AXISYMMETRICAL BENDING OSCILLATIONS OF STELLAR DISKS

Self-gravitating stellar disks with random motion support both exponen tially growing and, in some cases, purely oscillatory axisymmetric ben ding modes, unlike their cold disk counterparts. A razor-thin disk wit h even a very small degree of random motion in the plane is both unsta ble and possesses a discrete spectrum of neutral modes, irrespective o f the sharpness of the edge. Random motion normal to the disk plane is stabilizing but at the same time allows bending waves to couple to th e internal vibrations of the particles, which causes the formerly neut ral modes to decay through Landau damping. Focusing first on instabili ties, I here determine the degree of random motion normal to the plane needed to suppress global, axisymmetric, bending instabilities in a f amily of self-gravitating disks. As found previously, bending instabil ities are suppressed only when the thickness exceeds that expected fro m a naive local criterion when the degree of pressure support within t he disk plane is comparable to, or exceeds, the support from rotation. Nevertheless, a modest disk thickness would seem to be adequate for t he bending stability of most disk galaxies, except perhaps near their centers. The discretization of the neutral spectrum in a zero-thicknes s disk is due to the existence of a turning point for bending waves in a warm disk, which is absent when the disk is cold. When the disk is given a finite thickness, the discrete neutral modes generally become strongly damped through wave-particle interactions. It is surprising t herefore that I find some simulations of warm, stable disks can suppor t (quasi-)neutral, large-scale, bending modes that decay very slowly, if at all.