Global shearing modes of galactic disks

A new scheme has been devised to calculate discrete unstable global shearing spiral modes of gaseous disk models of galaxies. The scheme makes use of the Legendre expansion of eigen functions and the problem of stability analysis is reduced to an eigenvalue problem of an infinite matrix. The spiral patterns of these shearing wave solutions of linearized equations change their form in the course of time due to the differential rotation of the equilibrium disk. These shearing wave solutions are presumed to have intermediate characteristics between so-called density-waves and material arms. Comparison between these shearing modes and the non-shearing normal modes for a series of disk models is presented.