Eclipse-mapping study of the eclipsing binary KIC 3858884 with a hybrid <i>δ</i> Sct/<i>γ</i> Dor component

Aims. Pulsating stars in eclipsing binary systems offer a unique possibility to empirically identify pulsation modes using the geometric effect of the eclipses on the pulsation signals. Here we explore the δ Scuti-type pulsations in the eclipsing binary system KIC 3858884 with the aim of identifying the dominant modes using various photometric methods. Methods. We used the Kepler short-cadence photometry data. Refined binary model and pulsation parameters were determined using an iterative separation of the eclipsing binary and pulsation signals. We used the photometric residuals, a phase modulation study, and a double eclipse mapping (EM) to identify the host stars of the dominant pulsations. Échelle diagram diagnostics were employed to locate the frequencies most affected by the eclipses. Direct-fitting (DF) methods assuming spherical harmonic surface patterns were explored to determine an orientation for the symmetry axis and to infer surface mode numbers ℓ and m . Ancillary mode number estimates were obtained from reconstructions of general surface patterns using dynamic eclipse mapping (DEM). The use of these methods allowed mode identifications that are independent of asteroseismic models. Results. We unambiguously established the secondary star as the main source of the pulsations. Seven peaks were found to show pronounced modulations during the secondary eclipses. For the first time, we were able to detect two hidden modes with amplitude intensification during the eclipses. Only one additional frequency appears to originate from the primary. DF results point to an essentially aligned pulsation axis for the secondary. We successfully reconstructed surface patterns and determined mode numbers for most of the selected frequencies with both of our methods. We found one radial and three sectoral modes, (1,−1), (2,±2), and (3,±3). The two strongest modes were both found to be nonradial. The hidden modes were identified as (3,±1) and (2,±1), respectively. We find one additional radial mode to be a combination frequency. The partial disagreement between the results of the two methods may indicate that either the strongest modes deviate from strict spherical harmonics, or that the pulsation axis cannot be constrained by the photometric data alone. Future spectroscopic observations could help in resolving this discrepancy.