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 ) .
One formation scenario proposed for CEMP stars invokes wind mass transfer in the past from a thermally-pulsing asymptotic giant branch ( AGB ) primary star to a less massive companion star which is presently observed .
In this work we generate synthetic populations of binary stars at metallicity Z = 0.0001 ( [ \mathrm { Fe } / \mathrm { H } ] \approx - 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 that are not strongly enriched in r -process elements .
For these stars , 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 can not 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 .