tokens: of these frequencies as the result of nonlinear mode coupling. Note that we focus on the significant frequencies (S/N > 4) that appear both in the spectra of single-quarter data and all-quarter data. Other tidally induced pulsations with low amplitudes could also exist. For example, the peaks at 0.7095 day −1 and 4.3990 day −1 are 5 and 31 times the orbital frequency, respectively. Figure 5. Fourier spectrum of light curve residuals with eclipses masked. The upper panel was calculated from the quarter 1 long cadence data. The lower panel presents a similar plot but using all quarters (0–17) of long cadence data. The 10 dominant frequencies listed in Table 2 are labeled. Filled and open circles mark the harmonic and nonharmonic orbital frequencies, respectively. The spectral window is shown in the inset. Table 3 Main Oscillation Frequencies of KIC 3230227 Many frequency triplets can be seen in the spectrum, with equal spacing of orbital frequency. Close examination reveals that all these triplets have frequencies that are equal to times orbital frequency. Thus they can be explained as a combination of one real oscillation peak and two side-lobes due to the spectral window (Figure 5 ). The nonharmonic peaks generate side-lobes at and . We find that after pre-whitening , and f 4 , these triplets essentially disappear, and only peaks remain, supporting the above argument. Low amplitude m = 0 modes can also exist. At high inclination, these modes are expected to have low amplitudes. As discussed below, the Ledoux constant C nl (Ledoux 1951 ) is about 0.16 for the g -modes in the observed frequency range. This means the splitting is about for modes with frequencies much higher than f rot . If we adopt pseudo-synchronous rotation day −1 , are then 0.49 and 0.98 day −1 for m = 1 and m = 2, respectively. Thus the splittings will be located several orbital harmonics away from their central m = 0 peak. This also suggests that the splittings are not due to rotation. The amplitude variations of these oscillations are shown in Figure 6 and listed in Table 4 . Most of the frequencies have relatively stable amplitudes over 16 quarters, with variations less than 0.05 milli-mag. The exception seems to be f 3 , which decreased from 0.174 milli-mag in quarter 1 to 0.078 milli-mag in quarter 16. Figure 6. Amplitude variations of 10 dominant oscillation frequencies (Tables 3 and 4 ). Filled and open circles indicate the harmonic and nonharmonic orbital frequencies, respectively. Table 4 Amplitude Variations of the Main Frequencies ( mag) 3.2. Mode Identification from Phases For tidally induced oscillations in KIC 3230227, it is sufficient to consider only the dominant l = 2 term since higher order terms are at most times (an order of magnitude) smaller than the l = 2 term (Equation (8) in Burkart et al. 2012 ). Additionally, the observed amplitudes of higher order modes () are reduced by geometrical cancelation upon integration over the stellar surface, so
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