Hipparcos period-luminosity relations for Mira and semiregular variables

We present period-luminosity (P-L) diagrams for nearby Mira and semiregular variables, selecting stars with parallaxes better than 20% and well-determ ined periods. Using K-band magnitudes, we find two well-defined P-L sequenc es, one corresponding to the standard Mira P-L relation and the second shif ted to shorter periods by a factor of about 1.9. The second sequence contai ns only semiregular variables, while the Mira sequence contains both Mira a nd semiregular variables. Several semiregular stars show double periods tha t are in agreement with both relations. The Whitelock evolutionary track is shown to fit the data, indicating that the semiregular variables are Mira progenitors. The transition between the two sequences may correspond to a c hange in the pulsation mode or to a change in the stellar structure. Large- amplitude pulsations that lead to the classical Mira classification occur m ainly near the tip of the local asymptotic giant branch luminosity function .