Abstract
The carbon-enhanced metal-poor (CEMP) stars constitute approximately one fifth of the metal-poor ($[{\rm Fe}/{\rm H}] \la -2$) population but their origin is not well understood. The most widely accepted formation scenario, at least for the majority of CEMP stars which are also enriched in s-process elements, invokes mass-transfer of carbon-rich material from a thermally-pulsing asymptotic giant branch (TPAGB) primary star to a less massive main-sequence companion which is seen today. Recent studies explore the possibility that an initial mass function biased toward intermediate-mass stars is required to reproduce the observed CEMP fraction in stars with metallicity $[{\rm Fe}/{\rm H}]<-2.5$. These models also implicitly predict a large number of nitrogen-enhanced metal-poor (NEMP) stars which is not seen. In this paper we investigate whether the observed CEMP and NEMP to extremely metal-poor (EMP) ratios can be explained without invoking a change in the initial mass function. We construct binary-star populations in an attempt to reproduce the observed number and chemical abundance patterns of CEMP stars at a metallicity $[{\rm Fe}/{\rm H}]\sim-2.3$. Our binary-population models include synthetic nucleosynthesis in TPAGB stars and account for mass transfer and other forms of binary interaction. This approach allows us to explore uncertainties in the CEMP-star formation scenario by parameterization of uncertain input physics. In particular, we consider the uncertainty in the physics of third dredge up in the TPAGB primary, binary mass transfer and mixing in the secondary star. We confirm earlier findings that with current detailed TPAGB models, in which third dredge up is limited to stars more massive than about $1.25~M_{\odot}$, the large observed CEMP fraction cannot be accounted for. We find that efficient third dredge up in low-mass (less than $1.25~M_{\odot}$), low-metallicity stars may offer at least a partial explanation for the large observed CEMP fraction while remaining consistent with the small observed NEMP fraction.