Magnetohydrodynamic Instabilities in Shearing, Rotating, Stratified Winds and Disks
We investigate shear and buoyancy instabilities in radially stratified, magnetized, cylindrical flows, for application to magnetocentrifugally driven winds and to magnetized accretion disks. We identify and study nine principal types of instabilities/overstabilities. When magnetic fields are predominantly toroidal, as in protostellar winds, the system exhibits axisymmetric fundamental (FM) and toroidal resonance modes, axisymmetric and non-axisymmetric toroidal buoyancy (TB) modes, and non-axisymmetric magnetorotational instability (MRI) modes. Winds with sufficiently steep field gradients are unstable to the FM, which promotes narrow dense jets in the centers of wider winds. The TB modes promote small-scale radial mixing. The MRIs have very low growth rates under low-temperature wind conditions. The stabilization of buoyancy modes by shear, and of MRIs by compressibility, may be important in allowing protostellar winds to propagate over vast distances in space. When magnetic fields are predominantly poloidal, as in winds close to their source or in astrophysical disks, the system exhibits axisymmetric Balbus-Hawley (BH), poloidal buoyancy (PB), non-axisymmetric geometric buoyancy (GPB), and poloidal resonance modes. The BH mode has the fastest growth rate. The PB mode promotes radial mixing on small scales. The GPB mode at high m is readily stabilized by shear. We extend previous MRI analyses to focus on compressibility. We introduce a ``coherent wavelet'' technique to derive closed-form expressions for instantaneous instability criteria, growth rates, and net amplification factors for non-axisymmetric MRIs in compressible flows with both poloidal and toroidal fields. We confirm that these are in excellent agreement with the results of shearing-sheet temporal integrations.