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W.-T. Kim, E. C. Ostriker (University of Maryland)
We investigate magnetic shear and buoyancy instabilities in protostellar winds by solving a set of linearized ideal MHD equations for modes varying as ei(m\phi +k_{\rm z} z -\omega t). We derive a general wave equation for each such mode, assuming a cold background flow and magnetic field with axial and toroidal components and arbitrary radial shear. For particular realizations we use power-law cold wind equilibria: \rho \propto R-q, \vec{B} \propto R-(1+q)/2, and \vec{v} \propto R-1/2. For background states with these profiles, we derive the general non-axisymmetric local dispersion relation, and explore its solutions in various limits. We identify nine principal unstable or overstable modes. Our results primarily apply to winds but we also discuss applications in rotating disks.
When magnetic fields are predominantly toroidal, as in protostellar winds, the system exhibits axisymmetric fundamental and toroidal resonance modes, and non-axisymmetric toroidal buoyancy and magnetic shearing modes. Winds having a steep field gradient (0.76\!<\!q) are unstable to the long wavelength fundamental mode; this may be associated with the radial expansion of narrow jets into wide-angle winds. The toroidal buoyancy instability promotes radial mixing. The non-axisymmetric magnetoshearing instability has very small growth rates due to the low temperature in the wind.
When magnetic fields are predominantly poloidal, as in astrophysical disks or winds close to their source, the system exhibits axisymmetric compressible magnetoshearing Balbus-Hawley, axisymmetric and non-axisymmetric poloidal buoyancy and poloidal resonance modes. The well-known Balbus-Hawley mode has the fastest growth rate. When the magnetic field is nonuniform, the axisymmetric poloidal buoyancy mode promotes radial mixing on small scales when vertical shear is low. The non-axisymmetric poloidal buoyancy mode requires high m, thus is readily stabilized by shear.
Finally, we provide general compressible dispersion relations for magnetoshearing instabilities and compare physical mechanisms for toroidal and poloidal limits.
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