Determining the evolutionary stage of the delta Scuti star HIP 80088 with asteroseismology

We have computed a grid of theoretical models to fit the twelve oscillation modes of HIP 80088 observed by K2. HIP 80088 is determined to be a pre-main sequence star, in which CN cycle has not arrived at the equilibrium state. Mass fractions of C12 and N14 in metal composition are 0.1277$^{+0.0064}_{-0.0049}$ and 0.1092$^{+0.0057}_{-0.0074}$ respectively, indicating that twenty-eight percent of C12 have turned into N14. Meanwhile, our fitting results show that physical parameters of HIP 80088 converge to a small range: $M$ = 1.68$-$1.78 $M _{\odot}$, $Z$ = 0.015$-$0.018, $\upsilon_{\rm e}$ = 120$-$136 km s$^{-1}$, $\log g$ = 4.114$-$4.125, $R$ = 1.882$-$1.914 $R_{\odot}$, $\tau_{0}$ = 7636$-$7723 s, and age = 9.03$-$10.21 Myr. Based on our model fittings, $f_{3}$ is suggested to be one radial mode, $f_{2}$, $f_{4}$, $f_{8}$, and $f_{11}$ to be four $\ell$ = 1 modes, and $f_{1}$, $f_{5}$, $f_{6}$, $f_{7}$, $f_{9}$, $f_{10}$, and $f_{12}$ to be seven $\ell$ = 2 modes. In particularly, we find that ($f_{2}$, $f_{4}$, $f_{8}$) form one complete triplet with the averaged frequency spacing of 16.045 $\mu$Hz , and ($f_{5}$, $f_{7}$, $f_{9}$, $f_{10}$) form four components of one quintuplet with the averaged frequency spacing of 13.388 $\mu$Hz. The two averaged frequency spacings are not equal. Based on the best-fitting model, those $\ell$ = 2 modes of HIP 80088 are found to be mixed modes, which are p-dominated modes with pronounced g-mode features, while oscillation modes with $\ell$ = 1 are p modes.