Non-ideal Magnetohydrodynamic Instabilities in Protoplanetary Disks: Vertical Modes and Reflection Asymmetry

Magnetized disk winds and wind-driven accretion are an essential and intensively studied dispersion mechanism of protoplanetary disks. However, the stability of these mechanisms has yet to be adequately examined. This paper employs semi-analytic linear perturbation theories under non-ideal magnetohydrodynamics, focusing on disk models whose magnetic diffusivities vary by a few orders of magnitude from the disk midplane to its surface. Linear modes are distinguished by their symmetry with respect to the midplane. These modes have qualitatively different growth rates: symmetric modes almost always decay, while at least one anti-symmetric mode always has a positive growth rate. This growth rate decreases faster than the Keplerian angular velocity with cylindrical radius $R$ in the disk and scales steeper than $R^{-5/2}$ in the fiducial disk model. The growth of anti-symmetric modes breaks the reflection symmetry across the disk equatorial plane, and may occur even in the absence of the Hall effect. In the disk regions where fully developed anti-symmetric modes occur, accretion flows appear only on one side of the disk, while disk winds occur only on the other. This may explain the asymmetry of some observed protoplanetary-disk outflows.