The chemical enrichments detected in carbon- and s-element-enhanced metal-poor (CEMP-s) stars are believed to be the consequence of a past episode of mass transfer from a now extinct asymptotic-giant-branch primary star. This hypothesis is borne out by the evidence that most CEMP-s stars exhibit radial-velocity variations suggesting that they belong to binary systems in which the companion is not directly visible. We used the orbital-period distribution of an unbiased sample of observed CEMP-s stars to investigate the constraints it imposes on our models of binary evolution and on the properties of the metal-poor binary population in the Galactic halo. We generated synthetic populations of metal-poor binary stars using different assumptions about the initial period distribution and about the physics of the mass-transfer process, and we compared the predicted period distributions of our synthetic CEMP-s stars with the observed one. With a set of default assumptions often made in binary population-synthesis studies, the observed period distribution cannot be reproduced. The percentage of observed CEMP-s systems with periods shorter than about 2000 days is underestimated by almost a factor of three, and by about a factor of two between 3000 and 10 000 days. Conversely, about 40% of the simulated systems have periods longer than 104 days, which is approximately the longest measured period among CEMP-s stars. Variations in the assumed stability criterion for Roche-lobe overflow and the efficiency of wind mass transfer do not alter the period distribution enough to overcome this discrepancy. To reconcile the results of the models with the orbital properties of observed CEMP-s stars, one or both of the following conditions are necessary: (i) the specific angular momentum carried away by the material that escapes the binary system is approximately two to five times higher than currently predicted by analytical models and hydrodynamical simulations of wind mass transfer, and (ii) the initial period distribution of very metal-poor binary stars is significantly different from that observed in the solar vicinity and weighted towards periods shorter than about ten thousand days. Our simulations show that some, perhaps all, of the observed CEMP-s stars with apparently constant radial velocity could be undetected binaries with periods longer than 104 days, but the same simulations also predict that twenty to thirty percent of detectable binaries should have periods above this threshold, much more than are currently observed.
The Period Distribution of Close Binary Systems