Open Access
Table 4
Assessment of the dynamical model for the Kepler-221 system. Comments for different scenarios in different phases are listed.
| Phase | Section | Constraint | Condition/mechanism | Comment |
|---|---|---|---|---|
| I | 4.1 | First-order resonance chain with five planets | Large scale migration | • Formation of first-order 2BR is a natural result of convergent migration |
| I/II | 4.1 | Planets deep in resonance | Needs high eccentricities for planets | • High eccentricities ensure quick merger after resonances break |
| II | 4.1 | Breaking of resonance chain | Requires instability in the system | • Likely happens in many other systems |
| III | 4.3 | 3BR Reformation… | 1. No effects | – Zeroth-order (b, c, e) 3BR never reforms |
| 2. Anomalous damping on planet c (large Qc/Qd) | • Can lead to convergent migration but no clear reason why planet c stands out | |||
| 3. Positive torque on planet b | + Mechanism can also be applied to Phase IV | |||
| IV | 5.2 | Avoid (c, d, e) 3BR… | 1. Positive torque on planet b | • Mechanism can also be applied to Phase III |
| 2. Different assumption of the planet masses | + Needs no additional mechanisms and agrees with peas-in-a-pod scenario | |||
| IV | 6.3 | Long-term expansion | 1. System age much older | • No need for mechanisms like obliquity tides but inconsistent with age inference of Kepler-221 |
| 2. Obliquity tides | • Can explain the fast orbital expansion but hinders 3BR reformation in Phase III |
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