S stars and <i>s</i>-process in the <i>Gaia</i> era

S stars are late-type giants that transition objects between M-type and carbon on the asymptotic giant branch (AGB). They classified into two types: intrinsic or extrinsic, based presence absence of technetium (Tc). The Tc-rich thermally-pulsing (TP-)AGB internally producing s-process elements (including Tc) which brought to their surface via third dredge-up (TDU). Tc-poor extrinsic gained overabundances accretion s-process-rich material from an AGB companion has since turned a dim white dwarf. Our goal is investigate evolutionary status by locating them in Hertzsprung-Russell (HR) diagram using results Gaia early Data Release 3 (EDR3). We combine current sample 13 with our previous studies 10 determine observational onset TDU metallicity range [-0.7; 0]. also compare abundance determinations dedicated nucleosynthesis predictions. stellar parameters derived iterative tool combines HERMES high-resolution spectra, accurate EDR3 parallaxes, evolution models tailored MARCS model atmospheres for S-type stars. Using these we heavy-element abundances line synthesis. In HR diagram, located at higher luminosities than predicted TDU. These findings consistent being genuinely TP-AGB comparison profiles predictions provide overall good agreement. Stars highest [s/Fe] tend have C/O ratios.