DUETS: Setting expectations for asteroseismic binaries and binary products with synthetic populations

Context. Binary stars and products of binary evolution contribute significantly to shaping stellar populations, yet they are often neglected due to the difficulty involved in identifying them. With asteroseismology providing precise stellar parameters, we have the opportunity to better characterize binaries and their products, as well as to refine our understanding of their role in shaping Galactic populations. Aims. We estimate the occurrence rates, mass distributions, and evolutionary states of asteroseismic binaries that exhibit solar-like oscillations from both components, as well as those of products of binary interactions with detectable solar-like oscillations. Additionally, we explore the effects of mass accretion or loss on the relation between the "apparent age" and metallicity. Mehods. We simulated 121 deg2 of Kepler' s field of view using the TRILEGAL population synthesis code, adopting the Eggleton and Moe & Di Stefano distributions of initial binary parameters. We also generated an additional simulation with non-interacting binaries for comparison. Results. We find that asteroseismic binaries require an initial mass ratio that is close to 1 and that even small mass transfer events can prevent the detection of oscillations from both components. The noninteracting case yields the highest fraction of asteroseismic binaries for red giant stars with detectable oscillations (0.46%), while Eggleton yields the lowest (0.06%). Asteroseismic binaries composed of two red clump stars are not expected at separations smaller than 500 R· due to the interplay of stellar evolution and binary interactions. The simulation carried out with the Moe & Di Stefano distribution suggests that ∼1% of Kepler' s field red giants with detectable oscillations have undergone significant mass accretion or loss, appearing rejuvenated or prematurely aged. They could also potentially affect Galactic age-metallicity relations, although the occurrence and properties of these populations strongly depend on the assumed initial binary parameters. Conclusions. Comparing the predicted and observed asteroseismic binaries, as well as over- and under-massive stars, offers a way to constrain key binary evolution assumptions, such as the initial binary fraction and period distribution, and to reduce uncertainties in mass-transfer modeling.