KIC 4150611: A quadruply eclipsing heptuple star system with a g-mode period-spacing pattern - Asteroseismic modelling of the g-mode period-spacing pattern

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Volume 693 (January 2025)

A&A, 693 (2025) A184

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Table B.1.

Parameters of the best-fitting models from C-3PO’s high resolution sample for each pattern under different external constraints.

Pattern	Sample	M	X_c	R	f_ov	Z	log(T_eff)	log(g)	log(L)
		M_⊙	-	R_⊙	-	-	dex	dex	dex
`PAT_LI2020`	All	$1 . 958_{- 0.622}^{+ 0.02}$ $1.958^{+0.02}_{-0.622}$	$0 . 07_{- 0.018}^{+ 0.625}$ $0.07^{+0.625}_{-0.018}$	$3 . 051_{- 1.793}^{+ 0.86}$ $3.051^{+0.86}_{-1.793}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.019}$ $0.01^{+0.019}_{-0.0}$	$3 . 8554_{- 0.062}^{+ 0.0}$ $3.8554^{+0.0}_{-0.062}$	$3 . 7612_{- 0.2299}^{+ 0.6032}$ $3.7612^{+0.6032}_{-0.2299}$	$1 . 343_{- 0.8698}^{+ 0.0295}$ $1.343^{+0.0295}_{-0.8698}$
`PAT_LI2020`	Spectro	$1 . 958_{- 0.566}^{+ 0.02}$ $1.958^{+0.02}_{-0.566}$	$0 . 07_{- 0.017}^{+ 0.569}$ $0.07^{+0.569}_{-0.017}$	$3 . 051_{- 1.698}^{+ 0.164}$ $3.051^{+0.164}_{-1.698}$	$0 . 011_{- 0.0}^{+ 0.003}$ $0.011^{+0.003}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.005}$ $0.01^{+0.005}_{-0.0}$	$3 . 8554_{- 0.0109}^{+ 0.0}$ $3.8554^{+0.0}_{-0.0109}$	$3 . 7612_{- 0.0432}^{+ 0.5581}$ $3.7612^{+0.5581}_{-0.0432}$	$1 . 343_{- 0.7621}^{+ 0.0216}$ $1.343^{+0.0216}_{-0.7621}$
`PAT_LI2020`	R	$1 . 478_{- 0.1}^{+ 0.042}$ $1.478^{+0.042}_{-0.1}$	$0 . 471_{- 0.09}^{+ 0.013}$ $0.471^{+0.013}_{-0.09}$	$1 . 589_{- 0.038}^{+ 0.16}$ $1.589^{+0.16}_{-0.038}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 011_{- 0.0}^{+ 0.015}$ $0.011^{+0.015}_{-0.0}$	$3 . 8537_{- 0.0241}^{+ 0.0009}$ $3.8537^{+0.0009}_{-0.0241}$	$4 . 2057_{- 0.0979}^{+ 0.0113}$ $4.2057^{+0.0113}_{-0.0979}$	$0 . 7629_{- 0.0782}^{+ 0.0752}$ $0.7629^{+0.0752}_{-0.0782}$
`PAT_LI2020`	R and Spectro	$1 . 478_{- 0.035}^{+ 0.042}$ $1.478^{+0.042}_{-0.035}$	$0 . 471_{- 0.084}^{+ 0.013}$ $0.471^{+0.013}_{-0.084}$	$1 . 589_{- 0.038}^{+ 0.158}$ $1.589^{+0.158}_{-0.038}$	$0 . 011_{- 0.0}^{+ 0.003}$ $0.011^{+0.003}_{-0.0}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$3 . 8537_{- 0.0088}^{+ 0.0009}$ $3.8537^{+0.0009}_{-0.0088}$	$4 . 2057_{- 0.0788}^{+ 0.0113}$ $4.2057^{+0.0113}_{-0.0788}$	$0 . 7629_{- 0.0391}^{+ 0.0752}$ $0.7629^{+0.0752}_{-0.0391}$
`PAT_LI2020`	Tight R	$1 . 459_{- 0.081}^{+ 0.061}$ $1.459^{+0.061}_{-0.081}$	$0 . 424_{- 0.043}^{+ 0.06}$ $0.424^{+0.06}_{-0.043}$	$1 . 644_{- 0.093}^{+ 0.104}$ $1.644^{+0.104}_{-0.093}$	$0 . 014_{- 0.003}^{+ 0.001}$ $0.014^{+0.001}_{-0.003}$	$0 . 011_{- 0.0}^{+ 0.015}$ $0.011^{+0.015}_{-0.0}$	$3 . 8466_{- 0.017}^{+ 0.0079}$ $3.8466^{+0.0079}_{-0.017}$	$4 . 1703_{- 0.0624}^{+ 0.0467}$ $4.1703^{+0.0467}_{-0.0624}$	$0 . 7656_{- 0.0809}^{+ 0.0725}$ $0.7656^{+0.0725}_{-0.0809}$
`PAT_LI2020`	Tight R and Spectro	$1 . 459_{- 0.016}^{+ 0.061}$ $1.459^{+0.061}_{-0.016}$	$0 . 424_{- 0.037}^{+ 0.06}$ $0.424^{+0.06}_{-0.037}$	$1 . 644_{- 0.093}^{+ 0.103}$ $1.644^{+0.103}_{-0.093}$	$0 . 014_{- 0.003}^{+ 0.0}$ $0.014^{+0.0}_{-0.003}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$3 . 8466_{- 0.0018}^{+ 0.0079}$ $3.8466^{+0.0079}_{-0.0018}$	$4 . 1703_{- 0.0434}^{+ 0.0467}$ $4.1703^{+0.0467}_{-0.0434}$	$0 . 7656_{- 0.0418}^{+ 0.0725}$ $0.7656^{+0.0725}_{-0.0418}$

