Stellar limb darkening must be properly accounted for to accurately determine the radii of exoplanets at various wavelengths. The standard approach to address limb darkening involves either using laws with coefficients from modeled stellar spectra or determining the coefficients empirically during light-curve fitting of the data. Here, we test how accurately three common laws—quadratic, power, and a three-parameter law—can reproduce stellar limb darkening at different wavelengths and across a broad range of stars. We show that using a quadratic limb-darkening law, which is most frequently employed by the community, leads to wavelength-dependent offsets in retrieved transmission spectra. For planets with high impact parameters (b larger than about 0.5), the amplitude of these offsets can reach 1% of the transit depth, which in some cases is comparable to and can even exceed the expected signals from the planetary atmosphere. Furthermore, the quadratic law causes an offset in the value of the impact parameter when it is determined by fitting the broadband transit light curves. In contrast, using the Kipping–Sing three-parameter law leads to robust retrievals. We advocate the use of this law in retrievals, especially for transits with large impact parameters.

中文翻译：

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使用三参数 Limb-darkening Law 进行可靠的透射光谱提取


必须适当考虑恒星边缘变暗，才能准确确定各种波长的系外行星的半径。解决边变暗的标准方法包括使用来自建模恒星光谱的系数的定律，或者在数据的光曲线拟合过程中根据经验确定系数。在这里，我们测试了三个常见定律——二次定律、幂定律和一个三参数定律——如何准确地再现不同波长和大范围恒星的恒星边缘变暗。我们表明，使用社区最常采用的二次边变暗定律会导致检索到的透射光谱中出现波长依赖性的偏移。对于具有高撞击参数（b 大于约 0.5）的行星，这些偏移量的振幅可以达到凌日深度的 1%，在某些情况下，这与来自行星大气的预期信号相当，甚至可能超过预期信号。此外，当通过拟合宽带传输光曲线来确定影响参数时，二次定律会导致影响参数值发生偏移。相反，使用 Kipping-Sing 三参数定律会导致稳健检索。我们提倡在检索中使用该定律，尤其是对于具有较大影响参数的凌日。