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

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-ini(AGB) = 1.3, 1.4, 1.5, 2M(circle dot), -3.6 less than or similar to [Fe/H] less than or similar to -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] greater than or similar to 1.5 (CEMP-sII), and mild s-process enhanced stars, [hs/Fe] < 1.5 (CEMP-sI). 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] (similar to 2 dex). A degeneration of solutions is found with some exceptions: most main-sequence CEMP-sII stars with low [Na/Fe] can only be interpreted with M-ini(AGB) = 1.3-1.4 M-circle dot. Giants having suffered the first dredge-up (FDU) need a dilution greater than or similar to 1 dex (dil is defined as the mass of the convective envelope of the observed star, M(star)obs, over the material transferred from the AGB to the companion, M-AGB(trans)). Then AGB models with higher AGB initial masses (M-ini(AGB) = 1.5-2 M-circle dot) are adopted to interpret CEMP-sII giants. In general, solutions with AGB models in the mass range M-ini(AGB) = 1.3-2 M-circle dot and different dilution factors are found for CEMP-sI 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 similar 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.