`PAT_P04_PES`	All	$1 . 693_{- 0.367}^{+ 0.297}$ $1.693^{+0.297}_{-0.367}$	$0 . 185_{- 0.132}^{+ 0.512}$ $0.185^{+0.512}_{-0.132}$	$2 . 375_{- 1.099}^{+ 1.014}$ $2.375^{+1.014}_{-1.099}$	$0 . 013_{- 0.002}^{+ 0.002}$ $0.013^{+0.002}_{-0.002}$	$0 . 01_{- 0.0}^{+ 0.009}$ $0.01^{+0.009}_{-0.0}$	$3 . 8434_{- 0.019}^{+ 0.0112}$ $3.8434^{+0.0112}_{-0.019}$	$3 . 9158_{- 0.25}^{+ 0.4379}$ $3.9158^{+0.4379}_{-0.25}$	$1 . 0765_{- 0.5963}^{+ 0.2985}$ $1.0765^{+0.2985}_{-0.5963}$
`PAT_P04_PES`	Spectro	$1 . 471_{- 0.091}^{+ 0.519}$ $1.471^{+0.519}_{-0.091}$	$0 . 495_{- 0.436}^{+ 0.149}$ $0.495^{+0.149}_{-0.436}$	$1 . 553_{- 0.212}^{+ 1.612}$ $1.553^{+1.612}_{-0.212}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.005}$ $0.01^{+0.005}_{-0.0}$	$3 . 8544_{- 0.0099}^{+ 0.0002}$ $3.8544^{+0.0002}_{-0.0099}$	$4 . 2234_{- 0.4869}^{+ 0.1}$ $4.2234^{+0.1}_{-0.4869}$	$0 . 7447_{- 0.1775}^{+ 0.6304}$ $0.7447^{+0.6304}_{-0.1775}$
`PAT_P04_PES`	R	$1 . 471_{- 0.04}^{+ 0.05}$ $1.471^{+0.05}_{-0.04}$	$0 . 495_{- 0.098}^{+ 0.0}$ $0.495^{+0.0}_{-0.098}$	$1 . 553_{- 0.003}^{+ 0.175}$ $1.553^{+0.175}_{-0.003}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.006}$ $0.01^{+0.006}_{-0.0}$	$3 . 8544_{- 0.0126}^{+ 0.0002}$ $3.8544^{+0.0002}_{-0.0126}$	$4 . 2234_{- 0.0857}^{+ 0.0}$ $4.2234^{+0.0}_{-0.0857}$	$0 . 7447_{- 0.0363}^{+ 0.0927}$ $0.7447^{+0.0927}_{-0.0363}$
`PAT_P04_PES`	R and Spectro	$1 . 471_{- 0.032}^{+ 0.05}$ $1.471^{+0.05}_{-0.032}$	$0 . 495_{- 0.098}^{+ 0.0}$ $0.495^{+0.0}_{-0.098}$	$1 . 553_{- 0.003}^{+ 0.175}$ $1.553^{+0.175}_{-0.003}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.005}$ $0.01^{+0.005}_{-0.0}$	$3 . 8544_{- 0.0084}^{+ 0.0002}$ $3.8544^{+0.0002}_{-0.0084}$	$4 . 2234_{- 0.0781}^{+ 0.0}$ $4.2234^{+0.0}_{-0.0781}$	$0 . 7447_{- 0.0194}^{+ 0.0927}$ $0.7447^{+0.0927}_{-0.0194}$
`PAT_P04_PES`	Tight R	$1 . 494_{- 0.063}^{+ 0.027}$ $1.494^{+0.027}_{-0.063}$	$0 . 437_{- 0.04}^{+ 0.058}$ $0.437^{+0.058}_{-0.04}$	$1 . 65_{- 0.1}^{+ 0.078}$ $1.65^{+0.078}_{-0.1}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 011_{- 0.001}^{+ 0.005}$ $0.011^{+0.005}_{-0.001}$	$3 . 8546_{- 0.0128}^{+ 0.0}$ $3.8546^{+0.0}_{-0.0128}$	$4 . 1778_{- 0.04}^{+ 0.0456}$ $4.1778^{+0.0456}_{-0.04}$	$0 . 7952_{- 0.0869}^{+ 0.0421}$ $0.7952^{+0.0421}_{-0.0869}$
`PAT_P04_PES`	Tight R and Spectro	$1 . 494_{- 0.055}^{+ 0.027}$ $1.494^{+0.027}_{-0.055}$	$0 . 437_{- 0.04}^{+ 0.058}$ $0.437^{+0.058}_{-0.04}$	$1 . 65_{- 0.1}^{+ 0.078}$ $1.65^{+0.078}_{-0.1}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 011_{- 0.001}^{+ 0.003}$ $0.011^{+0.003}_{-0.001}$	$3 . 8546_{- 0.0086}^{+ 0.0}$ $3.8546^{+0.0}_{-0.0086}$	$4 . 1778_{- 0.0325}^{+ 0.0456}$ $4.1778^{+0.0456}_{-0.0325}$	$0 . 7952_{- 0.07}^{+ 0.0421}$ $0.7952^{+0.0421}_{-0.07}$

