  Context- S stars are late-type giants with spectra showing characteristic
molecular bands of ZrO in addition to the TiO bands typical of M stars. Their
overabundance pattern shows the signature of s-process nucleosynthesis.
Intrinsic, technetium (Tc)-rich S stars are the first objects, on the
Asymptotic Giant Branch (AGB), to undergo third dredge-up (TDU) events. Gaia
exquisite parallaxes now allow to precisely locate these stars in the
Hertzsprung-Russell (HR) diagram. Here we report on a population of low-mass,
Tc-rich S stars, previously unaccounted for by stellar evolution models. Aims-
Our aim is to derive parameters of a sample of low-mass Tc-rich S stars and
then, by comparing their location in the HR diagram with stellar evolution
tracks, to derive their masses and to compare their measured s-process
abundance profiles with recently derived STAREVOL nucleosynthetic predictions
for low-mass AGB stars. Methods- The stellar parameters were obtained using a
combination of HERMES high-resolution spectra, accurate Gaia Data Release 2
(Gaia-DR2) parallaxes, stellar-evolution models and newly-designed MARCS model
atmospheres for S-type stars. Results- We report on 6 Tc-rich S stars lying
close to the 1 Msun (initial mass) tracks of AGB stars of the corresponding
metallicity and above the predicted onset of TDU, as expected. This provides
direct evidence for TDUs occurring in AGB stars with initial masses as low as ~
1 Msun and at low luminosity, i.e. at the start of the thermally-pulsing AGB.
We present AGB models producing TDU in those stars with [Fe/H] in the range
-0.25 to -0.5. There is a reasonable agreement between the measured and
predicted s-process abundance profiles. For 2 objects however (CD -29 5912 and
BD +34 1698), the predicted C/O ratio and s-process enhancements do not match
simultaneously the measured ones.
