A periodic configuration of the Kepler-25 planetary system

We study proximity of the Kepler-25 planetary system to a periodic configuration, which is known to be the final state of a system that undergoes smooth migration resulting from the planet-disc interaction. We show that the system is close to the periodic configuration of 2:1 mean motion resonance (MMR) what indicates that its past migration was neither disturbed significantly by turbulence in the disc nor the orbits were perturbed by planetesimals that were left after the disc dispersal. We show that, because of the transit timing variations (TTVs) model degeneracy, a periodic configuration is difficult to be found when the standard modelling of the TTVs is used. The TTV signal of a periodic configuration (with anti-aligned apsidal lines) may be misinterpreted as an aligned non-resonant system. We demonstrate that the standard Markov Chain Monte Carlo (MCMC) modelling of the Kepler-25 TTVs is very sensitive to an a priori information on the eccentricities (prior probability distributions). Wide priors (of the order of the ones typically used in the literature) result in favouring the aligned non-resonant configurations with small planets' masses and moderate eccentricities, while for the narrower priors the most likely are the anti-aligned resonant systems with larger masses and very low eccentricities.