Waves and instabilities in neutrino magnetohydrodynamics

Neutrinos contribute significantly to system's evolution when they interact with dense and highly ionized plasma in variety of astrophysical environment such as supernova explosion, although it is well known that neutrinos interact very feebly with matter. This coupled interaction has been recently modeled in the magnetohydrodynamic (MHD) regime. Here the magnetohydrodynamic approach of treating plasma's electron and ion as charged fluids within the dynamics of magnetic field produced by them is extended to include weak interactions - the fundamental force, according to particle physics, responsible for the coupling between neutrinos and electrons. This formalism is termed as Neutrino Magnetohydrodynamics (NMHD) and is being used to model such systems. In the present paper, the usual normal mode analysis is carried out to derive a dispersion relation for such a system. It is seen that inclusion of neutrinos and their subsequent interaction with the magnetohydrodynamics fluid does not allow the flux freezing in such systems which hitherto has been a characteristic attribute of all astrophysical plasmas. Further, Friedrich's diagrams of the NMHD waves, which are polar plots depicting the variation of phase speeds and group speeds of waves with the direction of propagation (with respect to the direction of the ambient field) are drawn. Using this diagram the propagation characteristics of NMHD waves are discerned vis a vis the MHD waves in astrophysical plasmas. Incidence of instabilities of NMHD are also pointed out. (author)