The effect of the centrifugal acceleration on period spacings of gravito-inertial modes in intermediate-mass stars

International audienceContext. The Kepler and Transiting Exoplanet Survey Satellite (TESS) space telescopes delivered high-precision, long-duration photometric time series for hundreds of main-sequence stars, revealing their numerous gravito-inertial ( g ) pulsation modes. This high precision allows us to evaluate increasingly detailed theoretical stellar models. Recent theoretical work extended the traditional approximation of rotation, a framework to evaluate the effect of the Coriolis acceleration on g modes, to include the effects of the centrifugal acceleration in the approximation of slightly deformed stars, which so far have mostly been neglected in asteroseismology. This extension of the traditional approximation was conceived by re-deriving the traditional approximation in a centrifugally-deformed, spheroidal coordinate system. Aims. We explore the effect of the centrifugal acceleration on g modes and assess its detectability in space-based photometric observations. Methods. We implemented the new theoretical framework to calculate the centrifugal deformation of pre-computed 1D spherical stellar structure models and computed the corresponding g -mode frequencies, assuming uniform rotation. The framework was evaluated for a grid of stellar structure models covering a relevant parameter space for observed g -mode pulsators. Results. The centrifugal acceleration modifies the effect of the Coriolis acceleration on g modes, narrowing the equatorial band in which they are trapped. Furthermore, the centrifugal acceleration causes the pulsation periods and period spacings of the most common g modes (prograde dipole modes and r modes) to increase with values similar to the observational uncertainties of the measured period spacing values in Kepler and TESS data. Conclusions. The effect of the centrifugal acceleration on g modes is formally detectable in modern space photometry. The implementation of the used theoretical framework in stellar structure and pulsation codes will allow for more precise asteroseismic modelling of centrifugally deformed stars in order to assess its effect on mode excitation, trapping, and damping