The stellar population in the Galactic halo is characterised by a large fraction of CEMP stars. Most CEMP stars are enriched in $s$-elements (CEMP-$s$ stars), and some of these are also enriched in $r$-elements (CEMP-$s/r$ stars). One formation scena
rio proposed for CEMP stars invokes wind mass transfer in the past from a TP-AGB primary star to a less massive companion star which is presently observed. We generate low-metallicity populations of binary stars to reproduce the observed CEMP-star fraction. In addition, we aim to constrain our wind mass-transfer model and investigate under which conditions our synthetic populations reproduce observed abundance distributions. We compare the CEMP fractions and the abundance distributions determined from our synthetic populations with observations. Several physical parameters of the binary stellar population of the halo are uncertain, e.g. the initial mass function, the mass-ratio and orbital-period distributions, and the binary fraction. We vary the assumptions in our model about these parameters, as well as the wind mass-transfer process, and study the consequent variations of our synthetic CEMP population. The CEMP fractions calculated in our synthetic populations vary between 7% and 17%, a range consistent with the CEMP fractions among very metal-poor stars recently derived from the SDSS/SEGUE data sample. The results of our comparison between the modelled and observed abundance distributions are different for CEMP-$s/r$ stars and for CEMP-$s$ stars. For the latter, our simulations qualitatively reproduce the observed distributions of C, Na, Sr, Ba, Eu, and Pb. Contrarily, for CEMP-$s/r$ stars our model cannot reproduce the large abundances of neutron-rich elements such as Ba, Eu, and Pb. This result is consistent with previous studies, and suggests that CEMP-$s/r$ stars experienced a different nucleosynthesis history to CEMP-$s$ stars.
Many observed CEMP stars are found in binary systems and show enhanced abundances of $s$-elements. The origin of the chemical abundances of these CEMP-$s$ stars is believed to be accretion in the past of enriched material from a primary star in the A
GB phase. We investigate the mechanism of mass transfer and the process of nucleosynthesis in low-metallicity AGB stars by modelling the binary systems in which the observed CEMP-$s$ stars were formed. For this purpose we compare a sample of $67$ CEMP-$s$ stars with a grid of binary stars generated by our binary evolution and nucleosynthesis model. We classify our sample CEMP-$s$ stars in three groups based on the observed abundance of europium. In CEMP$-s/r$ stars the europium-to-iron ratio is more than ten times higher than in the Sun, whereas it is lower than this threshold in CEMP$-s/nr$ stars. No measurement of europium is currently available for CEMP-$s/ur$ stars. On average our models reproduce well the abundances observed in CEMP-$s/nr$ stars, whereas in CEMP-$s/r$ stars and CEMP-$s/ur$ stars the abundances of the light-$s$ elements are systematically overpredicted by our models and in CEMP-$s/r$ stars the abundances of the heavy-$s$ elements are underestimated. In all stars our modelled abundances of sodium overestimate the observations. This discrepancy is reduced only in models that underestimate the abundances of most of the $s$-elements. Furthermore, the abundance of lead is underpredicted in most of our model stars. These results point to the limitations of our AGB nucleosynthesis model, particularly in the predictions of the element-to-element ratios. Finally, in our models CEMP-$s$ stars are typically formed in wide systems with periods above 10000 days, while most of the observed CEMP-$s$ stars are found in relatively close orbits with periods below 5000 days.
AGB stars are responsible for producing a variety of elements, including carbon, nitrogen, and the heavy elements produced in the slow neutron-capture process ($s$-elements). There are many uncertainties involved in modelling the evolution and nucleo
synthesis of AGB stars, and this is especially the case at low metallicity, where most of the stars with high enough masses to enter the AGB have evolved to become white dwarfs and can no longer be observed. The stellar population in the Galactic halo is of low mass ($lesssim 0.85M_{odot}$) and only a few observed stars have evolved beyond the first giant branch. However, we have evidence that low-metallicity AGB stars in binary systems have interacted with their low-mass secondary companions in the past. The aim of this work is to investigate AGB nucleosynthesis at low metallicity by studying the surface abundances of chemically peculiar very metal-poor stars of the halo observed in binary systems. To this end we select a sample of 15 carbon- and $s$-element-enhanced metal-poor (CEMP-$s$) halo stars that are found in binary systems with measured orbital periods. With our model of binary evolution and AGB nucleosynthesis, we determine the binary configuration that best reproduces, at the same time, the observed orbital period and surface abundances of each star of the sample. The observed periods provide tight constraints on our model of wind mass transfer in binary stars, while the comparison with the observed abundances tests our model of AGB nucleosynthesis.
