Technetium and the third dredge up in AGB stars I. Field stars

We searched for Tc in a sample of long period variables selected by stellar luminosity derived from Hipparcos parallaxes. Tc, as an unstable s-process element, is a good indicator for the evolutionary status of stars on the asymptotic giant branch (AGB). In this paper we study the occurrence of Tc as a function of luminosity to provide constraints on the minimum luminosity for the third dredge up as estimated from recent stellar evolution models. A large number of AGB stars above the estimated theoretical limit for the third dredge up are found not to show Tc. We confirm previous findings that only a small fraction of the semiregular variables show Tc lines in their spectra. Contrary to earlier results by Little et al. (1987) we find also a significant number of Miras without Tc. The presence and absence of Tc is discussed in relation to the mass distribution of AGB stars. We find that a large fraction of the stars of our sample must have current masses of less than 1.5 .... Combining our findings with stellar evolution scenarios we conclude that the fraction of time a star is observed as a SRV or a Mira is dependent on its mass.