[ITAL]Hipparcos[/ITAL] Period-Luminosity Relations for Mira and Semiregular variables

We present period-luminosity diagrams for nearby Miras and semiregulars,selecting stars with parallaxes better than 20 per cent and well-determinedperiods. Using K-band magnitudes, we find two well-defined P-L sequences, onecorresponding to the standard Mira P-L relation and the second shifted toshorter periods by a factor of about 1.9. The second sequence only containssemiregular variables, while the Mira sequence contains both Miras andsemiregulars. Several semiregular stars show double periods in agreement withboth relations. The Whitelock evolutionary track is shown to fit the data,indicating that the semiregulars are Mira progenitors. The transition betweenthe two sequences may correspond to a change in pulsation mode or to a changein the stellar structure. Large amplitude pulsations leading to classical Miraclassification occur mainly near the tip of the local AGB luminosity function.Comment: 10 pages with figures, accepted by ApJ Letter