Massive stars are important building blocks of the Universe, and their stellar structure and evolution models are fundamental cornerstones of various fields in modern astrophysics. The precision of these models is limited by our lack of understanding of various internal mixing processes that significantly influence the lifetime of these objects (e.g. core overshoot, chemical mixing, or the internal differential rotation). Our goal is to calibrate models by extending the sample of available seismic studies of slowly pulsating B (SPB) stars, providing input for theoretical modelling efforts that will deliver precise constraints on the parameters describing the internal mixing processes in these objects. We used spectral synthesis and disentangling techniques to derive fundamental parameters and to determine precise orbital parameters from high-resolution spectra. We employed custom masks to construct light curves from the Kepler pixel data and used standard time-series analysis tools to construct a set of significant frequencies for each target. These sets were first filtered from combination frequencies, and then screened for period spacing patterns. We detect gravity mode period series of modes of the same degree l with consecutive radial order n in four new and one revisited SPB star. These predominantly prograde dipole series (covering ~10-40 radial orders) are influenced by rotation and carry signatures of chemical mixing processes. Our spectroscopic analysis, in addition to placing each object inside the SPB instability strip and identifying KIC 4930889 as an SB2 binary, reveals that KIC 11971405 is a fast rotator that shows very weak Be signatures. Together with the observed photometric outbursts this illustrates that this Be star is a fast rotating SPB star. We hypothesise that the outbursts might be connected to its very densely compressed oscillation spectrum.
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