Abstract Continuing advances in observational astronomy may detect exoplanets around exotic systems such as a binary of a compact object - white dwarf, neutron star or black hole - with a stellar companion. Their formation history includes tidal capture, familiar from studies of X-ray binaries, that may put exoplanets on co- or counter-rotating P-type orbits of the resulting binary. We here revisit the essential problem of dynamical stability of planetary orbits around stellar binaries, building on the coplanar three-body system of the Dvorak (1986), extending his stability diagram to include counter rotating P-type orbits, expressing change of stability across a gap between upper (UCO) and lower (LCO) critical orbital radius. A 24% width is found for the counter-rotating case, considerably larger than about 8% for the familiar corotation case. As the gap of the first lies below the second, counter rotation appears more stable, yet by width it is more chaotic. The gap between UCO and LCO follows a transition radius r g − = 0.92 − 2.47 e versus r g + = 2.39 + 2.53 e − 1.40 e 2 for the corotation case, the latter in agreement with the same of Dvorak to within 0.35%. This difference in stability may be expressed by r g + / r g − ≲ 2.57 for all e. Around dim binaries, therefore, a relatively close in habitable zone may still be populated with exoplanets on counter rotating orbits, distinct from the corotating case. The accurate numerical results presented here based on adaptive integration using MATLAB ODE45 may also serve as a novel benchmark of accurate N-body integrators of exosolar systems, e.g., to relax our model problem setting of co-planar orientation and equal mass-ratio binaries.

中文翻译：

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恒星双星周围P型轨道的稳定性：反向旋转轨道的延伸

摘要 观测天文学的不断进步可能会探测到外星系统周围的系外行星，例如一个致密天体——白矮星、中子星或黑洞——与一个恒星伴星的双星。它们的形成历史包括潮汐捕获，这在 X 射线双星研究中很常见，这可能会将系外行星置于由此产生的双星的同向或反向旋转 P 型轨道上。我们在这里重新讨论了围绕双星的行星轨道动力学稳定性的基本问题，建立在 Dvorak (1986) 的共面三体系统的基础上，将他的稳定性图扩展到包括反向旋转的 P 型轨道，表达了稳定性的变化上 (UCO) 和下 (LCO) 临界轨道半径之间的间隙。发现反向旋转外壳的宽度为 24%，远大于熟悉的同向旋转外壳的约 8%。由于第一个的间隙位于第二个下方，因此反向旋转看起来更稳定，但宽度上则更混乱。UCO 和 LCO 之间的差距遵循过渡半径 rg - = 0.92 - 2.47 e 与 rg + = 2.39 + 2.53 e - 1.40 e 2 对于共转情况，后者与 Dvorak 的差距在 0.35% 以内。对于所有 e，这种稳定性差异可以表示为 rg + / rg − ≲ 2.57。因此，在昏暗的双星周围，一个相对较近的宜居带可能仍然布满了在反向旋转轨道上的系外行星，这与共转情况不同。这里基于使用 MATLAB ODE45 自适应积分的精确数值结果也可以作为外太阳系精确 N 体积分器的新基准，例如，放松我们的共面取向和等质量比双星模型问题设置。