THE PARKER-SHEARING INSTABILITY IN AZIMUTHALLY MAGNETIZED DISCS

We describe the effects of both magnetic buoyancy and differential rot ation on a disc of isothermal gas embedded in a purely azimuthal magne tic field, in order to study the evolution and interplay of Parker and shearing instabilities.We perform a linear analysis of the evolution of perturbations in the shearing sheet model. Both instabilities occur on the slow MHD branch of the dispersion relation, and can affect the same waves. We put a stress on the natural polarization properties of the slow MHD waves to get a better understanding of the physics invol ved. The mechanism of the shearing instability is described in details . Differential rotation can transiently stabilize slow MHD waves with a vertical wavelength longer than the scale height of the disc, agains t the Parker instability. Waves with a vertical wavelength shorter tha n the scale height of the disc are subject to both the Parker and the transient shearing instabilities. They occur in different ranges of ra dial wavenumbers, i.e. at different times in the shearing evolution; t hese ranges can overlap or, on the contrary, be separated by a phase o f wave-like oscillations, depending on the strength of differential ro tation. These analytical results, obtained in a WKB approximation, are found to be in excellent agreement with numerical solutions of the fu ll set of linearized equations. Our results can be applied to both gal actic and accretion discs.