Hamiltonian hydrodynamics of eccentric discs
Hamiltonian hydrodynamics of eccentric discs
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DOI：
10.1093/mnras/sty3436
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发表时间：
2018-12
影响因子：
4.8
通讯作者：
G. Ogilvie;Elliot M. Lynch
中科院分区：
文献类型：
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作者：
G. Ogilvie;Elliot M. Lynch
我们证明了偏心天体物理盘的理想流体动力学可以从变分原理中得到。非线性长期理论描述了由于薄盘中的压力，一组连续的嵌套椭圆轨道的缓慢演化。在人造但被广泛考虑的2D圆盘的情况下，流体动力哈密顿量就是圆盘的轨道平均内能，可以使用椭圆轨道的几何形状从其偏心分布确定。在3D光盘的实际情况下，需要修改哈密顿量以考虑光盘的动态垂直结构。该理论最简单的解是均匀推进非线性偏心模，使能量在角动量固定的情况下保持不变。我们给出了非线性偏心模的数值例子，直到它们的极限振幅。虽然它缺乏耗散，这在许多天体物理背景下是重要的，但这种形式允许一个比从应力积分导出的更简单的理论方法来研究偏心圆盘的非线性动力学，并且在圆盘与一个或多个轨道伴侣引力相互作用的情况下，也更好地与天体力学的现有方法相结合。
We show that the ideal hydrodynamics of an eccentric astrophysical disc can be derived from a variational principle. The nonlinear secular theory describes the slow evolution of a continuous set of nested elliptical orbits as a result of the pressure in a thin disc. In the artificial but widely considered case of a 2D disc, the hydrodynamic Hamiltonian is just the orbit-averaged internal energy of the disc, which can be determined from its eccentricity distribution using the geometry of the elliptical orbits. In the realistic case of a 3D disc, the Hamiltonian needs to be modified to take into account the dynamical vertical structure of the disc. The simplest solutions of the theory are uniformly precessing nonlinear eccentric modes, which make the energy stationary subject to the angular momentum being fixed. We present numerical examples of nonlinear eccentric modes up to their limiting amplitudes. Although it lacks dissipation, which is important in many astrophysical contexts, this formalism allows a simpler theoretical approach to the nonlinear dynamics of eccentric discs than that derived from stress integrals, and also connects better with established methods of celestial mechanics for cases in which the disc interacts gravitationally with one or more orbital companion.