Local magneto-shear instability in Newtonian gravity

Abstract

ABSTRACT The magneto-rotational instability (MRI), which is due to an interplay between a sheared background and the magnetic field, is commonly considered a key ingredient for developing and sustaining turbulence in the outer envelope of binary neutron star merger remnants. To assess whether (or not) the instability is active and resolved, criteria originally derived in the accretion disc literature, thus exploiting the symmetries of such systems, are often used. In this paper, we discuss the magneto-shear instability as a truly local phenomenon, relaxing common symmetry assumptions on the background on top of which the instability grows. This makes the discussion well suited for highly dynamical environments such as binary mergers. We find that, although this is somewhat hidden in the usual derivation of the MRI dispersion relation, the instability crucially depends on the assumed symmetries. Relaxing the symmetry assumptions in the background, we find that the role of the magnetic field is significantly diminished, as it affects the modes’ growth but does not drive it. We conclude by making contact with a suitable filtering operation, as this is key to separating background and fluctuations in highly dynamical systems.