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

Asteroseismology gives us the opportunity to better characterize binaries and their products, and shed light on their role in Galactic populations. We estimate occurrence rates, mass distributions, and evolutionary states of asteroseismic binaries, exhibiting solar-like oscillations from both components, and of products of binary interactions with detectable solar-like oscillations. Additionally, we explore the effects of mass accretion or loss on apparent age-metallicity relations. Using the TRILEGAL code, we simulate Kepler's field of view adopting the Eggleton and Moe & Di Stefano distributions of initial binary parameters, and run an additional simulation with non-interacting binaries for comparison. We find that asteroseismic binaries require an initial mass ratio close to one, and even small mass transfer events can prevent the detection of oscillations from both components. The fraction of asteroseismic binaries for red giant stars with detectable oscillations ranges from 0.5\% for non-interacting binaries to a minimum of 0.06% when taking interactions into account. Moreover, asteroseismic binaries composed of two red clump stars are not expected at separations $\leq 500~\text{R}_\odot$ due to the interplay of stellar evolution and binary interactions. Finally, we estimate that at least ~1% of the Kepler red giants with detectable oscillations have undergone significant mass accretion or loss, potentially affecting Galactic age-metallicity relations, although there is a strong dependence on the assumed initial binary parameters. Comparing predicted and observed asteroseismic binaries, as well as over- and under-massive stars, offers a way to constrain key binary evolution assumptions, and to reduce uncertainties in mass-transfer modeling.