由恒星旋转斑点引起的开普勒凌日的时间变化--一种区分Pende和retrograde motion的方法I.理论
Time variation of Kepler transits induced by stellar rotating spots - a way to distinguish between prograde and retrograde motion I. Theory
摘要：
开普勒任务发现的一些凌日行星显示出由恒星斑点引起的凌日时间变化（TTV），这些恒星斑点在其母星的可见半球上旋转。当行星穿过一个点并改变凌日光变曲线的形状时，可以观察到诱导的TTV，即使数据的时间分辨率不允许检测到穿越事件本身。我们提出了一种方法，可以在某些情况下，使用派生的TTV的行星，以区分一个逆行和逆行的行星运动相对于恒星旋转。假设有一个比星盘更暗的点，如果穿越发生在凌日的前半段（后半段），那么行星穿越的点可以引起测量到的正（负）TTV。另一方面，光斑朝向（远离）恒星可见光盘中心的运动导致恒星亮度降低（增加）。因此，对于一颗行星的轨道运动，当凌日时恒星流量的局部斜率为负时，诱导TTV为正，反之亦然。因此，我们可以预期观察到TTV和逆（逆行）运动的光度斜率之间的负（正）相关性。使用一个简单的分析近似，也是公开可用的SOAP-T工具，以产生光变曲线的过境点交叉事件，我们显示在某些情况下，如何诱导TTV依赖于当地恒星光度斜率的过境时间。在具有足够高的信噪比的开普勒凌日系统中检测到这种相关性，可以让我们区分行星的逆行和逆行运动。在未来的论文中，我们提出了分析的KOIS和开普勒食双星，以下的形式主义在这里发展。
英文摘要：
Some transiting planets discovered by the Kepler mission display transit timing variations (TTVs) induced by stellar spots that rotate on the visible hemisphere of their parent stars. An induced TTV can be observed when a planet crosses a spot and modifies the shape of the transit light curve, even if the time resolution of the data does not allow to detect the crossing event itself. We present an approach that can, in some cases, use the derived TTVs of a planet to distinguish between a prograde and a retrograde planetary motion with respect to the stellar rotation. Assuming a single spot darker than the stellar disc, spot crossing by the planet can induce measured positive (negative) TTV, if the crossing occurs in the first (second) half of the transit. On the other hand, the motion of the spot towards (away from) the center of the stellar visible disc causes the stellar brightness to decrease (increase). Therefore, for a planet with prograde motion, the induced TTV is positive when the local slope of the stellar flux at the time of transit is negative, and vice versa. Thus, we can expect to observe a negative (positive) correlation between the TTVs and the photometric slopes for prograde (retrograde) motion. Using a simplistic analytical approximation, and also the publicly available SOAP-T tool to produce light curves of transits with spot-crossing events, we show for some cases how the induced TTVs depend on the local stellar photometric slopes at the transit timings. Detecting this correlation in Kepler transiting systems with high enough signal-to-noise ratio can allow us to distinguish between prograde and retrograde planetary motions. In coming papers we present analyses of the KOIs and Kepler eclipsing binaries, following the formalism developed here.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
