RELATIONSHIP BETWEEN LOW AND HIGH FREQUENCIES IN δ SCUTI STARS: PHOTOMETRICKEPLERAND SPECTROSCOPIC ANALYSES OF THE RAPID ROTATOR KIC 8054146

Abstract

Two years of Kepler data of KIC 8054146 (δ Sct/γ Dor hybrid) revealed 349 statistically significant frequencies between 0.54 and 191.36 cycles day −1 (6.3 μHz 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 2.8-3.0 cycles day −1 (32-35 μHz) 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 δ Sct pressuremode 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 (υ sin i = 300 ± 20 km s −1 ) 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.

A unifying explanation of complex frequency spectra of γ Dor, SPB and Be stars: combination frequencies and highly non-sinusoidal light curves

“…Wu 2001 andMontgomery 2005). Combination frequencies dominate the amplitude spectra of some δ Sct stars, for example KIC 11754974 (Murphy et al 2013) and KIC 8054146 (Breger et al 2012;Breger & Montgomery 2014), where the astrophysical implications and uses of the combination frequencies are more uncertain than for white dwarf stars.…”

The classification of frequencies in the γ Doradus/δ Scuti hybrid star HD 49434★

“…The above computation of the frequency spacings also allowed a comparison with the results of Chapellier et al (2012) and Breger et al (2012), where frequency spacings from the dominant δ Scuti frequencies were found to match those of the high-amplitude γ Doradus frequencies. A search for frequency combinations in the spectroscopic data revealed only a possible link between f7, f8 and f35.…”

“…The spectroscopic frequency results are surprising and show several unexplained phenomena, yet the clear distinction in the shape of the standard deviation and phase profiles of the higher and lower frequencies that are found suggests an interesting physical origin. With the recent studies of hybrids in the Kepler field as a whole Balona et al 2011;) and individual CoRoT and Kepler (Chapellier et al 2012) and kic 8054146 (Breger et al 2012 hybrid stars (Chapellier et al 2012;Breger et al 2012) more questions are raised about these stars. The existence of the hybrid phenomenon is already in question and the spectroscopic results for HD 49434 so far add weight to both sides of the debate.…”

“…The amplitudes do appear to vary by up to 25%, but it is not clear that this is not an effect of the different size and data quality encompassed in each set. All but the most extreme amplitude variation would be extremely difficult to detect in the best groundbased spectroscopic campaigns and Blazhko-like variability (non-symmetric changes in the maximum and minimum amplitudes), as seen in Breger et al (2012), is beyond the precision of current spectroscopic methods. It is thus still possible that HD 49434 has variations in the amplitudes of its pulsations, but this cannot be confirmed in this study.…”

Pulsations of rapidly rotating stars with compositional discontinuities

“…For instance, García Hernández et al (2009Hernández et al ( , 2013 found recurrent frequency spacings in two δ Scutis observed by CoRoT, thereby allowing the construction of an echelle diagram in the latter case. Similarly, Breger et al (2012Breger et al ( , 2013 found multiple sequences of very uniformly spaced frequencies in a δ Scuti observed by Kepler. These observations show that although the pulsation spectra of δ Scuti stars lack the simple frequency patterns present in solar-type pulsators, regular patterns do exist in such stars and need to be explained.…”