Signatures of nonlinear mode interactions in the pulsating hot B subdwarf star KIC 10139564

Context. The unprecedented photometric quality and time coverage offered by the Kepler spacecraft has opened up new opportunities to search for signatures of nonlinear effects that affect oscillation modes in pulsating stars. Aims. The data accumulated on the pulsating hot B subdwarf KIC 10139564 are used to explore in detail the stability of its oscillation modes, focusing in particular on evidences of nonlinear behaviors. Methods. We analyzed 38 months of contiguous short-cadence data, concentrating on mode multiplets induced by the star rotation and on frequencies forming linear combinations that show intriguing behaviors during the course of the observations. Results. We find clear signatures that point toward nonlinear effects predicted by resonant mode coupling mechanisms. These couplings can induce various mode behaviors for the components of multiplets and for frequencies related by linear relationships. We find that a triplet at 5760 mu Hz, a quintuplet at 5287 mu Hz and a (l > 2) multiplet at 5412 mu Hz, all induced by rotation, show clear frequency and amplitude modulations which are typical of the so-called intermediate regime of a resonance between the components. One triplet at 316 mu Hz and a doublet at 394 mu Hz show modulated amplitude and constant frequency which can be associated with a narrow transitory regime of the resonance. Another triplet at 519 mu Hz appears to be in a frequency-locked regime where both frequency and amplitude are constant. Additionally, three linear combinations of frequencies near 6076 mu Hz also show amplitude and frequency modulations, which are likely related to a three-mode direct resonance of the type nu(0) similar to nu(1) + nu(2). Conclusions. The identified frequency and amplitude modulations are the first clear-cut signatures of nonlinear resonant couplings occurring in pulsating hot B subdwarf stars. However, the observed behaviors suggest that the resonances occurring in these stars usually follow more complicated patterns than the simple predictions from current nonlinear theoretical frameworks. These results should therefore motivate further work to develop the theory of nonlinear stellar pulsations, considering that stars such as KIC 10139564 now offer remarkable testbeds to do so.