TRADES: A new software to derive orbital parameters from observed transit times and radial velocities

Abstract

Aims. With the purpose of determining the orbital parameters of exoplanetary systems from observational data, we have developed a software, named TRADES (TRAnsits and Dynamics of Exoplanetary Systems), to simultaneously fit observed radial velocities and transit times data. Methods. We implemented a dynamical simulator for N-body systems, which also fits the available data during the orbital integration and determines the best combination of the orbital parameters using grid search, $\chi^2$ minimization, genetic algorithms, particle swarm optimization, and bootstrap analysis. Results. To validate TRADES, we tested the code on a synthetic three-body system and on two real systems discovered by the Kepler mission: Kepler-9 and Kepler-11. These systems are good benchmarks to test multiple exoplanet systems showing transit time variations (TTVs) due to the gravitational interaction among planets. We have found that orbital parameters of Kepler-11 planets agree well with the values proposed in the discovery paper and with a a recent work from the same authors. We analyzed the first three quarters of Kepler-9 system and found parameters in partial agreement with discovery paper. Analyzing transit times (T0s) covering 12 quarters of Kepler data, that we have found a new best-fit solution. This solution outputs masses that are about 55% of the values proposed in the discovery paper; this leads to a reduced semi-amplitude of the radial velocities of about 12.80 m/s.