On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems
On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems
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DOI：
10.1051/0004-6361/201015218
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发表时间：
2011-02
影响因子：
6.5
通讯作者：
B. Funk;Anne-Sophie Libert;Á. Süli;E. Pilat-Lohinger
中科院分区：
文献类型：
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作者：
B. Funk;Anne-Sophie Libert;Á. Süli;E. Pilat-Lohinger
目标。在受限三体问题中，我们研究了由恒星、气态巨星和无质量测试行星组成的具有可忽略引力效应的类地小天体(以下称为无质量测试行星)的倾斜测试粒子的长期演化。这颗测试行星最初在圆形轨道上，绕恒星运行的距离比这颗气体巨星更近。目的是为了显示气体巨星的偏心率和质量对动力学的影响，对于试验行星的不同倾角，并更详细地研究椭圆问题中的Kozai机制。方法：研究方法。我们进行了参数研究，整合了初始条件分布在半长轴倾斜面上的测试粒子的轨道演化。这颗气体巨星最初的偏心程度各不相同。在计算中，我们使用了李积分方法，在某些情况下还使用了Bulirsch-Stoer算法。采用最大偏心率和李雅普诺夫特征指标对结果进行了分析。所有积分都是对气巨星的105个周期进行的。结果。我们的计算表明，倾斜的无质量测试行星可以在圆形或椭圆形轨道上与气体巨星处于稳定的构型。气体巨星的偏心率越大，测试行星在半长轴上的可能射程就越小。对于圆形轨道上的气体巨星，我们的结果说明了与Kozai机制相关的众所周知的结果，该机制不允许稳定的轨道超过大约40°的临界倾角。对于偏心轨道上的气体巨星，动力学非常相似，无质量的伴星在偏心程度上表现出有限的变化。此外，我们发现在35°附近有一个由长期稳定的低偏心轨道组成的区域。我们表明这些结果对地球质量伴星也是有效的，因此它们可以应用于太阳系外系统：例如，太阳系外行星系统HD 154345在宜居带可以有一个35°倾斜的近圆形的地球质量伴星。
Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem. Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis - inclination plane. The gas giant's initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 10 5 periods of the gas giant. Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone.