Tango of celestial dancers: A sample of detached eclipsing binary systems containing g-mode pulsating components. A case study of KIC9850387

Eclipsing binary systems with components that pulsate in gravity modes ($g$ modes) allow for simultaneous and independent constraints of the chemical mixing profiles of stars. We aim to assemble a sample of $g$-mode pulsators in detached eclipsing binaries with the purpose of finding good candidates for future evolutionary and asteroseismic modelling. In addition, we present a case study of the eclipsing binary KIC9850387, identified as our most promising candidate. We selected all of the detached eclipsing binaries in the Kepler eclipsing binary catalogue and performed a visual inspection to determine the presence and density of $g$ modes, and the presence of $g$-mode period-spacing patterns in their frequency spectra. We then characterised our sample based on their $g$-mode pulsational parameters and binary and atmospheric parameters. A spectroscopic follow-up of KIC9850387 was then performed. We then performed spectral disentangling followed by atmospheric modelling and abundance analysis for the primary star. We utilised an iterative approach to simultaneously optimise the pulsational and eclipse models, and subsequently performed an analysis of the pressure- ($p$-) and $g$-mode pulsational frequencies. We compiled a sample of 93 Kepler eclipsing binary stars with $g$-mode pulsating components and identified clear $g$-mode period-spacing patterns in the frequency spectra of seven of these systems. We found that the $g$-mode pulsational parameters and the binary and atmospheric parameters of our sample are weakly correlated at best. We find that the eclipsing binary KIC9850387 is a double-lined spectroscopic binary in a near-circular orbit with an intermediate-mass primary, and a solar-like secondary. We find $\ell=1$ and $\ell=2$ period-spacing patterns in the frequency spectrum of KIC9850387 spanning more than ten radial orders each.