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We study orbital evolution of multi-planet systems that form a resonantchain, with nearest neighbours close to first order commensurabilities,incorporating orbital circularisation produced by tidal interaction with thecentral star. We develop a semi-analytic model applicable when the relativeproximities to commensurability, though small, are large compared toepsilon^(2/3) , with epsilon being a measure of the characteristic planet tocentral star mass ratio. This enables determination of forced eccentricities aswell as which resonant angles enter libration. When there are no active linkedthree body Laplace resonances, the rate of evolution of the semi-major axes mayalso be determined. We perform numerical simulations of the HD 158259 and EPIC245950175 systems finding that the semi-analytic approach works well in theformer case but not so well in the latter case on account of the effects ofthree active three body Laplace resonances which persist during the evolution.For both systems we estimate that if the tidal parameter, Q', significantlyexceeds 1000, tidal effects are unlikely to have influenced period ratiossignificantly since formation. On the other hand if Q' < ~ 100 tidal effectsmay have produced significant changes including the formation of three bodyLaplace resonances in the case of the EPIC 245950175 system.

celestial mechanics and dynamical astronomy/celestial mechanics and dynamical astronomy

The orbital evolution of resonant chains of exoplanets incorporating  circularisation produced by tidal interaction with the central star with  application to the HD 158259 and EPIC 245950175 systems