Table 1
Parameters of the five systems in resonant chain analyzed in this work.
| M⋆(M⊙) | t⋆ (Gyr) | mi (m⊕) | ρi(ρ⊕) | Pi (days) | (p+q)/p | Δ(p+q)/p |  |
||
|---|---|---|---|---|---|---|---|---|---|
| Kepler-80 | f | 0.73 | 2 ± 1 | – | – | 0.98678 | – | ||
| d | 5.95 | 14.6 | 3.07222 | 3/1 | 0.1133 | 8.8 × 104 | |||
| e | 2.97 | 6.9 | 4.64489 | 3/2 | 0.0118 | 2.4 × 105 | |||
| b | 3.5 | 1.45 | 7.05246 | 3/2 | 0.0186 | 9.7 × 104 | |||
| 4/3 | 0.0168 | ||||||||
| c | 3.49 | 1.22 | 9.52355 | 3/2 | 0.0385 | 3.2 × 105 | |||
| g | 0.065 | – | 14.6455 | – | |||||
| Kepler-223 | b | 1.125 | ~6 | 7.4 | 0.279 | 7.38449 | 1 × 105 | ||
| c | 5.1 | 0.129 | 9.84564 | 4/3 | 0.0000 | 1.3 × 105 | |||
| d | 8 | 0.056 | 14.78869 | 3/2 | 0.0021 | 1.4 × 105 | |||
| e | 4.8 | 0.051 | 19.72567 | 4/3 | 0.0005 | 5.9 × 105 | |||
| K2-138 | b | 0.93 |  |
3.1 | 0.89 | 2.3531 | 8.1 × 103 | ||
| c | 6.3 | 0.51 | 3.56 | 3/2 | 0.0129 | 1.2 × 104 | |||
| d | 7.9 | 0.58 | 5.4048 | 3/2 | 0.0182 | 7.8 × 104 | |||
| e | 13 | 0.33 | 8.2615 | 3/2 | 0.0285 | 1.4 × 105 | |||
| f | 8.7 | 0.38 | 12.7576 | 3/2 | 0.0442 | 1.5 × 106 | |||
| TOI-178 | b | 0.65 |  |
1.5 | 0.98 | 1.914558 | 4.9 × 104 | ||
| c | 4.77 | 1.02 | 3.23845 | 5/3 | 0.0248 | 2.4 × 104 | |||
| d | 3.01 | 0.177 | 6.5577 | 2/1 | 0.0250 | 3.7 × 104 | |||
| e | 3.86 | 0.360 | 9.961881 | 3/2 | 0.0191 | 6.3 × 105 | |||
| f | 7.72 | 0.65 | 15.231915 | 3/2 | 0.0290 | 6.7 × 106 | |||
| g | 3.94 | 0.166 | 20.7095 | 4/3 | 0.0263 | 4.1 × 106 | |||
| TRAPPIST-1 | b | 0.898 | 7.6 ± 2.2 | 1.374 | 0.987 | 1.510826 | 5.1 × 102 | ||
| c | 1.308 | 0.991 | 2.421937 | 3/2 | 0.1031 | 4.1 × 103 | |||
| d | 0.388 | 0.792 | 4.049219 | 5/3 | 0.0052 | 5.9 × 104 | |||
| e | 0.692 | 0.889 | 6.101013 | 3/2 | 0.0067 | 2.9 × 105 | |||
| f | 1.039 | 0.911 | 9.207540 | 3/2 | 0.0092 | 1.3 × 106 | |||
| g | 1.321 | 0.917 | 12.352446 | 4/3 | 0.0082 | 4.2 × 106 | |||
| h | 0.326 | 0.755 | 18.772866 | 3/2 | 0.0198 | 4.7 × 107 |
Notes. The columns successively give for each system the star mass and age, planetary masses and densities, orbital periods, 2-planet MMRs between adjacent planets, resonance offsets, and e-damping timescales due to tides raised by the star using Q′ = 0.05. Data for Kepler-80 was taken from MacDonald et al. (2016, 2021), for Kepler-223 from Mills et al. (2016), for K2-138 from Lopez et al. (2019), for TOI-178 from Leleu et al. (2021), and for TRAPPIST-1 from Burgasser & Mamajek (2017); Agol et al. (2021).
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