The Nature of Strange Modes in Classical Variable Stars

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Strange modes have been found in the radial spectrum of many luminous stars, most recently in Cepheids and RR Lyrae. We show that there is nothing strange about these modes -- they must exist even in the adiabatic limit. With a change of variables and without approximation the adiabatic linear pulsation equation is reduced to a Schroedinger equation in which the radial coordinate is the local sound-traversal time. In this formulation, the narrow hydrogen partial ionization region is seen to act as a potential barrier, separating the star into two regions. Resonances between the two regions result in the strange modes, for which the ratio of interior to exterior amplitude is at a minimum. The relative location of the barrier changes with the stellar parameters, and this gives rise to avoided level-crossings along a sequence of models. 2 The appearance of strange modes and the associated level crossings are exhibited with an analytic toy-model with the potential barrier approximated by a delta function. This toy-model is readily extensible to nonadiabatic modes. Hydrodynamical calculations find that pure strange mode limit-cycles have extremely small photospheric velocities and luminosity variations in the milli-magnitude range. They are therefore expected to be difficult to observe.