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KIC 7582608: A new Kepler roAp star with frequency variability

We analyse the fifth roAp star reported in the Kepler field, KIC 7582608, discovered with the SuperWASP project. The object shows a high frequency pulsation at 181.7324 d$^{-1}$ (P=7.9 min) with an amplitude of 1.45 mmag, and low frequency rotational modulation corresponding to a period of 20.4339 d with an amplitude of 7.64 mmag. Spectral analysis confirms the Ap nature of the target, with characteristic lines of Eu II, Nd III and Pr III present. The spectra are not greatly affected by broadening, which is consistent with the long rotational period found from photometry. From our spectral observations we derive a lower limit on the mean magnetic field modulus of <B> = 3.05$\pm$0.23 kG. Long Cadence Kepler observations show a frequency quintuplet split by the rotational period of the star, typical for an oblique pulsator. We suggest the star is a quadrupole pulsator with a geometry such that $i\sim66^\circ$ and $β\sim33^\circ$. We detect frequency variations of the pulsation in both the WASP and Kepler data sets on many time scales. Linear, non-adiabatic stability modelling allows us to constrain a region on the HR diagram where the pulsations are unstable, an area consistent with observations.