超低频单色平面引力波入射到引力束缚二体系统的轨道效应
Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system
摘要：
本文解析计算了在单色平面引力波作用下，实验粒子绕中心体运动的长期轨道变化。我们假设受扰二体系统的特征尺寸远小于波的波长。此外，我们还假设波的频率比粒子的轨道频率小得多。我们既不对波矢的方向作先验假设，也不对行星的轨道几何作先验假设。我们发现，而半长轴不受影响，偏心率，倾角，经度的升交点，近心经度和平均异常经历非零的长期变化。它们不是长期趋势，因为潮汐矩阵系数和轨道要素本身引入了缓慢的调制。它们可能有助于独立地约束可能在BICEP 2实验中间接检测到的超低频波。一般来说，我们的计算适用于任何特征频率远大于外部波频率的引力束缚二体系统。它也适用于一个通用的扰动潮汐类型的常数系数超过时间尺度的顺序的轨道周期的扰动粒子。
英文摘要：
We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency is much smaller than the particle's orbital one. We make neither a priori assumptions about the direction of the wavevector nor on the orbital geometry of the planet. We find that, while the semi-major axis is left unaffected, the eccentricity, the inclination, the longitude of the ascending node, the longitude of pericenter and the mean anomaly undergo non-vanishing long-term changes. They are not secular trends because of the slow modulation introduced by the tidal matrix coefficients and by the orbital elements themselves. They could be useful to indepenedently constrain the ultra-low frequency waves which may have been indirectly detected in the BICEP2 experiment. Our calculation holds, in general, for any gravitationally bound two-body system whose characteristic frequency is much larger than the frequency of the external wave. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.
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