DYNAMICS AND TRANSIT VARIATIONS OF RESONANT EXOPLANETS
DYNAMICS AND TRANSIT VARIATIONS OF RESONANT EXOPLANETS
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DOI：
10.3847/0004-637x/823/2/72
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
D. Nesvorný;D. Vokrouhlický
中科院分区：
文献类型：
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作者：
D. Nesvorný;D. Vokrouhlický
凌日时变（TTVs）是测量到的凌日中间时间与精确周期的偏差。其中一个最有趣的原因是行星之间的引力相互作用。这里我们考虑两个行星的平均运动共振（轨道周期与小整数之比）的情况。这种情况很重要，因为共振相互作用可以放大TTV效应，使行星更容易被探测到。我们建立了一个适用于小轨道偏心率的共振动力学解析模型，并用它来推导主TTV项。我们发现一个共振系统应该显示具有两个基本周期（及其谐波）的TTV项。共振的TTV周期成比例(m/ m *)−2/3，其中m和m *是行星和恒星的质量。例如，当m = 10−4 m *时，TTV周期超过轨道周期约两个数量级。共振TTV项的幅值与振动幅值呈线性关系。两颗共振行星的TTV振幅之比与它们的质量之比成反比。正文中讨论的这些关系和其他关系可用于帮助解释TTV观测结果。
Transit timing variations (TTVs) are deviations of the measured midtransit times from the exact periodicity. One of the most interesting causes of TTVs is the gravitational interaction between planets. Here we consider a case of two planets in a mean motion resonance (orbital periods in a ratio of small integers). This case is important because the resonant interaction can amplify the TTV effect and allow planets to be detected more easily. We develop an analytic model of the resonant dynamics valid for small orbital eccentricities and use it to derive the principal TTV terms. We find that a resonant system should show TTV terms with two basic periods (and their harmonics). The resonant TTV period is proportional (m/M*)−2/3, where m and M* are the planetary and stellar masses. For m = 10−4 M*, for example, the TTV period exceeds the orbital period by about two orders of magnitude. The amplitude of the resonant TTV terms scales linearly with the libration amplitude. The ratio of the TTV amplitudes of two resonant planets is inversely proportional to the ratio of their masses. These and other relationships discussed in the main text can be used to aid the interpretation of TTV observations.