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

Abstract

There are many Slowly Pulsating B (SPB) stars and γ Dor stars in the Kepler Mission data set. The light curves of these pulsating stars have been classified phenomenologically into stars with symmetric light curves and with asymmetric light curves. In the same effective temperature ranges as the γ Dor and SPB stars, there are variable stars with downward light curves that have been conjectured to be caused by spots. Among these phenomenological classes of stars, some show 'frequency groups' in their amplitude spectra that have not previously been understood. While it has been recognised that nonlinear pulsation gives rise to combination frequencies in a Fourier description of the light curves of these stars, such combination frequencies have been considered to be a only a minor constituent of the amplitude spectra. In this paper we unify the Fourier description of the light curves of these groups of stars, showing that many of them can be understood in terms of only a few base frequencies, which we attribute to g mode pulsations, and combination frequencies, where sometimes a very large number of combination frequencies dominate the amplitude spectra. The frequency groups seen in these stars are thus tremendously simplified. We show observationally that the combination frequencies can have amplitudes greater than the base frequency amplitudes, and we show theoretically how this arises. Thus for some γ Dor and SPB stars combination frequencies can have the highest observed amplitudes. Among the B stars are pulsating Be stars that show emission lines in their spectra from occasional ejection of material into a circumstellar disk. Our analysis gives strong support to the understanding of these pulsating Be stars as rapidly rotating SPB stars, explained entirely by g mode pulsations.

Short-term variability and mass loss in Be stars

“…First, the data are analyzed using the generalized LS periodogram, just as described above, but now in the frequency range of astrophysical interest from 0.2 c/d to 25 c/d; the latter is about the Nyquist frequency of the long cadence data (24.469 c/d). As this method is the traditional way of analyzing such a light-curve, it yields essentially identical results to the ones described by Balona et al (2011) and Kurtz et al (2015).…”

“…HD 186567 is considered as an example for a Be star by Kurtz et al (2015). The original source of this classification is unclear, but since that the star shows several Be-star typical outbursts (see Fig.…”

“…Although A 2 is correlated with A 3 , even in the wavelet analysis it is not possible to identify a single, stable frequency that would just have variable amplitude. Kurtz et al (2015) state that the period values in a periodogram computed over observing quarters 0 to 9 are the same as the ones over quarters 10 to 17. We have repeated this exercise with quarters 0 to 5, 6 to 11, and 12 to 17, that is with a somewhat finer sampling, less susceptible to averaging.…”

“…Rotation also poses a certain challenge to the suggestion by Kurtz et al (2015) that combination frequencies are responsible for non-linear appearance of some light-curves. Combination frequencies are observed frequencies that relate to other observed frequencies via…”

“…Be stars benefit in particular because they are variable on a wide range of time scales from hours (and sometimes even minutes, but only in the very high energy domain) to decades. In the literature three Be stars have been published that were observed during the original Kepler mission (Balona et al 2011;Kurtz et al 2015).…”