Detection of non-linear resonances among gravity modes of slowly pulsating B stars: Results from five iterative pre-whitening strategies

Context. Slowly pulsating B (SPB) stars are main-sequence multi-periodic oscillators that display non-radial gravity modes. For a fraction of these pulsators, 4-year photometric light curves obtained with the Kepler space telescope reveal period spacing patterns from which their internal rotation and mixing can be inferred. In this inference, any direct resonant mode coupling is usually ignored. Aims. We re-analyse the light curves of a sample of 38 known Kepler SPB stars. For 26 of them, the internal structure, including rotation and mixing, was recently inferred from their dipole prograde oscillation modes. Our aim is to detect direct non-linear resonant mode coupling among the largest-amplitude gravity modes. Methods. We extract up to 200 periodic signals per star with five different iterative pre-whitening strategies based on linear and non-linear regression applied to the light curves. We then identify candidate coupled gravity modes by verifying whether they fulfil resonant phase relations. Results. For 32 of the 38 SPB stars we find at least one candidate resonance that is detected in both the linear and the best non-linear regression model fit to the light curve and involves at least one of the two largest-amplitude modes. Conclusions. The majority of the Kepler SPB stars reveal direct non-linear resonances based on the largest-amplitude modes. These stars are thus prime targets for the non-linear asteroseismic modelling of intermediate-mass dwarfs to assess the importance of mode couplings in probing their internal physics