`PAT_P04_OPT`	All	$1 . 512_{- 0.187}^{+ 0.487}$ $1.512^{+0.487}_{-0.187}$	$0 . 424_{- 0.374}^{+ 0.275}$ $0.424^{+0.275}_{-0.374}$	$1 . 678_{- 0.43}^{+ 2.586}$ $1.678^{+2.586}_{-0.43}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.02}$ $0.01^{+0.02}_{-0.0}$	$3 . 8558_{- 0.0639}^{+ 0.0086}$ $3.8558^{+0.0086}_{-0.0639}$	$4 . 1681_{- 0.6915}^{+ 0.1995}$ $4.1681^{+0.1995}_{-0.6915}$	$0 . 8188_{- 0.3604}^{+ 0.6574}$ $0.8188^{+0.6574}_{-0.3604}$
`PAT_P04_OPT`	Spectro	$1 . 512_{- 0.127}^{+ 0.477}$ $1.512^{+0.477}_{-0.127}$	$0 . 424_{- 0.368}^{+ 0.273}$ $0.424^{+0.273}_{-0.368}$	$1 . 678_{- 0.363}^{+ 1.689}$ $1.678^{+1.689}_{-0.363}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.02}$ $0.01^{+0.02}_{-0.0}$	$3 . 8558_{- 0.0115}^{+ 0.0086}$ $3.8558^{+0.0086}_{-0.0115}$	$4 . 1681_{- 0.488}^{+ 0.1762}$ $4.1681^{+0.1762}_{-0.488}$	$0 . 8188_{- 0.259}^{+ 0.5865}$ $0.8188^{+0.5865}_{-0.259}$
`PAT_P04_OPT`	R	$1 . 512_{- 0.094}^{+ 0.047}$ $1.512^{+0.047}_{-0.094}$	$0 . 424_{- 0.053}^{+ 0.125}$ $0.424^{+0.125}_{-0.053}$	$1 . 678_{- 0.126}^{+ 0.069}$ $1.678^{+0.069}_{-0.126}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.02}$ $0.01^{+0.02}_{-0.0}$	$3 . 8558_{- 0.0147}^{+ 0.0086}$ $3.8558^{+0.0086}_{-0.0147}$	$4 . 1681_{- 0.0481}^{+ 0.0591}$ $4.1681^{+0.0591}_{-0.0481}$	$0 . 8188_{- 0.1058}^{+ 0.059}$ $0.8188^{+0.059}_{-0.1058}$
`PAT_P04_OPT`	R and Spectro	$1 . 512_{- 0.071}^{+ 0.047}$ $1.512^{+0.047}_{-0.071}$	$0 . 424_{- 0.035}^{+ 0.125}$ $0.424^{+0.125}_{-0.035}$	$1 . 678_{- 0.126}^{+ 0.069}$ $1.678^{+0.069}_{-0.126}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.02}$ $0.01^{+0.02}_{-0.0}$	$3 . 8558_{- 0.011}^{+ 0.0086}$ $3.8558^{+0.0086}_{-0.011}$	$4 . 1681_{- 0.0405}^{+ 0.0591}$ $4.1681^{+0.0591}_{-0.0405}$	$0 . 8188_{- 0.0873}^{+ 0.059}$ $0.8188^{+0.059}_{-0.0873}$
`PAT_P04_OPT`	Tight R	$1 . 492_{- 0.074}^{+ 0.067}$ $1.492^{+0.067}_{-0.074}$	$0 . 441_{- 0.07}^{+ 0.108}$ $0.441^{+0.108}_{-0.07}$	$1 . 639_{- 0.086}^{+ 0.109}$ $1.639^{+0.109}_{-0.086}$	$0 . 012_{- 0.001}^{+ 0.003}$ $0.012^{+0.003}_{-0.001}$	$0 . 01_{- 0.0}^{+ 0.02}$ $0.01^{+0.02}_{-0.0}$	$3 . 8556_{- 0.0145}^{+ 0.0089}$ $3.8556^{+0.0089}_{-0.0145}$	$4 . 1831_{- 0.0631}^{+ 0.0441}$ $4.1831^{+0.0441}_{-0.0631}$	$0 . 7925_{- 0.0795}^{+ 0.0853}$ $0.7925^{+0.0853}_{-0.0795}$
`PAT_P04_OPT`	Tight R and Spectro	$1 . 492_{- 0.051}^{+ 0.067}$ $1.492^{+0.067}_{-0.051}$	$0 . 441_{- 0.052}^{+ 0.108}$ $0.441^{+0.108}_{-0.052}$	$1 . 639_{- 0.086}^{+ 0.109}$ $1.639^{+0.109}_{-0.086}$	$0 . 012_{- 0.001}^{+ 0.003}$ $0.012^{+0.003}_{-0.001}$	$0 . 01_{- 0.0}^{+ 0.02}$ $0.01^{+0.02}_{-0.0}$	$3 . 8556_{- 0.0108}^{+ 0.0089}$ $3.8556^{+0.0089}_{-0.0108}$	$4 . 1831_{- 0.0555}^{+ 0.0441}$ $4.1831^{+0.0441}_{-0.0555}$	$0 . 7925_{- 0.061}^{+ 0.0853}$ $0.7925^{+0.0853}_{-0.061}$

