Direct-imaging techniques of exoplanets have made significant progress recently, and will eventually enable to monitor photometric and spectroscopic signals of earth-like habitable planets in the future. The presence of clouds, however, would remain as one of the most uncertain components in deciphering such direct-imaged signals of planets. We attempt to examine how the planetary obliquity produce different cloud patterns by performing a series of GCM (General Circulation Model) simulation runs using a set of parameters relevant for our Earth. Then we use the simulated photometric lightcurves to compute their frequency modulation due to the planetary spin-orbit coupling over an entire orbital period, and attempt to see to what extent one can estimate the obliquity of an Earth-twin. We find that it is possible to estimate the obliquity of an Earth-twin within the uncertainty of several degrees with a dedicated 4 m space telescope at 10 pc away from the system if the stellar flux is completely blocked. While our conclusion is based on several idealized assumptions, a frequency modulation of a directly-imaged earth-like planet offers a unique methodology to determine its obliquity.

中文翻译：

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类地行星直接成像光变频调制的倾斜度：一般环流模型模拟的模拟分析

系外行星的直接成像技术最近取得了重大进展，最终将能够在未来监测类地宜居行星的光度和光谱信号。然而，云的存在仍然是破译行星的这种直接成像信号中最不确定的组成部分之一。我们尝试通过使用一组与地球相关的参数执行一系列 GCM（一般环流模型）模拟运行来检查行星倾斜度如何产生不同的云模式。然后，我们使用模拟的光度光曲线来计算由于整个轨道周期内行星自旋轨道耦合引起的频率调制，并试图看看人们可以在多大程度上估计地球双胞胎的倾角。我们发现，如果恒星通量被完全阻挡，则可以在距离系统 10 pc 处使用专用的 4 m 太空望远镜在几度的不确定性内估计地球孪生体的倾角。虽然我们的结论基于几个理想化的假设，但直接成像的类地行星的频率调制提供了一种独特的方法来确定其倾斜度。