Stringent upper limit on Be star fractions produced by binary interaction

Context. Binary evolution can result in fast-rotating stars through accretion of angular momentum during mass-transfer phases. These fast-rotating stars are predicted to be observable as Be stars. Current models struggle to produce a satisfactory description of Be star populations, even though numerous pieces of observational evidence indicate that the accretion process might be the dominant Be formation channel. Aims. Given the distinct uncertainties in detailed binary evolution calculations, we investigate a rigorous and model-independent upper limit for the production of Be stars through binary interaction and aim to confront this limit with observations of Be stars in young star clusters. Methods. Using extreme assumptions, we calculate the number ratio of post-interaction to pre-interaction binary systems in a coeval population. This ratio describes an upper limit to Be star formation through mass transfer. A detailed comparison is made between our derived upper limit and relevant observations of Be stars, which allows us to probe several aspects of binary star physics. Results. We find that in coeval populations, binary interaction can at most account for one-third of all main-sequence stars being Be stars. Near the cluster turn-off region, this limit appears to be realised in the clusters studied. Away from the turn-off, a good fit to the observed Be fraction as a function of mass is obtained by applying simple assumptions about which systems undergo unstable mass-transfer produces. Conclusions. We find that assuming distinct physics, binary evolution alone can in principle match the high numbers of Be stars that are observed in open clusters. Whether the required binary physics is realised in nature remains to be investigated.