Improving the stellar age determination through joint modeling of binarity and asteroseismology - Grid modeling of the seismic red giant binary KIC 9163796

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Volume 696 (April 2025)

A&A, 696 (2025) A42

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Table 4.

Cases considered for modeling KIC 9163796 and the associated stellar parameters determined from χ_red²-minimization.

Case	M₁	M₂	Y	Z	α_MLT, 1	α_MLT, 2	Common age	χ_red²
	[M_⊙]	[M_⊙]					[Gyr]
A0	1.35 ± 0.06	1.33 ± 0.06	0.28 ± 0.03	0.004 ± 0.002	1.5	1.5	2.68 $_{- 1.30}^{+ 3.12}$ $^{+3.12}_{-1.30}$	0.001
A1	1.35 ± 0.06	1.33 ± 0.06	0.28 ± 0.03	0.004 ± 0.002	1.5	1.5	2.19 $_{- 0.69}^{+ 0.53}$ $^{+0.53}_{-0.69}$	0.001
A2	1.36 ± 0.06	1.34 ± 0.06	0.28 ± 0.03	0.006^( * )	1.4	1.6	2.08 $_{- 0.53}^{+ 0.36}$ $^{+0.36}_{-0.53}$	0.05
A3	1.36 ± 0.06	1.34 ± 0.06	0.30 ± 0.03	0.006 ± 0.002	1.4	1.5	1.99 $_{- 0.41}^{+ 0.32}$ $^{+0.32}_{-0.41}$	0.008
B1	1.37 ± 0.06	1.35 ± 0.06	0.27 ± 0.03	0.007 ± 0.002	1.4	1.5	2.22 $_{- 0.77}^{+ 1.28}$ $^{+1.28}_{-0.77}$	0.002
B2	1.36 ± 0.06	1.34 ± 0.06	0.30 ± 0.03	0.006^( * )	1.4	1.4	2.09 $_{- 0.53}^{+ 1.00}$ $^{+1.00}_{-0.53}$	0.03
B3	1.36 ± 0.06	1.34 ± 0.06	0.30 ± 0.03	0.006 ± 0.002	1.4	1.5	2.09 $_{- 0.52}^{+ 1.33}$ $^{+1.33}_{-0.52}$	0.006
C1	1.35 ± 0.06	1.33 ± 0.06	0.27 ± 0.03	0.004 ± 0.002	1.4	1.5	2.32 $_{- 0.54}^{+ 0.32}$ $^{+0.32}_{-0.54}$	0.05
C2	1.31 ± 0.06	1.29 ± 0.06	0.30 ± 0.03	0.006^( * )	1.4	1.6	2.35 $_{- 0.28}^{+ 0.20}$ $^{+0.20}_{-0.28}$	0.3
C3	1.31 ± 0.06	1.29 ± 0.06	0.30 ± 0.03	0.006 ± 0.002	1.6	1.4	2.25 $_{- 0.27}^{+ 0.48}$ $^{+0.48}_{-0.27}$	0.07
D1	1.31 ± 0.06	1.29 ± 0.06	0.27 ± 0.03	0.004 ± 0.002	1.5	1.4	2.58 $_{- 0.42}^{+ 0.39}$ $^{+0.39}_{-0.42}$	0.4
D2	1.32 ± 0.06	1.30 ± 0.06	0.30 ± 0.03	0.006^( * )	1.6	1.4	2.44 $_{- 0.20}^{+ 0.25}$ $^{+0.25}_{-0.20}$	0.9
D3	1.32 ± 0.06	1.30 ± 0.06	0.29 ± 0.03	0.005 ± 0.002	1.6	1.4	2.52 $_{- 0.36}^{+ 0.31}$ $^{+0.31}_{-0.36}$	0.7

Notes. The first column provides the naming of the different optimization, while the second and third column provide the mass of the primary M₁ and secondary M₂ for the best-fitting model, respectively. The fourth and fifth column provide the initial helium Y and initial metallicity Z for this model, respectively. The sixth and seventh column show the mixing length parameters obtained from the model. The eighth column indicates the common age (Age₁ = Age₂) the χ_red²-minimization provides, including the respective error bars, obtained as described in Sect. 4.2. The last column indicates the minimum χ_red² value obtained for this case. No error bars for metallicity are given in the cases marked with ^( * ) since, in those cases, we forced the metallicity to be at the value of 0.006.

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