Kelvin-Helmholtz instabilities and resonant flow instabilities for a coronal plume model with plasma pressure

In this paper we continue the study of the effect of the velocity shear between the coronal plume and the interplume region on the spectrum of MHD waves trapped in the plume. In Andries et al. (2000) we have illustrated the concept of resonant flow instability of the trapped modes both in a 1-D slab model and a 1-D cylindrical model for a coronal plume in which plasma-pressure was neglected. The important result of that paper was that the threshold values of the velocity shear are significantly smaller for resonant instability than for Kelvin-Helmholtz instability to occur. The aim of this paper is to study the effect of plasma pressure on the eigenmodes of the plume. As expected we find slow waves in addition to the fast waves. Furthermore there are two different types of Kelvin-Helmholtz instability. Along with the fact that now not only Alfven but also slow resonances can occur this all leads to a wide variety of ranges of the velocity shear for which instability can be present. Estimates of these ranges for different equilibrium quantities can be obtained without going through the elaborate numerical procedures of calculating the eigenmodes. We show that the instability that will most probably occur in coronal plumes is due to an Alfven resonance of slow body modes. These instabilities could lead to disruption of the coronal plumes and to the mixing with interplume plasma. However we point out that there might be a strong dependence of the resonant flow instability upon the velocity profile that is to be investigated further.