TIC 308396022: δ Scuti-γ Doradus hybrid with large-amplitude radial fundamental mode and regular g-mode period spacing

We analyse the pulsating behaviour of TIC 308396022, based on observations by the TESS mission. The star is a high-amplitude δ Sct star that shows a very rich amplitude spectrum using the 3-yr light curve. Among these frequencies, the strongest peak of f₁ = 13.20362567(12) d⁻¹ is identified as the radial fundamental mode, and we also find the first and second overtones (f₂ and f₃). In the low-frequency range (< 2.5 d⁻¹), 22 peaks are identified as gravity modes, which show a regular period spacing of about 2460 s and have an angular degree of l = 1. The period spacing pattern does not show a significant downward trend, suggesting the star is rotating slowly. We note that this is a δ Sct-γ Dor hybrid star containing a high-amplitude radial fundamental mode and a regular g-mode period spacing pattern. With the O − C analysis, we find the star shows a significant time delay, implying that the star has a companion and it is likely to be a white dwarf. The history of possible mass transfer provides a great opportunity for testing the current theories of binary evolution, mass transfer, and pulsation.