This paper substantiates earlier suggestions that the maintenance and excitation of spiral structures in galaxies can occur via spiral modes which are dominated by the dynamics of stellar motions within a galactic disk. A physical derivation, certain numerical results, and some general properties are presented for that type of spiral mode which involves 'feedback' and consists of temporally growing spiral waves that rotate rigidly about the galactic center with a fixed-pattern rotation frequency. The discrete values of allowed pattern frequencies are determined through a global dispersion relationship in the form of a standing-wave condition, this condition is evaluated in terms of the radial wavenumber throughout an annular region between two galactocentric reflection circles, and growth rates of the spiral modes are computed. A numerical example is given for a galaxy model with a total mass of 20 billion solar masses and a rotation curve typical of galaxies with a low central concentration of matter.
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J.W.K. Mark (1977) studied this question.