Calculating the Tidal, Spin, and Dynamical Evolution of Extrasolar Planetary Systems
Calculating the Tidal, Spin, and Dynamical Evolution of Extrasolar Planetary Systems
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DOI：
10.1086/340752
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发表时间：
2002-07
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影响因子：
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通讯作者：
R. Mardling;D. Lin
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文献类型：
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作者：
R. Mardling;D. Lin
基于Heggie和Eggleton的公式，我们提出了一种有效的方法，用于计算自洽的潮汐，自旋和动力学演化的多体系统，这里特别强调行星系统。星星和最里面的行星（或者通常是系统中最接近的一对天体）被赋予了结构，而其他天体被视为点质量。的自旋速率和扩展机构的量子数的演变计算（为任意初始量子数），是最内层轨道的潮汐演变。此外，最内层行星的半径是根据其有效耗散潮汐能的能力而演变的。相对论效应包括后牛顿秩序。对于共振系统，如GJ 876，演化方程必须直接积分，以允许半长轴的变化（而不是潮汐阻尼）和不稳定的可能性。对于像仙女座变星这样两颗内行星的周期比很小的系统，最内层的轨道可以被平均，这样可以减少50倍的计算时间。为了说明公式的通用性，我们考虑三个假设的原始地球-月球-太阳-木星系统。前两个模型中的参数和初始条件是相同的，除了地球的Love数，这导致了显着不同的演化路径。第三个系统是一个研究的Touma &智慧，并作为一个测试的数值公式在这里提出的再现两个长期的平均运动共振（驱逐和驱逐共振）。该方法可用于任何身体系统。
Based on formulations by Heggie and by Eggleton, we present an efficient method for calculating self-consistently the tidal, spin, and dynamical evolution of a many-body system, here with particular emphasis on planetary systems. The star and innermost planet (or in general the closest pair of bodies in the system) are endowed with structure while the other bodies are treated as point masses. The evolution of the spin rates and obliquities of the extended bodies are calculated (for arbitrary initial obliquities), as is the tidal evolution of the innermost orbit. In addition, the radius of the innermost planet is evolved according to its ability to efficiently dissipate tidal energy. Relativistic effects are included to post-Newtonian order. For resonant systems such as GJ 876, the evolution equations must be integrated directly to allow for variation of the semimajor axes (other than from tidal damping) and for the possibility of instability. For systems such as Upsilon Andromedae in which the period ratio of the two inner planets is small, the innermost orbit may be averaged producing (in this case) a 50-fold reduction in the calculation time. In order to illustrate the versatility of the formulation, we consider three hypothetical primitive Earth-Moon-Sun-Jupiter systems. The parameters and initial conditions are identical in the first two models except for the Love number of the Earth, which results in dramatically different evolutionary paths. The third system is one studied by Touma & Wisdom and serves as a test of the numerical formulations presented here by reproducing two secular mean motion resonances (the evection and eviction resonances). The methods may be used for any system of bodies.