`PAT_STS`	All	$1 . 506_{- 0.164}^{+ 0.491}$ $1.506^{+0.491}_{-0.164}$	$0 . 434_{- 0.376}^{+ 0.26}$ $0.434^{+0.26}_{-0.376}$	$1 . 659_{- 0.394}^{+ 1.544}$ $1.659^{+1.544}_{-0.394}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.005}$ $0.01^{+0.005}_{-0.0}$	$3 . 8561_{- 0.0252}^{+ 0.0023}$ $3.8561^{+0.0023}_{-0.0252}$	$4 . 1764_{- 0.4517}^{+ 0.1851}$ $4.1764^{+0.1851}_{-0.4517}$	$0 . 8087_{- 0.3264}^{+ 0.5706}$ $0.8087^{+0.5706}_{-0.3264}$
`PAT_STS`	Spectro	$1 . 506_{- 0.129}^{+ 0.491}$ $1.506^{+0.491}_{-0.129}$	$0 . 434_{- 0.376}^{+ 0.235}$ $0.434^{+0.235}_{-0.376}$	$1 . 659_{- 0.342}^{+ 1.544}$ $1.659^{+1.544}_{-0.342}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.004}$ $0.01^{+0.004}_{-0.0}$	$3 . 8561_{- 0.0118}^{+ 0.0023}$ $3.8561^{+0.0023}_{-0.0118}$	$4 . 1764_{- 0.4503}^{+ 0.1617}$ $4.1764^{+0.1617}_{-0.4503}$	$0 . 8087_{- 0.2635}^{+ 0.5706}$ $0.8087^{+0.5706}_{-0.2635}$
`PAT_STS`	R	$1 . 506_{- 0.075}^{+ 0.0}$ $1.506^{+0.0}_{-0.075}$	$0 . 434_{- 0.045}^{+ 0.034}$ $0.434^{+0.034}_{-0.045}$	$1 . 659_{- 0.09}^{+ 0.068}$ $1.659^{+0.068}_{-0.09}$	$0 . 011_{- 0.0}^{+ 0.004}$ $0.011^{+0.004}_{-0.0}$	$0 . 01_{- 0.0}^{+ 0.004}$ $0.01^{+0.004}_{-0.0}$	$3 . 8561_{- 0.0137}^{+ 0.0}$ $3.8561^{+0.0}_{-0.0137}$	$4 . 1764_{- 0.0443}^{+ 0.03}$ $4.1764^{+0.03}_{-0.0443}$	$0 . 8087_{- 0.0825}^{+ 0.0062}$ $0.8087^{+0.0062}_{-0.0825}$
