Mode coupling coefficients between the convective core and radiative envelope of $γ\,$Doradus and slowly pulsating B stars

Abstract: Signatures of coupling between an inertial mode in the convective core and a gravito-inertial mode in the envelope have been found in four-year Kepler light curves of 16 rapidly rotating $\gamma\,$Doradus ($\gamma\,$Dor) stars. This makes it possible to obtain a measurement of the rotation frequency in their convective core. Despite their similar internal structure and available data, inertial modes have not yet been reported for slowly pulsating B (SPB) stars. We aim to provide a numerical counterpart of the recently published theoretical expressions for the mode-coupling coefficients, $\varepsilon$ and $\tilde{\varepsilon}$. These coefficients represent the two cases of a continuous and a discontinuous Brunt-V\"ais\"al\"a frequency profile at the core-envelope interface, respectively. We used asteroseismic forward models of two samples consisting of 26 SPB stars and 37 $\gamma\,$Dor stars to infer their numerical values of $\varepsilon$. The asteroseismically inferred values of $\varepsilon$ for the two samples are between 0.0 and 0.34. While $\varepsilon$ is most strongly correlated with the near-core rotation frequency for $\gamma\,$Dor stars, the fractional radius of the convective core instead provides the tightest correlation for SPB stars. We find $\varepsilon$ to decrease mildly as the stars evolve. Our asteroseismic results for the mode coupling support the theoretical interpretation and reveal that young, fast-rotating $\gamma\,$Dor stars are most suitable for undergoing couplings between inertial modes in the rotating convective core and gravito-inertial modes in the radiative envelope. The phenomenon has been found in 2.4\% of such pulsators with detected period spacing patterns, whereas it has not been seen in any of the SPB stars so far. (shortened abstract to meet the arXiv limits)