Detection, Confirmation and Characterization of Multi-planet Systems by Transit Time Variations

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Multi-planet systems are crucial for the understanding of the formation and dynamical evolution of planetary systems. Only a small number of confirmed planets with true masses is known (compared to the number of all planetary candidates) because there is not enough telescope time available to cover all pending confirmations, in particular for faint stars. The mass determination for Earth- or Neptune-sized planets by radial velocity (RV) is in particular difficult with current telescopes and instrumental technique because of their small gravitational influence onto their host star. Thus it is not expected to get masses from all planetary candidates covering the full radii and orbital period ranges. Another method to characterize the planetary system and to complete this sample with regard to longer periods is the Transit Time Variation (TTV). This method uses only the information from the light curve and can detect, confirm and characterize transiting as well as non-transiting planets in multi-planet systems.Are there more undetected planets in a system? How closely packed are these systems? These questions may be answered by studying the orbital evolution of multi-planet systems: How do the orbital eccentricity and semi-major axis change with time? What are the influences of tides and general relativity on extremely short period TTV-planets? In recent TTV studies and in all existing TTV analysis software tools only the gravitational force is considered. This simplification may be valid for the majority of the analyzed systems but not for all. The inclusion of other forces is crucial for close-in planets (tides, general relativity), planets orbiting close to each other (planet-planet interaction) and for non-transiting planets perturbing the known transiting planet. By analyzing and comparing all forces together, the knowledge of the orbit, the stellar mass, the masses of the transiting planet and the perturbing planet may be verified and/or improved in particular for candidates difficult to be verified by RV observations. The questions above shall be answered by the analysis of light curves from existing planetary systems showing TTV as well as the search for more systems with TTV in ´new´ light curves from the Kepler and K2 missions. The already existing software package developed at RIU-PF shall become fully automated by implementing a Monte Carlo Markov Chain to search the whole parameter space for the best solution. Tides, general relativity and stellar oblateness shall be implemented in the orbit simulation for a full characterization of the planetary system. TTV is mostly the only chance to characterize a detected planetary system. The direct application, however, is the verification of transiting planets independent from ground-based observations. In consequence, TTV is also the detection of an unknown planet perturbing the known planet and therefore the detection of a multi-planet system which can be directly characterized by TTV.