Relationship between low and high frequencies in Delta Scuti stars: Photometric Kepler and spectroscopic analyses of the rapid rotator KIC 8054146

Two years of Kepler data of KIC 8054146 (delta Sct/gamma Dor hybrid) revealed 349 statistically significant frequencies between 0.54 and 191.36 c/d (6.3 microHz to 2.21 mHz). The 117 low frequencies cluster in specific frequency bands, but do not show the equidistant period spacings predicted for gravity modes of successive radial order, n, and reported for at least one other hybrid pulsator. The four dominant low frequencies in the 2.8 to 3.0 c/d (32 to 35 microHz) range show strong amplitude variability with timescales of months and years. These four low frequencies also determine the spacing of the higher frequencies in and beyond the delta Sct pressure-mode frequency domain. In fact, most of the higher frequencies belong to one of three families with spacings linked to a specific dominant low frequency. In the Fourier spectrum, these family regularities show up as triplets, high-frequency sequences with absolutely equidistant frequency spacings, side lobes (amplitude modulations) and other regularities in frequency spacings. Furthermore, within two families the amplitude variations between the low and high frequencies are related. We conclude that the low frequencies (gravity modes, rotation) and observed high frequencies (mostly pressure modes) are physically connected. This unusual behavior may be related to the very rapid rotation of the star: from a combination of high and low-resolution spectroscopy we determined that KIC 8054146 is a very fast rotator (v sin i = 300 +/- 20 km/s) with an effective temperature of 7600 +/- 200 K and a surface gravity log g of 3.9 +/- 0.3. Several astrophysical ideas explaining the origin of the relationship between the low and high frequencies are explored.