Constraining the interiors of exoplanets by measuring the Love number k_2

我们将开发一个新的软件包来模拟具有潮汐和旋转扭曲分量的系外行星的过境光曲线。这项工作是从一个已经存在的基于罗氏模型的代码开始的（罗氏模型包括一个无质量的，但发射和/或反射的，潮汐和旋转扭曲的包络层，以及一个位于天体中心的包含物体全部质量的核心）。这样的模型被发现适合于主序星。代码将被修改，使其适用于系外行星。因此，它将通过非均匀的内部质量分布成分进行扩展，并将考虑到主恒星引起的辐射压力，因为这对于具有扩展，密集大气的近距离系外行星很重要。由于行星（透镜）和恒星（源）双星系统中的引力微透镜被认为是导致观测到的光曲线扭曲的原因，我们计划将这种效应添加到代码中。临边变暗将是一个可调参数，独立于现有的恒星大气模型，但我们计划允许用户修改这个给定的恒星大气模型的可能性。我们将改进现有的代码，通过开发和添加红噪声（自回归和/或高斯过程）模型来包括恒星变异性现象。然后，代码将能够根据测量的凌日光曲线确定凌日系外行星的极地半径和赤道半径的比值。此外，我们将对多色光度法的适用性进行研究。在不同波长获得的观测可能有助于解决不同参数之间的简并。最后，测量的极地平坦值将与系外行星的内部结构联系起来。这需要了解系外行星的旋转周期。首先，我们假设离我们最近的系外行星是潮汐锁定的。更复杂的估计可以基于形状畸变，因为离心力是轴对称的，而潮汐力有一个特征方向。代码将能够分离这些效果。SP6的预期结果是对几颗系外行星的极平面化的估计，以及对旋转周期、引力四极矩J_2和洛芬数k_{2，f}的约束。这些数字可以与理论预期进行比较，从而可以用于进一步完善我们对系外行星内部的了解。基于SP1-3和SP7-9获得的EoS数据，SP4和SP5的内部模型可以作为我们工作中的初始估计。然后我们就可以预测哪一种光曲线的畸变可以被观测到。将观测数据与我们的模型计算进行比较，可以使我们改进k_{2，f} Love-number值，并给出关于极平面化的可观测性的反馈，代码将能够约束这一内部结构参数。

We will develop a new software package to model transit light curves of exoplanets with tidally and rotationally distorted components. This work is starting from an already existing code based on the Roche-model (which consists of a massless, but emitting and/or reflecting, tidally and rotationally distorted envelope, and a core in the center of the celestial object that contains the entire mass of the object). Such a model was found to be appropriate for main sequence stars. The code will be modified to make it appropriate for exoplanets. Therefore, it will be extended by non-homogeneous internalmass distribution components and it will take into account the radiation pressure caused by the host star because this is important for close-in exoplanets with extended, dense atmospheres. Since gravitational microlensing in the binary system of the planet (lense) and star (source) is thought to contribute to the observed light curve distortions, we plan to add this effect into the code. Limb darkening will be an adjustable parameter independent of existing stellar atmosphere models, but we plan to allow the user the possibility to modify this for a given stellar atmosphere model. We will improve our existing code to include stellar variability phenomena by developing and adding a red-noise (autoregressive and/or Gaussian Process) model. Then the code will be able to determine the ratio of the polar and the equatorial radii of the transiting exoplanet from a measured transit light curve.In addition, we will perform studies on applicability of multicolour photometry. Observations obtained at different wavelengths may help to resolve the degeneracy between different parametersFinally, the measured polar flattening values will be linked to the internal structure of the exoplanet. This requires knowledge of the rotational period of the exoplanet. To first approximation, we assume that the closest exoplanets are tidally locked. A more sophisticated estimate can be based on the shape-distortion, because the centrifugal force is axially symmetric while tidal forces have a characteristic orientation. The code will be able to separate these effects.The expected result of SP6 is an estimate of the polar flattening of several exoplanets and constraints for the rotational period, gravitational quadrupole moment J_2 and Lovenumber k_{2,f}. These numbers can be compared to theoretical expectations and thus can be used for further refinement of our knowledge on exoplanets' interiors.The interior models of SP4 and SP5 based on EoS data obtained by SP1-3 and SP7-9 can be used as initial estimates in our work. Then we can make predictions concerning which kind of light curve distortions can be observed. A comparison of the observed data and our model calculations may allow us to refine the k_{2,f} Love-number values and giving a feedback about the observability of polar flattening as well as the code will be able to constrain this interior structure parameter.