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Asteroseismology of a $δ$ Scuti star CoRoT 102749568

For $δ$ Scuti star CoRoT 102749568, 52 independent frequencies were obtained by Papar$\acute{o}$ et al. 2013. We find that there are 4 multiplets and 8 doublets with nearly equal split caused by rotation. Differential rotation is suggested instead of rigid body rotation to explain the equal split phenomenon. Grids of models are computed with MESA to fit observational frequencies of CoRoT 102749568. After rejecting modes of $m\neq0$ in multiplets and doublets, we identify 31 modes of $m = 0$ and 3 modes of $m\neq0$, including 4 modes of $l = 0$, 9 modes of $l=1$, 11 modes of $l=2$, and 10 modes of $l=3$. The mean error is 0.447$μ$Hz for the best-fitting model, and the physical parameters of the corresponding model are as followings: $M=1.95$ $\rm M_{\odot}$, $Z=0.025$, $T_{\rm eff}=7096$ K, log$g=3.727$, $L=22.77$ $\rm L_{\odot}$, $Age=1.113$ Gyr.