Exploring the dynamical evolution of Cepheid multiplicity in star clusters and its implications for B-star multiplicity at birth

Context. Classical Cepheid variable stars provide a unique probe of binary evolution in intermediate-mass stars over the course of several tens to hundreds of Myr. In addition, understanding binary evolution with the inclusion of cluster dynamics is desirable for obtaining a more complete picture of these stars, especially as they play a vital role in distance determinations. Aims. We studied the binary and multiple properties of Cepheids, assuming that all mid-B stars form in binaries inside star clusters. We also estimated the birth multiplicity of mid-B stars by comparing the observed multiplicity statistics of Cepheids with models based on particular assumptions. Methods. The clusters were modelled with the NBODY6 code, including synthetic stellar and binary evolutionary tracks. The Cepheids were identified from their position on the Hertzsprung-Russell diagram. Results. The dynamical cluster environment results in a higher binary fraction among the Cepheids that remain in star clusters (approximate to 60%) than among the Cepheids which have escaped to the field (approximate to 35%). The fraction of Cepheids in triples (approximate to 30% and approximate to 10% in clusters and field, respectively) follows the same trend. In clusters, the binary, triple, and multiple fraction decreases with increasing cluster mass. More massive clusters have binaries of shorter orbital periods than lower mass clusters and field Cepheids. Mergers are very common with approximate to 30% of mid-B stars not evolving to Cepheids because of the interaction with their companion. Approximately 40% of Cepheids have merged with their companion, and the merger event impacts stellar evolution, so that approximate to 25% of all Cepheids occur at an age by more than 40% different than what would be expected from their mass and the current cluster age; the expected age of Cepheids can differ from the age of their host cluster. Our models predict that one in five Cepheids is the result of a merger between stars with mass below the lower mass limit for Cepheids; in clusters, these objects occur substantially later than expected from their mass. Approximately 10% of binary Cepheids have a different companion from the zero-age main sequence (ZAMS) one, and approximate to 3 to 5% of all Cepheids have a compact companion (approximate to 0.15% of all Cepheids are accompanied by a black hole). Conclusions. The binary fraction derived from our simulations (42%) underestimates the observed binary Cepheid fraction by approximately a factor of 2. This suggests that the true multiplicity fraction of B-stars at birth could be substantially larger than unity and, thus, that mid-B stars may typically form in triple and higher order systems.