Pulsations of Three Rapidly Oscillating Ap Stars TIC 96315731, TIC 72392575, and TIC 318007796

Abstract: We analyze the frequencies of three known roAp stars, TIC 96315731, TIC 72392575, and TIC 318007796, using the light curves from the Transiting Exoplanet Survey Satellite (TESS). For TIC 96315731, the rotational and pulsational frequencies are $0.1498360\,\mathrm{d}^{-1}$ and $165.2609\,\mathrm{d}^{-1}$, respectively. In the case of TIC 72392575, the rotational frequency is $0.25551\,\mathrm{d}^{-1}$. We detect a quintuplet of pulsation frequencies with a center frequency of $135.9233\,\mathrm{d}^{-1}$, along with two signals within the second pair of rotational sidelobes of the quintuplet separated by the rotation frequency. These two signals may correspond to the frequencies of a dipole mode. In TIC 318007796, the rotational and pulsational frequencies are $0.2475021\,\mathrm{d}^{-1}$, $192.73995\,\mathrm{d}^{-1}$, and $196.33065\,\mathrm{d}^{-1}$, respectively. Based on the oblique pulsator model, we calculate the rotation inclination $\left( i \right)$ and magnetic obliquity angle $\left( \beta \right)$ for the stars, which provides the geometry of the pulsation modes. Combining the phases of the frequency quintuplets, the pulsation amplitude and phase modulation curves, and the results of spherical harmonic decomposition, we conclude that the pulsation modes of frequency quintuplets in TIC 96315731, TIC 72392575, and TIC 318007796 correspond to distorted dipole mode, distorted quadrupole mode, and distorted dipole mode, respectively.