Dynamics of the Bending of the Galaxy

A mathematical theory describing infinitesimal bending oscillations and/or responses of very thin, rotating disks of self-gravitating material is developed. This theory is applied in detail to two representa- tive families of thin-disk models, and many possible bending eigenmodes are found. It is also shown, how- ever, that the frequency spectrum of such oscillations is not necessarily discrete; on the contrary, for any disk whose density tapers sufficiently gradually to zero near its edge, that spectrum is at least partly continuous, and the corresponding long-term response to transient forcing is dispersive. The results of this study argue against certain proposed explanations of the observed warp of the "plane" of this Galaxy. Those include primordial free oscillations and any tidal forcing from the Magel- lanic Clouds at more or less their present distance. The hypothesis most favored by our analyses is that at least the Large Cloud passed within a distance of the order of 20 kpc of the galactic center approximately 5 X 108 years ago, and that the present warp evolved from the tidal distortion established during that era. Even with so close an approach, however, a mass of at least 2 X 1010 Mo seems required of the LMC

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