The origin and 9:7 MMR dynamics of the Kepler-29 system

Abstract

We analyse the Transit Timing Variation (TTV) measurements of a~system of two super-Earths detected as Kepler-29, in order to constrain the planets' masses and orbital parameters. A dynamical analysis of the best-fitting configurations constrains the masses to be $\sim 6$ and $\sim 5$ Earth masses for the inner and the outer planets, respectively. The analysis also reveals that the system is likely locked in the 9:7~mean motion resonance. However, a variety of orbital architectures regarding eccentricities and the relative orientation of orbits is permitted by the observations as well as by stability constraints. We attempt to find configurations preferred by the planet formation scenarios as an additional, physical constraint. We show that configurations with low eccentricities and anti-aligned apsidal lines of the orbits are a natural and most likely outcome of the convergent migration. However, we show that librations of the critical angles are not necessary for the Kepler-29 system to be dynamically resonant, and such configurations may be formed on the way of migration as well. We argue, on the other hand, that aligned configurations with $e \gtrsim 0.03$ may be not consistent with the migration scenario.