Rossby Wave Instability of Keplerian Accretion Disks

We find a linear instability of non-axisymmetric Rossby waves in a thinnon-magnetized Keplerian disk when there is a local maximum in the radialprofile of a key function ${\cal L}(r) \equiv {\cal F}(r) S^{2/\Gamma}(r)$,where ${\cal F}^{-1} = \hat {\bf z}\cdot ({\bf \nabla}\times {\bf v}) /\Sigma$is the potential vorticity, $S = P/\Sigma^\Gamma$ is the entropy, $\Sigma$ isthe surface mass density, $P$ is the vertically integrated pressure, and$\Gamma$ is the adiabatic index. We consider in detail the special case wherethere is a local maximum in the disk entropy profile $S(r)$. This maximum actsto trap the waves in its vicinity if its height to width ratio ${\rmmax}(S)/\Delta r$ is larger than a threshold value. The pressure gradientderived from this entropy variation provides the restoring force for the wavegrowth. We show that the trapped waves act to transport angular momentumoutward. A plausible way to produce an entropy variation is when an accretiondisk is starting from negligible mass and temperature, therefore negligibleentropy. As mass accumulates by either tidal torquing, magnetic torquing, orRoche-lobe overflow, confinement of heat will lead to an entropy maximum at theouter boundary of the disk. Possible nonlinear developments from thisinstability include the formation of Rossby vortices and the formation ofspiral shocks. What remains to be determined from hydrodynamic simulations iswhether or not Rossby wave packets (or vortices) ``hold together'' as theypropagate radially inward.Comment: Accepted to ApJ (Part 1), aaspp4 format, 15 pages, 3 figure