The possible origin of the spiral-arm instability

Abstract

Physical argumenls suggest the spiral arms may be manifestations of the galaxy not being in dynamical equilibrium - in the sense that the kinetic energy of its stars and gas is less relative to its binding energy than that dictated by the virial theorem. Without constant cooling of the galactic disk (i.e., a progressive increase in the binding energy of the galaxy) such a departure from dynamical equilibrium would be corrected and the spiral arms destroyed in about i09 yr due to an increase in the velocity dispersion of the stars in the disk resulting from their interacting with the spiral arms. The rate of cooling required to maintain the spiral arms, about 6 x 104 L| may be provided by mass loss from stars in the disk population. The cooling arises from the average scale-heights and velocities of these stars being larger than that of the gas in the disk, so that there is a net loss of kinetic energy and an increase in the binding energy of the galaxy due to the ejected gas settling down to a lower terminal velocity and scale-height in the galactic disk. In this paper we suggest an instability mechanism that may be responsible for the existence of spiral arms in galaxies. Although the gravitational-wave theory of spiral structure, as formulated by Lin and Shu (1964), has enjoyed considerable success in explaining many properties of spiral arms, there is no satisfactory theory of why these arms exist. The situation is similar to the study of stellar pulsations where it is possible to determine many dynamical properties of a pulsating star without knowing the instability mechanism responsible for the pulsations. Even without knowing what pro- duces the spiral arms one can, for example, demonstrate that a standing spiral-wave pattern can exist in a galaxy and relate the angular rotational velocity of this pattern to the radial spacing of the spiral arms. The source of excitation of the spiral arms in galaxies may not be unique. Different mechanisms may excite the waves without affecting their overall appearance just as the permissible standing waves in an open pipe are largely independent of the mechanisms employed to excite them. However, the wide-spread occurrence of spiral arms in disk galaxies suggests that these galaxies have some internal default mechanism which is capable of exciting the waves even in an isolated system. We propose a possible mechanism of this type.