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Parametric Study of the Rossby Wave Instability in a Two-Dimensional Barotropic Disk

Protoplanetary disks with non-axisymmetric structures have been observed. The Rossby wave instability (RWI) is considered as one of the origins of the non-axisymmetric structures. We perform linear stability analyses of the RWI in barotropic flow using four representative types of the background flow on a wide parameter space. We find that the co-rotation radius is located at the background vortensity minimum with large concavity if the system is marginally stable to the RWI, and this allows us to check the stability against the RWI easily. We newly derive the necessary and sufficient condition for the onset of the RWI in semi-analytic form. We discuss the applicability of the new condition in realistic systems and the physical nature of the RWI.