Exploring the helium core of the δ Scuti star CoRoT 102749568 with asteroseismology
Based on regularities in rotational splitting, we seek possible multiplets for the observed frequencies of CoRoT 102749568. There are 21 sets of multiplets identified, including four sets of multiplets with l = 1, nine sets of multiplets with l = 2, and eight sets of multiplets with l = 3. In particular, there are three complete triplets (f{sub 10}, f{sub 12}, f{sub 14}), (f{sub 31}, f{sub 34}, f{sub 35}), and (f{sub 41}, f{sub 43}, f{sub 44}). The rotational period of CoRoT 102749568 is estimated to be 1.34{sub −0.05}{sup +0.04} days. When doing model fittings, three l = 1 modes (f{sub 12}, f{sub 34}, and f{sub 43}) and the radial first overtone f{sub 13} are used. Our results shows that the three nonradial modes (f{sub 12}, f{sub 34}, and f{sub 43}) are mixed modes, which mainly provide constraints on the helium core. The radial first overtone f{sub 13} mainly provides constraint on the stellar envelope. Hence the size of the helium core of CoRoT 102749568 is determined to be M{sub He} = 0.148 ± 0.003 M{sub ⊙} and R{sub He} = 0.0581 ± 0.0007 R{sub ⊙}. The fundamental parameters of CoRoT 102749568 are determined to be M = 1.54 ± 0.03 M{sub ⊙}, Z=0.006, f{sub ov}=0.004±0.002, log g=3.696±0.003, T{sub eff}=6886±70 K, R = 2.916 ± 0.039 R{sub ⊙}, and L = 17.12 ± 1.13 L{sub ⊙}.