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High‐resolution spectroscopic observations of 100 metal‐poor carbon and  s ‐rich stars (CEMP‐ s ) collected from the literature are compared with the theoretical nucleosynthesis models of the asymptotic giant branch (AGB) presented in Paper I (  M  AGB  ini = 1.3,  1.4,  1.5,  2  M ⊙ , − 3.6 ≲ [ Fe/H ] ≲− 1.5 ). The  s ‐process enhancement detected in these objects is associated with binary systems: the more massive companion evolved faster through the thermally pulsing AGB phase (TP‐AGB), synthesizing  s ‐elements in the inner He intershell, which are partly dredged up to the surface during the third dredge‐up (TDU) episode. The secondary observed low‐mass companion became CEMP‐ s  by the mass transfer of C‐ and  s ‐rich material from the primary AGB.  We analyse the light elements C, N, O, Na and Mg, as well as the two  s ‐process indicators, [hs/ls] (where ls =〈Y, Zr〉 is the the light‐ s  peak at N = 50 and hs =〈La, Nd, Sm〉 the heavy‐ s  peak at N = 82) and [Pb/hs]. We distinguish between CEMP‐ s  with high  s ‐process enhancement, [hs/Fe]  &gt; rsim   1.5 (CEMP‐ s II), and mild  s ‐process enhanced stars, [hs/Fe] &lt; 1.5 (CEMP‐ s I). To interpret the observations, a range of  s ‐process efficiencies at any given metallicity is necessary. This is confirmed by the high spread observed in [Pb/hs] (∼2 dex). A degeneration of solutions is found with some exceptions: most main‐sequence CEMP‐ s II stars with low [Na/Fe] can only be interpreted with  M  AGB  ini = 1.3–1.4 M ⊙ . Giants having suffered the first dredge‐up (FDU) need a dilution  &gt; rsim  1 dex ( dil  is defined as the mass of the convective envelope of the observed star,  M  obs  ★ , over the material transferred from the AGB to the companion,  M  trans  AGB ). Then AGB models with higher AGB initial masses ( M  AGB  ini = 1.5–2 M ⊙ ) are adopted to interpret CEMP‐ s II giants. In general, solutions with AGB models in the mass range  M  AGB  ini = 1.3–2 M ⊙  and different dilution factors are found for CEMP‐ s I stars.  About half of the CEMP‐ s  stars with europium measurements show a high  r ‐process enhancement (CEMP‐ s / r ). The scenario for the origin of CEMP‐ s / r  stars is a debated issue. We propose that the molecular cloud from which the binary system formed was previously enriched in  r ‐process elements, most likely by local SN II pollution. This initial  r ‐enrichment does not affect the  s ‐process nucleosynthesis. However, for a high  r ‐process enrichment ([r/Fe] ini = 2) the  r ‐process contributions to solar La, Nd and Sm (30, 40 and 70 per cent) have to be considered. This increases the maximum [hs/ls] up to ∼0.3 dex. CEMP‐ s / r  stars reflect this behaviour, showing higher [hs/ls] than observed in CEMP‐ s  on average.  Detailed analyses for individual stars will be provided in Paper III.

The s ‐process in low‐metallicity stars – II. Interpretation of high‐resolution spectroscopic observations with asymptotic giant branch models