Magnetohydrodynamic instabilities in shearing, rotating, stratified winds and disks

We investigate shear and buoyancy instabilities in radially stratified, mag netized, cylindrical flows, for application to magnetocentrifugally driven winds-such as these from protostars-and to magnetized accretion disks. Our motivation is to characterize the susceptibility of cold MHD disk winds to growing internal perturbations and to understand the relation of wind insta bilities to known accretion disk instabilities. Using four different linear analysis techniques, we identify and study nine principal types of unstabl e or overstable disturbances, providing numerical and analytic solutions fo r growth rates for a wide range of parameters. When magnetic fields are pre dominantly toroidal, as in protostellar winds far from their source, we fin d the system is susceptible to growth of five different kinds of perturbati ons: axisymmetric fundamental and toroidal resonance modes, axisymmetric an d nonaxisymmetric toroidal buoyancy modes, and nonaxisymmetric magnetorotat ional modes. Winds having a sufficiently steep field gradient (d ln B/d ln R < -0.75 for a purely toroidal-field case) are globally unstable to the lo ng-wavelength fundamental mode concentrated at small radii; these promote t he establishment of narrow dense jets in the centers of wider winds. Long-w avelength outer-wind modes are all stable for power-law wind equilibria. Th e toroidal buoyancy instabilities promote small-scale radial mixing provide d the equilibrium has nonzero magnetic forces. For low-temperature toroidal -B winds, both axisymmetric and nonaxisymmetric magnetorotational instabili ties have very low growth rates. The stabilization of buoyancy instabilitie s by shear and of magnetorotational instabilities by compressibility may be important in allowing cold MHD winds to propagate over vast distances in s pace. When magnetic fields are predominantly poloidal, as may occur in prot ostellar winds close to their source or in astrophysical disks, we find the system is susceptible to four additional growing modes: axisymmetric magne torotational (Balbus-Hawley), axisymmetric poloidal buoyancy, nonaxisymmetr ic geometric buoyancy, and poloidal resonance modes. The well-known axisymm etric Balbus-Hawley mode has the fastest growth rate. When the magnetic fie ld is nonuniform, the axisymmetric poloidal buoyancy mode promotes radial m ixing on small scales. The geometric poloidal buoyancy mode requires high m , thus is readily stabilized by shear. Previous work on magnetorotational i nstabilities has concentrated on near-incompressible systems (accretion dis ks or stellar interiors). We extend this analysis to allow for compressibil ity (important in winds). We introduce a "coherent wavelet" technique (a WK B temporal approximation) and derive closed-form analytic expressions for i nstantaneous instability criteria, growth rates, and net amplification fact ors for generalized nonaxisymmetric magnetorotational instabilities in comp ressible flows with both poloidal and toroidal fields. We confirm that thes e are in excellent agreement with the results of shearing-sheet temporal in tegrations and that "locally axisymmetric" perturbations have the largest a mplifications only provided (k . nu(A))/Omega less than or similar to 1.