Kepler Object of Interest Network. II. Photodynamical modelling of Kepler-9 over 8 years of transit observations

Context. The Kepler Object of Interest Network (KOINet) is a multi-site network of telescopes around the globe organised to follow up transiting planet-candidate Kepler objects of interest (KOIs) with large transit timing variations (TTVs). Its main goal is to complete their TTV curves, as the Kepler telescope no longer observes the original Kepler field.
Aims: Combining Kepler and new ground-based transit data we improve the modelling of these systems. To this end, we have developed a photodynamical model, and we demonstrate its performance using the Kepler-9 system as an example.
Methods: Our comprehensive analysis combines the numerical integration of the system's dynamics over the time span of the observations along with the transit light curve model. This provides a coherent description of all observations simultaneously. This model is coupled with a Markov chain Monte Carlo algorithm, allowing for the exploration of the model parameter space.
Results: Applied to the Kepler-9 long cadence data, short cadence data, and 13 new transit observations collected by KOINet between the years 2014 and 2017, our modelling provides well constrained predictions for the next transits and the system's parameters. We have determined the densities of the planets Kepler-9b and 9c to the very precise values of ρ_b = 0.439 ± 0.023 g cm^-3 and ρ_c = 0.322 ± 0.017 g cm^-3. Our analysis reveals that Kepler-9c will stop transiting in about 30 yr due to strong dynamical interactions between Kepler-9b and 9c, near 2:1 resonance, leading to a periodic change in inclination.
Conclusions: Over the next 30 years, the inclination of Kepler-9c (-9b) will decrease (increase) slowly. This should be measurable by a substantial decrease (increase) in the transit duration, in as soon as a few years' time. Observations that contradict this prediction might indicate the presence of additional objects in this system. If this prediction turns out to be accurate, this behaviour opens up a unique chance to scan the different latitudes of a star: high latitudes with planet c and low latitudes with planet b.

Ground-based photometry is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/618/A41