Rotational splitting and asteroseismic modelling of the delta Scuti star EE Camelopardalis

Abstract

According to the rotational splitting law of g modes, the frequency spectra of EE Cam can be disentangled only with oscillation modes of $\ell$ = 0, 1, and 2. Fifteen sets of rotational splits are found, containing five sets of $\ell=1$ multiplets and ten sets of $\ell=2$ multiplets. The rotational period of EE Cam is deduced to be $P_{\rm rot}$ = $1.84_{-0.05}^{+0.07}$ days. When we do model fittings, we use two nonradial oscillation modes ($f_{11}$ and $f_{32}$) and the fundamental radial mode $f_{1}$. The fitting results show that $\chi^{2}$ of the best-fitting model is much smaller than those of other theoretical models. The physical parameters of the best-fitting model are $M$ = 2.04 $M_{\odot}$, $Z=0.028$, $T_{\rm eff}$ = 6433 K, $\log L/L_{\odot}$ = 1.416, $R$ = 4.12 $R_{\odot}$, $\log g$ = 3.518, and $\chi^{2}$ = 0.00035. Furthermore, we find $f_{11}$ and $f_{32}$ are mixed mode, which mainly characterize the features of the helium core. The fundamental radial mode $f_{1}$ mainly restrict the features of the stellar envelope. Finally, the acoustic radius $\tau_{0}$ and the period separation $\Pi_{0}$ are determined to be 5.80 hr and 463.7 s respectively, and the size of the helium core of EE Cam is estimated to be $M_{\rm He}$ = 0.181 $M_{\odot}$ and $R_{\rm He}$ = 0.0796 $R_{\odot}$.