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Table 2

Physical and orbital parameters of confirmed circumbinary systems, and tidal parameters estimated with our model.

α e2 M2 Viscosity regime αcrit,g αcrit,s Migration direction
Kepler-16 (1) 0.318 0.0069 0.175 Gaseous 0.086 0.260 Outward 3 × 1013 6 × 1014
Kepler-34 (2) 0.210 0.182 0.250 Gaseous 0.309 1.340 Inward 7 × 1013 3 × 1012
Kepler-35 (2) 0.292 0.042 0.249 Gaseous 0.171 0.559 Outward 2 × 1012 1× 1012
Kepler-38 (3) 0.316 0.023 0.165 ? 0.162 0.492 ? 5 × 1012 8 × 1012
Kepler-47b (4) 0.283 0.021 0.194 Gaseous 0.135 0.455 Outward 3× 1012 6× 1012
Kepler-47d (5) 0.116 0.024 0.194 Gaseous 0.100 0.701 Outward 2 × 1015 3 × 1013
Kepler-47c (4) 0.085 0.044 0.194 ? 0.121 1.070 Inward 7 × 1015 7 × 1013
Kepler-64 (6) 0.267 0.0702 0.166 Gaseous 0.261 0.921 Outward 1 × 1015 1 × 1013
Kepler-413 (7) 0.286 0.1181 0.240 Gaseous 0.290 0.966 Inward 5 × 1013 3 × 1011
Kepler-453 (8) 0.235 0.0359 0.142 Gaseous 0.191 0.753 Outward 3 × 1014 3 × 1013
Kepler-1647 (9) 0.047 0.0581 0.247 Gaseous 0.098 1.367 Inward 3 × 1018 1 × 1016
Kepler-1661 (10) 0.295 0.057 0.181 Gaseous 0.235 0.761 Outward 2 × 1014 3 × 1013
TOI-1338 (11) 0.287 0.093 0.173 Gaseous 0.303 1.007 Inward 5 × 1012 1 × 1011

Notes. The viscosity regime of the CB planet is inferred from the mass and radius, compared with the γ2-values estimated for the Solar System planets in Ferraz-Mello (2013). The critical α-values and the migration direction are discussed in Sect. 4.2.1., while the tidal timescales for the semimajor axis evolution are explained in Sect. 4.2.2. For Kepler-38 we consider the mass estimated by means of a mass-radius fit in Zoppetti et al. (2019a), while the eccentricity adopted corresponds to the forced eccentricity.

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