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Pulsations of the roAp star KIC 10685175 revisited by TESS

KIC 10685175 (TIC 264509538) was discovered to be a rapidly oscillating Ap star from {\it Kepler} long cadence data using super-Nyquist frequency analysis. It was re-observed by TESS with 2-min cadence data in Sectors 14 and 15. We analyzed the TESS light curves, finding that the previously determined frequency is a Nyquist alias. The revised pulsation frequency is $191.5151 \pm 0.0005$d$^{-1}$ ($P = 7.52$min) and the rotation frequency is $0.32229 \pm 0.00005$d$^{-1}$ ($P_{\rm rot} = 3.1028$d). The star is an oblique pulsator with pulsation amplitude modulated by the rotation, reaching pulsation amplitude maximum at the time of the rotational light minimum. The oblique pulsation generates a frequency quintuplet split by exactly the rotation frequency. The phases of sidelobes, the pulsation phase modulation, and a spherical harmonic decomposition all show this star to be pulsating in a distorted quadrupole mode. Following the oblique pulsator model, we calculated the rotation inclination $i$ and magnetic oblique $β$ of this star, which provide detailed information of pulsation geometry. The $i$ and $β$ derived by the best fit of pulsation amplitude and phase modulation through a theoretical model differ from those calculated for a pure quadrupole, indicating the existence of strong magnetic distortion. The model also predicts the polar magnetic field strength is as high as about 6kG which is predicted to be observed in a high resolution spectrum of this star.