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Rotational Instability in the Outer Region of Protoplanetary Disks

We analytically calculate the marginally stable surface density profile for rotational instability of protoplanetary disks. The derived profile can be utilized for considering the region in a rotating disk where radial pressure gradient force is comparable to the gravitational force, such as an inner edge, steep gaps or bumps and an outer region of the disk. In this paper we especially focus on the rotational instability in the outer region of disks. We find an protoplanetary disk with a surface density profile of similarity solution becomes rotationally unstable at a certain radius, depending on its temperature profile and a mass of the central star. If the temperature is relatively low and the mass of the central star is high, disks have rotationally stable similarity profiles. Otherwise, deviation from the similarity profiles of surface density could be observable, using facilities with high sensitivity, such as ALMA.