Analytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons
Analytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons
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DOI：
10.3847/1538-3881/ac4017
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发表时间：
2021-03
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通讯作者：
R. Luger;E. Agol;F. Bartoli'c;D. Foreman-Mackey
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作者：
R. Luger;E. Agol;F. Bartoli'c;D. Foreman-Mackey
无论是在掩星内还是从掩星外的反射光中，我们都能得到从球面行星或卫星测得的通量的有效的、封闭的、可微的和数值稳定的解。我们的表达式适用于计算系外行星的散射光相位曲线、光学中的二次日食光曲线，或未来行星-月亮和行星-行星掩星的测量，以及太阳系天体的光度测量。我们推导了点源照明的朗伯体的解，但将其扩展到有限角度大小的照明源和具有相变散射的粗糙表面的模型。我们的算法是在开源的Starry映射框架内用Python语言实现的，并且在设计时考虑了高效的基于梯度的推理。该算法比直接数值计算方法∼快4-5个数量级，∼精度高10个数量级。我们展示了这里开发的技术有朝一日可能会如何导致构建陆地行星表面的二维地图，从而潜在地能够探测到宜居带系外行星上的大陆和海洋。6 6 https://github.com/rodluger/starrynight https://github.com/rodluger/starrynight
We derive efficient, closed-form, differentiable, and numerically stable solutions for the flux measured from a spherical planet or moon seen in reflected light, either in or out of occultation. Our expressions apply to the computation of scattered light phase curves of exoplanets, secondary eclipse light) curves in the optical, or future measurements of planet–moon and planet–planet occultations, as well as to photometry of solar system bodies. We derive our solutions for Lambertian bodies illuminated by a point source, but extend them to model illumination sources of finite angular size and rough surfaces with phase-dependent scattering. Our algorithm is implemented in Python within the open-source starry mapping framework and is designed with efficient gradient-based inference in mind. The algorithm is ∼4–5 orders of magnitude faster than direct numerical evaluation methods and ∼10 orders of magnitude more precise. We show how the techniques developed here may one day lead to the construction of two-dimensional maps of terrestrial planet surfaces, potentially enabling the detection of continents and oceans on exoplanets in the habitable zone. 6 6 https://github.com/rodluger/starrynight https://github.com/rodluger/starrynight