Mode switching in the nearby Mira-like variable R Doradus

We discuss visual observations spanning nearly 70 years of the nearby semir egular variable R Doradus, Using wavelet analysis, we show that the star sw itches back and forth between two pulsation modes having periods of 332 d a nd about 175 d, the latter with much smaller amplitude. Comparison with mod el calculations suggests that the two modes are the first and third radial overtone, with the physical diameter of the star making fundamental-mode pu lsation unlikely. The mode changes occur on a time-scale of about 1000 d, w hich is too rapid to be related to a change in the overall thermal structur e 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 do minant 332-d period, places it exactly on the period-luminosity (P-L) relat ion of Miras in the Large Magellanic Cloud. Our results imply first-overton e pulsation for all Miras which fall on the P-L relation. We argue that sem iregular variables with long periods may largely be a subset of Miras and s hould be included in studies of Mira behaviour. The semiregulars may contai n the immediate evolutionary Mira progenitors, or stars may alternate betwe en periods of semiregular and Mira behaviour.