TRAnsits and Dynamics of Exoplanetary Systems Software for Detecting, Refining Transit Detections

TRADES: a new software to derive orbital parameters from observed Transit Times and Radial Velocities. Revisiting Kepler-11 and Kepler-9

Authors:

Borsato et al

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 system which also fits the available data during the orbital integration and determines the best combination of the orbital parameters using grid search, χ2 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 orbital parameters of Kepler-11 planets in good agreement 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 we have found a new best-fit solution. This solution outputs masses that are about the 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.

Revising the Kepler-9 System

Kepler-9 revisited 60% the mass with six times more data

Authors:

Dreizler et al

Abstract:

Kepler-9 was the first case where transit timing variations have been used to confirm the planets in this system. Following predictions of dramatic TTVs - larger than a week - we re-analyse the system based on the full Kepler data set. We re-processed all available data for Kepler-9 removing short and long term trends, measured the times of mid-transit and used those for dynamical analysis of the system. The newly determined masses and radii of Kepler-9b and -9c change the nature of these planets relative to the one described in Holman et al. 2010 (hereafter H10) with very low, but relatively well charcterised (to better than 7%), bulk densities of 0.18 and 0.14 g cm3 (about 1/3 of the H10 value). We constrain the masses (45.1 and 31.0 M⊕, for Kepler-9b and -9c respectively) from photometry alone, allowing us to see possible indications for an outer non-transiting planet in the radial velocity data. At 2R⊕ Kepler-9d is determined to be larger than suggested before - suggesting that it is a low-mass low-density planet. The comparison between the H10 analysis and our new analysis suggests that small formal error in the TTV inversion may be misleading if the data does not cover a significant fraction of the interaction time scale.