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 M_{\sun}. 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.Comment: 10 pages, 4 figures, accepted for publication in A&
