Rossby Wave Instability of Keplerian Accretion Disks

Abstract

We find a linear instability of non-axisymmetric Rossby waves in a thin nonmagnetized Keplerian disk when there is a local maximum in the radial profile of a key function L(r) j F(r)S 2=\\Gamma (r), where F \\Gamma1 = z \\Delta (r \\Theta v)=\\Sigma is the potential vorticity, S = P=\\Sigma \\Gamma is the entropy, \\Sigma is the surface mass density, P is the vertically integrated pressure, and \\Gamma is the adiabatic index. We consider in detail the special case where there is a local maximum in the disk entropy profile S(r). This maximum acts to trap the waves in its vicinity if its height to width ratio max(S)=\\Deltar is larger than a threshold value. The pressure gradient derived from this entropy variation provides the restoring force for the wave growth. We show that the trapped waves act to transport angular momentum outward. A plausible way to produce an entropy variation is when an accretion disk is starting from negligible mass and temperature, therefore negligible entropy. A...