双星比它们看起来更软：外部势对双星散射动力学的影响
Binaries are softer than they seem: Effects of an external potential on the scattering dynamics of binaries
摘要：
双星的演化受到稠密环境中与其他恒星的动力散射的影响。赫吉定律指出，由于它们的环境，硬双星（其轨道能量超过单星的典型能量）倾向于硬化（增加其轨道能量），而软双星通常会软化。在这里，我们表明，Heggie定律有时需要修改，占外部潜力，例如，在核恒星盘或AGN光盘，这是由中央大质量黑洞，或二进制星子在原行星盘，受宿主恒星的影响。我们发现，在这样的环境中，希尔半径是有限的，二进制单散射可以有不同的结果。特别是，三体相遇可能会因为恒星被抛出希尔半径之外而缩短，从而停止参与进一步的近距离相互作用。这导致了碰撞所带来的能量变化的系统性差异，特别是减缓了二进制的硬化，甚至导致一些硬二进制平均软化，而不是硬化。我们使用我们以前推导出的分析，统计解决方案的约束混沌三体问题，以定量的硬化-软化相变和演化的二进制文件的修订。我们还提供了一个分析计算的平均硬化率的二进制文件在任何环境中（也再现详细的N体模拟的结果）。我们发现，后者表现出一个非平凡的依赖于希尔半径引起的环境。
英文摘要：
Binary evolution is influenced by dynamical scattering with other stars in dense environments. Heggie's law states that, due to their environments, hard binaries (whose orbital energy surpasses the typical energy of single stars) tend to harden (increase their orbital energy), while soft binaries typically soften. Here, we show that Heggie's law sometimes needs to be revised, by accounting for an external potential, for example, for binaries in nuclear stellar discs or AGN discs, that are affected by the central massive black hole, or binary planetesimals in proto-planetary discs, affected by the host star. We find that in such environments, where the Hill radius is finite, binary-single scattering can have different outcomes. In particular, a three-body encounter could be cut short due to stars being ejected beyond the Hill radius, thereby ceasing to participate in further close interactions. This leads to a systematic difference in the energy changes brought about by the encounter, and in particular slows binary hardening, and even causes some hard binaries to soften, on average, rather than harden. We use our previously derived analytical, statistical solution to the bound chaotic three-body problem to quantitatively characterise the revision of the hardening-softening phase transition and evolution of binaries. We also provide an analytical calculation of the mean hardening rate of binaries in any environment (also reproducing the results of detailed N-body simulations). We show that the latter exhibits a non-trivial dependence on the Hill radius induced by the environment.
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