One-armed oscillations of a non-selfgravitating polytropic disk

One-armedglobal oscillations in a non-selfgravitating polytropic disk rotating around a star are investigated. The unperturbed disk is axisymmetric, geometrically thin, and extends infinitely in the radial direction keeping its thickness constant. Perturbations considered are inviscid and adiabatic. It is found that there are one-armed retrograde wave modes which are trapped in an inner region of the disk. The eignefrequency of the lowest order mode is given by _K(r _s)(z ₀/r _s)₂, wherer _s is the radius of the central star,z ₀ is the half-thickness of the disk, and _K(r _s) is the Keplerian angular frequency at the surface of the star.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.