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

多行星系统对于理解行星系统的形成和动力学演化是至关重要的。与所有候选行星的数量相比，只有一小部分已确认的真实质量的行星是已知的，因为没有足够的望远镜时间来覆盖所有悬而未决的确认，特别是对于昏暗的恒星。通过径向速度(RV)确定地球或海王星大小的行星的质量，对于目前的望远镜和仪器技术来说尤其困难，因为它们对其宿主恒星的引力影响很小。因此，预计它不会从覆盖整个半径和轨道周期范围的所有行星候选者那里获得质量。另一种描述行星系统特征并完成较长周期样本的方法是凌日时间变化(TTV)。该方法仅利用光曲线信息，即可探测、确认和表征多行星系统中的凌日行星和非凌日行星，系统中是否存在更多未探测到的行星？这些系统的紧密程度如何？这些问题可以通过研究多行星系统的轨道演化来回答：轨道偏心率和半长轴是如何随时间变化的？潮汐和广义相对论对极短周期的TTV行星有什么影响？在最近的TTV研究和所有现有的TTV分析软件工具中，只考虑了引力。这种简化可能适用于大多数分析系统，但不适用于所有系统。其他力的加入对于接近的行星(潮汐、广义相对论)、彼此轨道接近的行星(行星-行星相互作用)以及非凌日行星扰动已知的凌日行星至关重要。通过对所有作用力的分析和比较，可以验证和/或改进关于轨道、恒星质量、凌日行星和摄动行星的质量的知识，特别是对于难以被RV观测证实的候选者。上述问题将通过对显示TTV的现有行星系统的光曲线的分析以及在开普勒和K2任务的“新”光曲线中寻找更多具有TTV的系统来回答。在RIU-PF开发的现有软件包将通过实施蒙特卡罗马尔可夫链来搜索整个参数空间以寻找最佳解决方案，从而实现完全自动化。在轨道模拟中应采用潮汐、广义相对论和恒星扁平度，以全面描述行星系统。TTV基本上是描述探测到的行星系统的唯一机会。然而，直接的应用是验证凌日行星独立于地面观测。因此，TTV也是对未知行星对已知行星的扰动的探测，因此也是对可以由TTV直接表征的多行星系统的探测。

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.