Gravity darkening and tidally perturbed stellar pulsation in the misaligned exoplanet system WASP-33

WASP-33 is one of the few $\delta$ Sct stars with a known planetary companion. By analyzing stellar oscillations, we search for possible star-planet interactions in pattern pulsation. We made use Transit and Light Curve Modeller (TLCM) to solve light curve from Transiting Exoplanet Survey Satellite (TESS). include gravity darkening into our analysis. The oscillation clearly shows signs several tidally perturbed modes. find that there are peaks frequency spectrum at or near $3$rd, $12$th $25$th orbital harmonics ($f_{orb} \sim 0.82$ d$^{-1}$). Also, prominent overabundance pulsational frequencies rightwards harmonics, being characteristic pulsation, which an outcome misaligned system. There both $\gamma$ Dor ranges Fourier spectrum, implying -- hybrid pulsator. transit curves best fitted by darkened model, planet parameters consistent earlier determinations.