Erratum: Resonant Excitation of Disk Oscillations in Deformed Disks. VI. Stability Criterion Revisited

Abstract

We re-examine the excitation of a set of disk oscillations in a deformed disk by a resonant process. We assume that the disk is deformed from an axisymmetric steady state by an oscillatory deformation with frequency !D and azimuthal wavenumber mD. Then, we consider two normal mode oscillations with a set of frequencies and the azimuthal wavenumber being (!1,m1) and (!2,m2) and satisfying the resonant conditions (!1 +!2 +!D = 0 and m1 +m2 +mD = 0). These oscillations are resonantly excited ifE1E2> 0, whereE1 andE2 are the wave energies of the above two oscillations, when the deformation is maintained by external forces, or has a large amplitude compared with the oscillations. This instability condition is rather general as long as the unperturbed density and pressure vanish on the surface of the system. The possibility of applications to superhumps and negative superhumps in the superoutburst state of dwarf novae are briefly discussed.