T). The other fixed parameter values are $n_0=10^{34}$ m$^{-3}$, $k=10^2$ m$^{-1}$, $\lambda=\pi/4$, and $\Omega_r=5\times 10^{3}$ s$^{-1}$.
• Figure 3: Instability growth rates [when all the effects as for $\gamma_{\rm{\nu oc}}^{\pm}$ in Fig. \ref{['fig2-fsmag_b']} are included] of fast [subplot (a)] and slow [subplot (b)] oblique magnetosonic waves are shown against the propagation angle $\theta$ for different values of the plasma density $n_0$ and the obliqueness of the axis of rotation $\lambda$ as in the legends. The magnetic field is $B_0=5\times 10^{6}$ T. All other fixed parameter values are as for Fig. \ref{['fig2-fsmag_b']}.
• Figure 4: Instability growth rates corresponding to fast [with a plus sign; subplot (a)] and slow [with a minus sign; subplots (b)] shear Alfvén modes are shown against the propagation angle $\theta$. The blue solid ($\gamma_{\nu c}^{\pm}$) and red dashed ($\gamma_{\nu oc}^{\pm}$) lines correspond to the instability growth rates when (i) only the neutrino beam effects and the effects of coupling with the magnetosonic modes in the presence of the Coriolis force are present and (ii) the neutrino beam, two-flavor effects, and the effects of coupling with the magnetosonic modes in the presence of the Coriolis force are present, respectively. The black dash-dotted line is for the growth rate $\gamma_{\nu oc}^{\pm}$ with an increased magnetic field as in the legends. We have considered the rotational frequency as $\Omega_r=5\times 10^{3}$ s$^{-1}$ and other fixed parameter values as for Fig. \ref{['fig3-fsmag_n']}.
• Figure 5: Instability growth rates [when all the effects as for $\gamma_{\rm{\nu oc}}^{\pm}$ in Fig. \ref{['fig5-gr-alfven']} are included] corresponding to fast [with a plus sign; subplot (a)] and slow [with a minus sign; subplots (b)] shear Alfvén modes are shown against the propagation angle $\theta$ for different values of the plasma density $n_0$ and the obliqueness of the angle of rotation $\lambda$ as in the legends. We have considered the magnetic field and the rotational frequency as $B_0=10^7$ T and $\Omega_r=5\times 10^{3}$ s$^{-1}$. All other fixed parameter values are as for Fig. \ref{['fig3-fsmag_n']}.