IS THE OORT A-VALUE A UNIVERSAL GROWTH-RATE LIMIT FOR ACCRETION DISK SHEAR INSTABILITIES

A weak-field local MHD instability that is of importance to accretion disks and has recently been studied by the authors is reexamined in more detail. The maximum growth rate of the instability is found to be not only independent of the magnetic field strength but independent of field geometry as well. In particular, all Keplerian disks are unstable in the presence of any-weak poloidal field, with the ratio of the maximum growth rate to disk angular velocity given by 3/4. More generally the maximum growth rate of any weak field configuration that is not purely toroidal is given by the local Oort A-value of the disk. We investigate the reasons behind this remarkably general behavior by using a form of the dynamical Hill equations. It is conjectured that the Oort A-value is an upper bound to the growth rate of any instability feeding upon the free energy of differential rotation.