$\it COD:$一种基于拓扑优化的凌日天体形状重建算法
$\it COD:$ An Algorithm for Shape Reconstruction of Transiting Celestial Bodies through Topological Optimization
摘要：
介绍了一种新的算法，$\textit{COD}$ -紧凑的不透明度分布，已被观察到的天体掩星的形状重建，使用光度的时间序列观测的掩星。$\textit{COD}$发现一个解决方案的光变曲线反演问题的光学厚掩星具有近似凸的形状，连同其大小的估计，碰撞参量和速度，相对于被掩的恒星。该算法是基于一个优化方案，使用拓扑约束和目标函数的几何形状的遮挡。问题的约束遵循线性关系，这使得可以使用线性规划优化作为数学框架。进行了多次测试的算法，所有这些都导致了高相关性的模拟和获得的形状的掩星物体，与误差在$5\%$内的投影速度和水平大小，并在$0.1$内的碰撞参量。这些测试包括火卫一日食的视频，正如美国宇航局的好奇号火星车所看到的那样，它被折叠成相应的光曲线，然后重建。我们将$\textit{COD}$应用于VVV-WIT-08的神秘案例--一颗巨星持续200多天的单次深掩星（$\sim 96 \%$）。该分析没有假设任何特定形状的掩星，提出了一个物体，其投影不透明度分布类似于椭圆，偏心率为$\sim 0.5$，相对于运动方向倾斜$\sim 30$度，半短轴类似于恒星半径。
英文摘要：
We introduce a novel algorithm, $\textit{COD}$ -- Compact Opacity Distribution, for shape reconstruction of a celestial body that has been observed to occult a star, using the photometric time-series observations of the occultation. $\textit{COD}$ finds a solution to the light-curve inversion problem for an optically thick occulter having an approximately convex shape, together with an estimate of its size, impact parameter and velocity, relative to the occulted star. The algorithm is based on an optimization scheme that uses topological constraints and an objective function for the geometry of the occulter. The constraints of the problem follow linear relations, which enable the use of linear programming optimization as the mathematical framework. Multiple tests of the algorithm were performed, all of which resulted in high correlations between the simulated and obtained shapes of the occulting objects, with errors within $5\%$ in their projected velocities and horizontal sizes, and within $0.1$ in their impact parameters. These tests include a video of a solar eclipse by Phobos, as seen by NASA's Curiosity rover, which was collapsed into its corresponding light curve and reconstructed afterwards. We applied $\textit{COD}$ to the mysterious case of VVV-WIT-08 -- a single deep occultation ($\sim 96 \%$) of a giant star lasting for over 200 days. The analysis, which did not assume any specific shape of the occulter, suggested an object with a projected opacity distribution resembling an ellipse with an eccentricity of $\sim 0.5$, tilted at $\sim 30$ degrees relative to the direction of motion, with a semi-minor axis similar to the stellar radius.
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