Mode switching in the nearby Mira-like variable R Doradus

We discuss visual observations spanning nearly 70 years of the nearby semiregular variable R Doradus, Using wavelet analysis, we show that the star switches back and forth between two pulsation modes having periods of 332 d and about 175 d, the latter with much smaller amplitude. Comparison with model calculations suggests that the two modes are the first and third radial overtone, with the physical diameter of the star making fundamental-mode pulsation unlikely. The mode changes occur on a time-scale of about 1000 d, which is too rapid to be related to a change in the overall thermal structure of the star and may instead be related to weak chaos. The Hipparcos distance to R Dor is 62.4 +/- 2.8 pc which, taken with its dominant 332-d period, places it exactly on the period-luminosity (P-L) relation of Miras in the Large Magellanic Cloud. Our results imply first-overtone pulsation for all Miras which fall on the P-L relation. We argue that semiregular variables with long periods may largely be a subset of Miras and should be included in studies of Mira behaviour. The semiregulars may contain the immediate evolutionary Mira progenitors, or stars may alternate between periods of semiregular and Mira behaviour.