`PAT_STS`	R and Spectro	$1 . 506_{- 0.071}^{+ 0.0}$ $\mathbf{1.506^{+0.0}_{-0.071}}$	$0 . 434_{- 0.045}^{+ 0.034}$ $\mathbf{0.434^{+0.034}_{-0.045}}$	$1 . 659_{- 0.09}^{+ 0.068}$ $\mathbf{1.659^{+0.068}_{-0.09}}$	$0 . 011_{- 0.0}^{+ 0.004}$ $\mathbf{0.011^{+0.004}_{-0.0}}$	$0 . 01_{- 0.0}^{+ 0.004}$ $\mathbf{0.01^{+0.004}_{-0.0}}$	$3 . 8561_{- 0.0116}^{+ 0.0}$ $\mathbf{3.8561^{+0.0}_{-0.0116}}$	$4 . 1764_{- 0.0443}^{+ 0.03}$ $\mathbf{4.1764^{+0.03}_{-0.0443}}$	$0 . 8087_{- 0.0807}^{+ 0.0062}$ $\mathbf{0.8087^{+0.0062}_{-0.0807}}$
`PAT_STS`	Tight R	$1 . 455_{- 0.024}^{+ 0.051}$ $1.455^{+0.051}_{-0.024}$	$0 . 434_{- 0.045}^{+ 0.034}$ $0.434^{+0.034}_{-0.045}$	$1 . 632_{- 0.063}^{+ 0.094}$ $1.632^{+0.094}_{-0.063}$	$0 . 014_{- 0.003}^{+ 0.001}$ $0.014^{+0.001}_{-0.003}$	$0 . 012_{- 0.001}^{+ 0.003}$ $0.012^{+0.003}_{-0.001}$	$3 . 8463_{- 0.0039}^{+ 0.0098}$ $3.8463^{+0.0098}_{-0.0039}$	$4 . 1756_{- 0.0434}^{+ 0.0308}$ $4.1756^{+0.0308}_{-0.0434}$	$0 . 7589_{- 0.0327}^{+ 0.056}$ $0.7589^{+0.056}_{-0.0327}$
`PAT_STS`	Tight R and Spectro	$1 . 455_{- 0.02}^{+ 0.051}$ $1.455^{+0.051}_{-0.02}$	$0 . 434_{- 0.045}^{+ 0.034}$ $0.434^{+0.034}_{-0.045}$	$1 . 632_{- 0.063}^{+ 0.094}$ $1.632^{+0.094}_{-0.063}$	$0 . 014_{- 0.003}^{+ 0.001}$ $0.014^{+0.001}_{-0.003}$	$0 . 012_{- 0.001}^{+ 0.003}$ $0.012^{+0.003}_{-0.001}$	$3 . 8463_{- 0.0018}^{+ 0.0098}$ $3.8463^{+0.0098}_{-0.0018}$	$4 . 1756_{- 0.0434}^{+ 0.0308}$ $4.1756^{+0.0308}_{-0.0434}$	$0 . 7589_{- 0.0309}^{+ 0.056}$ $0.7589^{+0.056}_{-0.0309}$

Notes. The externally constrained PAT_STS pattern is the preferred solution, and marked in bold. The units of T_eff, g, and L are K, g cm⁻³, and L_⊙. The subsamples are described in Table 1.

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