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The s-Process in Low Metallicity Stars. II. Interpretation of High-Resolution Spectroscopic Observations with AGB models

High-resolution spectroscopic observations of a hundred metal-poor Carbon and s-rich stars (CEMP-s) collected from the literature are compared with the theoretical nucleosynthesis models of asymptotic giant branch (AGB) presented in Paper I (M = 1.3, 1.4, 1.5, 2 Msun, -3.6 < [Fe/H] < -1.5). The s-process enhancement detected in these objects is associated to binary systems: the more massive companion evolved faster through the thermally pulsing AGB phase (TP-AGB), synthesising in the inner He-intershell the s-elements, 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 mass transfer of C and s-rich material from the primary AGB. We analyse the light elements as 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] > 1.5 (CEMP-sII), and mild s-process enhanced stars, [hs/Fe] < 1.5 (CEMP-sI). To interpret the observations, .... . Detailed analyses for individual stars will be provided in Paper III.