  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.
