Two high-amplitude $\delta$ Scuti-$\gamma$ Doradus hybrids constrained by the radial fundamental p and equally spaced g modes

Abstract

Based on 2-minute cadence TESS data, we investigate pulsations of TIC 65138566 and TIC 139729335 and discover them to be two new HADS stars with equally spaced g modes. We recognize the radial fundamental mode $f_1$ = 18.3334 c/d and the first overtone $f_3$ = 23.6429 c/d for TIC 65138566, and identify the highest peak $f_1$ = 19.0955 c/d as the radial fundamental mode for TIC 139729335. For g modes, both stars display a regular period spacing of 2413 s. Through detailed seismological analysis, we deduce that these period spacing patterns correspond to modes with $\ell$ = 1. Moreover, our analysis reveals that with the increase in masses and metallicities, the star should display a higher degree of evolution to match a specific period spacing $\Pi_0$. Conversely, the star should have a lower extent of evolution to match the radial fundamental mode. These two contradictory behaviors allow us to precisely obtain stellar physical parameters. TIC 65138566 and TIC 139729335 are determined to be two main sequence stars that have almost the same range of masses and metallicities, with $M$ = 1.36 $\pm$ 0.06 $M_{\odot}$ and $Z$ = 0.005 $\pm$ 0.002. The hydrogen abundance in the core of TIC 65138566 is estimated to be about 0.28, while TIC 139729335 has a slightly higher value of around 0.31. Finally, we suggest that the HADS $\delta$ Scuti-$\gamma$ Doradus star TIC 308396022 is a main sequence star with $M$ = 1.54 $\pm$ 0.08 $M_{\odot}$, $Z$ = 0.007 $\pm$ 0.001, and $X_{\rm c}$ = 0.18 $\pm$ 0.02.