K2 observations of the rapidly oscillating Ap star 33 Lib (HD 137949): new frequencies and unique non-linear interactions

We present the analysis of K2 short cadence data of the rapidly oscillating Ap (roAp) star, 33 Librae (HD 137949). The precision afforded to the K2 data allow us to identify at least 11 pulsation modes in this star, compared to the three previously reported. Reoccurring separations between these modes leads us to suggest a large frequency separation, $\Delta\nu$, of 78.9 $\mu$Hz, twice that reported in the literature. Other frequency separations we detect may represent the small frequency separation, $\delta\nu$, but this is inconclusive at this stage due to magnetic perturbation of the frequencies. Due to the highly non-linear pulsation in 33 Lib, we identify harmonics to four times the principal frequency. Furthermore, we note a unique occurrence of non-linear interactions of the 11 identified modes. The frequency separations of the modes around the principal frequency are replicated around the first harmonic, with some interaction with the second harmonic also. Such a phenomenon has not been seen in roAp stars before. With revised stellar parameters, linear non-adiabatic modelling of 33 Lib shows that the pulsations are not greater than the acoustic cutoff frequency, and that the $\kappa$-mechanism can excite the observed modes. Our observations are consistent with 33 Lib having a rotation period much larger than 88 d as presented in the literature.