Pulsation Modes in M Giants

We review the problem of the pulsation modes in the Mira stars, and then use the models of Ostlie and (Art) Cox (1986 ApJ 311, 864) to investigate the pulsation modes in small-amplitude red giant variables through: (i) Q values, determined with new interferometric effective temperatures and Eggen and Iben's (1991 AJ 101, 1377) temperature-luminosity relation; and (ii) period ratios in about a dozen mode-switching small-amplitude variables. [So far, there are no known examples of mode-switching in Mira stars.] It appears that Mira stars pulsate in the first overtone, and small-amplitude variables pulsate in the first and higher overtones, though we cannot rule out the possibility that some of both types pulsate in the fundamental mode. The situation should soon be improved (especially for the small-amplitude variables) by the availability of HIPPARCOS parallaxes and photometry.