How plausible are the proposed formation scenarios of CEMP-r/s stars?

CEMP-r/s stars are metal-poor stars with enhanced abundances of carbon and heavy elements associated with the slow and rapid neutron-capture process (s- and r-elements, respectively). It is believed that carbon and s-elements were accreted in the past from the wind of a primary star in the asymptotic giant branch (AGB) phase of evolution, a scenario that is generally accepted to explain the formation of CEMP stars that are only enhanced in s-elements (CEMP-s stars). The origin of r-element-enrichment in CEMP-r/s stars is currently debated and many formation scenarios have been put forward.We aim to determine the likelihood of the scenarios proposed to explain the formation of CEMP-r/s stars.We calculate the frequency of CEMP-r/s stars among CEMP-s stars for a variety of formation scenarios, and we compare it with that determined from an observed sample of CEMP-r/s stars collected from the literature.The theoretical frequency of CEMP-r/s stars predicted in most formation scenarios underestimates the observed ratio by at least a factor of five. If the enrichments in s- and r-elements are independent, the model ratio of CEMP-r/s to CEMP-s stars is about 22%, that is approximately consistent with the lowest estimate of the observed ratio. However, this model predicts that about one third of all carbon-normal stars have [Ba/Fe] and [Eu/Fe] higher than one, and that 40% of all CEMP stars have [Ba/Eu] ≤ 0. Stars with these properties are at least ten times rarer in our observed sample.The intermediate or I-process, which is supposedly active in some circumstances during the AGB phase, could provide an explanation of the origin of CEMP-r/s stars, similar to that of CEMP-s stars, in the context of wind mass accretion in binary systems. Further calculations of the nucleosynthesis of the I-process and of the detailed evolution of late AGB stars are needed to investigate if this scenario predicts a CEMP-r/s star frequency consistent with the observations.