Mode coupling coefficients between the convective core and radiative envelope of ? Doradus and slowly pulsating B stars

Context. 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. Aims. We aim to provide a numerical counterpart of the recently published theoretical expressions for the mode-coupling coe fficients, epsilon and (epsilon) over tilde. These coe fficients represent the two cases of a continuous and a discontinuous Brunt-Vaisala frequency profile at the core-envelope interface, respectively. We consider gamma Dor and SPB stars to shed light on the di fference between these two classes of intermediate-mass gravito-inertial mode pulsators in terms of core and envelope mode coupling. Methods. We used asteroseismic forward models of two samples consisting of 26 SPB stars and 37 gamma Dor stars to infer their numerical values of epsilon and (epsilon) over tilde. For both samples, we also computed: the linear correlation coe fficients between epsilon or (epsilon) over tilde and the near-core rotation frequency, the chemical gradient, the evolutionary stage, the convective core masses and radii, and the Schonberg-Chandrasekhar limiting mass representing the maximum mass of an inert helium core at central hydrogen exhaustion that can still withstand the pressure of the overlaying envelope. Results. The asteroseismically inferred values of epsilon and (epsilon) over tilde for the two samples are between 0.0 and 0.34. While epsilon 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 epsilon to decrease mildly as the stars evolve. For the SPB stars, epsilon and (epsilon) over tilde have similar moderate correlations with respect to the core properties. For the gamma Dor stars, (epsilon) over tilde reveals systematically lower and often no correlation to the core properties; their epsilon is mainly determined by the near-core rotation frequency. The Schonberg-Chandrasekar limit is already surpassed by the more massive SPB stars, while none of the gamma Dor stars have reached it yet. Conclusions. 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.

Automated summary

This study investigates the mode coupling coefficients of γ Dor and SPB stars using asteroseismic forward models and finds that young, fast-rotating γ Dor stars exhibit strong coupling between inertial modes in the rotating convective core and gravito-inertial modes in the radiative envelope. In contrast, no such coupling has been observed in SPB stars.