摘要: We analyse the pulsating behaviour of TIC 308396022 observed by the TESS
mission. The star is a high-amplitude $\delta$ Sct star (HADS) that shows a
very rich amplitude spectrum using the 3-yr light curve. Among these
frequencies, the strongest peak of $f_{1}= 13.20362567(12) \rm{d^{-1}}$ is
identified as the radial fundamental mode, and we also find the first and
second overtones ($f_2$ and $f_3$). In the low frequency range (< 2.5
$\rm{d^{-1}}$), 22 peaks are identified to be gravity modes, which show a
regular period spacing of about 2460\,s and have the angular degree $l = 1$.
The period spacing pattern does not show a significant downward trend,
suggesting the star rotates slowly. We note that this is a $\delta$
Sct--$\gamma$ Dor hybrid star containing a high-amplitude radial fundamental
mode and a regular g-mode period spacing pattern. With O-C analysis, we find
the star shows a significant time delay, implying that the star has a companion
which is likely to be a white dwarf. The history of possible mass transfer
provides a great opportunity to test the current theories of binary evolution,
mass transfer, and pulsation.