The pulsation, temperatures and metallicities of Mira and semiregular variables in different stellar systems

Data on angular diameters and infrared photometry for late-type stars are assembled. It is shown that a consistent T-eff scale can be established, combining results for Mira and non-Mira M-type stars. The log T-eff versus (J-K) relation is much steeper than previously adopted, but is consistent with predictions from model stellar atmospheres. Comparison of the linear diameters of Miras measured in the red spectral region with those measured in the infrared shows that models successfully predict the extension observed in the red, and the combined data provide strong evidence that Miras are pulsating in their first overtone. Data on Miras and semiregular (SR) variables in globular clusters are compared with predictions from stellar evolution and pulsation theory. These data also support a steep log T-eff versus (J-K) relation at low temperatures. The Miras and SR variables in 47 Tuc conform to theoretical expectation if they are undergoing an average mass loss of similar to 3 x 10(-7) M. yr(-1). SR variables in both metal-rich and metal-poor globular clusters are probably pulsating, like the Miras in their first overtone. The general agreement between observation and theory now found suggests that infrared colour-period relations can be used to investigate overall metallicity differences between Miras in different stellar systems, at least at the shorter periods where circumstellar extinction is probably negligible. A comparison of Miras in Galactic globular clusters of known metallicity with those in the LMC and in the SgrI window of the Galactic Bulge indicates that Miras of periods 100 to 300 d in the LMC have a mean metallicity log z similar to -0.6, whilst those in SgrI have log z similar to -0.2, close to that of K giants in the NGC 6522 Bulge window. No evidence has yet been found for a dependence of the Mira period-luminosity relation on metallicity, and it is pointed out that theory does not at present give a definitive prediction of such an effect. Some stars of special interest are discussed in an appendix.