Abstract
The stellar population in the Galactic halo is characterised by a large fraction of carbon-enhanced metal-poor (CEMP) stars. Most CEMP stars have enhanced abundances of s-process elements (CEMP-s stars), and some of these are also enriched in r-process elements (CEMP-s/r stars). In one formation scenario proposed for CEMP stars, the observed carbon excess is explained by invoking wind mass transfer in the past from a more massive thermally-pulsing asymptotic giant branch (AGB) primary star in a binary system.In this work we generate synthetic populations of binary stars at metallicity Z = 0.0001 ([Fe/H] ≈ − 2.3), with the aim of reproducing the observed fraction of CEMP stars in the halo. In addition, we aim to constrain our model of the wind mass-transfer process, in particular the wind-accretion efficiency and angular-momentum loss, and investigate under which conditions our model populations reproduce observed distributions of element abundances.We compare the CEMP fractions determined from our synthetic populations and the abundance distributions of many elements with observations. Several physical parameters of the binary stellar population of the halo are uncertain, in particular the initial mass function, the mass-ratio distribution, the orbital-period distribution, 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 resulting fractions are more than a factor of three higher than those determined with default assumptions in previous population-synthesis studies, which typically underestimated the observed CEMP fraction. We find that most CEMP stars in our simulations are formed in binary systems with periods longer than 10 000 days. Few CEMP stars have measured orbital periods, but all that do have periods up to a few thousand days. Our results are consistent only if this small subpopulation represents the short-period tail of the underlying period distribution. The results of our comparison between the modelled and observed abundance distributions are significantly different for CEMP-s/r stars and for CEMP-s stars without strong enrichment in r-process elements. For the latter, our simulations qualitatively reproduce the observed distributions of carbon, sodium, and heavy elements such as strontium, barium, europium, and lead. Contrarily, for CEMP-s/r stars our model cannot reproduce the large abundances of neutron-rich elements such as barium, europium, and lead. This result is consistent with previous studies, and suggests that CEMP-s/r stars experienced a different nucleosynthesis history to CEMP-s stars.