TRADES: A new software to derive orbital parameters from observed transit times and radial velocities. Revisiting Kepler-11 and Kepler-9

TL;DR

TRADES is a software tool that combines transit timing and radial velocity data to accurately determine exoplanetary system parameters, validated on synthetic and real Kepler systems, improving existing orbital solutions.

Contribution

The paper introduces TRADES, a novel software that simultaneously fits transit times and radial velocities using advanced optimization methods for exoplanet orbital analysis.

Findings

Validated TRADES on synthetic and Kepler systems.

Found orbital parameters consistent with previous studies for Kepler-11.

Derived a new best-fit solution for Kepler-9 with adjusted planetary masses.

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.