论文标题
一种用于计算行星宿主星和轨道最佳半径的数值方法，并应用于Kepler-11，Kepler-90，Kepler-215，HD 10180，HD 10180，HD 34445和Trappist-1
A numerical method for computing optimum radii of host stars and orbits of planets, with application to Kepler-11, Kepler-90, Kepler-215, HD 10180, HD 34445, and TRAPPIST-1
论文作者
论文摘要
在所谓的“全局多面部模型”中，我们假设静水平衡中的行星系统在复杂平面中求解了车道 - 填充方程。因此，我们发现多层球形壳为行星提供托管轨道。在此模型的基础上，我们开发了一种具有三个版本的数值方法。在其三维版本中，该方法对于观察到的宿主星形半径和特定行星的轨道（与其他行星的轨道中的不确定性相比）对具有很大不确定性的系统有效；该方法用作固定入口值的剩余行星的观察到的轨道。在其二维版本中，该方法对宿主星形半径上有很大不确定性的系统有效。在这种情况下，该方法用作固定入口值观察到的行星轨道。一维版本以前是开发并应用于多个系统的。在此版本中，宿主星形半径和行星轨道的观察值被视为固定的入口值。我们的方法可以计算模拟术语系统，行星轨道的全局多环形模型的多粒子索引的最佳值，以及（不包括宿主星形半径的一维版本）。
In the so-called "global polytropic model", we assume planetary systems in hydrostatic equilibrium and solve the Lane--Emden equation in the complex plane. We thus find polytropic spherical shells providing hosting orbits to planets. On the basis of this model, we develop a numerical method which has three versions. In its three-dimensional version, the method is effective for systems with substantial uncertainties in the observed host star radius, and in the orbit of a particular planet (compared to the uncertainties in the orbits of the other planets); the method uses as fixed entry values the observed orbits of the remaining planets. In its two-dimensional version, the method is effective for systems with substantial uncertainty in the host star radius; in this case, the method uses as fixed entry values the observed orbits of the planets. The one-dimensional version was previously developed and applied to several systems; in this version, the observed values of the host star radius and of the planetary orbits are taken as fixed entry values. Our method can compute optimum values for the polytropic index of the global polytropic model which simulates the exoplanetary system, for the orbits of the planets, and (excluding the one-dimensional version) for the host star radius.
