Transit时变的数值和解析模拟
Numerical and Analytical Modelling of Transit Time Variations
摘要：
我们开发和应用的方法来提取行星的质量和偏心率从观测到的过境时间变化（TTVs）。首先，我们推导出简单的解析表达式的TTV，包括一阶和二阶共振的影响。其次，我们使用N体马尔可夫链蒙特卡罗（MCMC）模拟，以及分析公式，测量开普勒发现的10颗行星的质量和偏心率，以前没有分析过。这十颗行星中的大多数密度都很低。使用的解析表达式，以部分规避简并，我们测量几个百分点或更少的小偏心率。
英文摘要：
We develop and apply methods to extract planet masses and eccentricities from observed transit time variations (TTVs). First, we derive simple analytic expressions for the TTV that include the effects of both first- and second-order resonances. Second, we use N-body Markov chain Monte Carlo (MCMC) simulations, as well as the analytic formulae, to measure the masses and eccentricities of ten planets discovered by Kepler that have not previously been analyzed. Most of the ten planets have low densities. Using the analytic expressions to partially circumvent degeneracies, we measure small eccentricities of a few percent or less.
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