论文标题
三级诱导的黑洞二进制合并中的自旋轨道错位：理论分析
Spin-Orbit Misalignments in Tertiary-Induced Black-Hole Binary Mergers: Theoretical Analysis
论文作者
论文摘要
由第三级同伴重力扰动驱动的黑洞（BH）二进制合并构成了一类重要的动态形成通道，用于由Ligo/pirgo检测到的紧凑型二进制物。最近的作品从数值上检查了BH二进制文件的轨道和自旋动力学，这些动力学经历了大型Lidov-Kozai（LK）偏心率振荡，由高度倾斜的伴侣引起，并通过重力波辐射合并。但是，极端的偏心差异使得这样的系统难以分析表征。在本文中，我们开发了一种分析形式主义，以理解经过LK引起的合并的二进制BHS的自旋动力学。我们表明，在某些条件下，可以将二进制的偏心振荡进行平均，以平滑地确定BH旋转的长期行为。特别是，我们证明了最终的自旋轨道未对准角$θ_ {\ rm sl} $通常与二进制的原始旋转方向有关，这是通过近似绝热不变的。 Our theory explains the "$90^\circ$ attractor" (as found in recent numerical studies) for the evolution of $θ_{\rm sl}$ when the initial BH spin is aligned with the orbital axis and the octupole LK effects are negligible -- such a "$90^\circ$ attractor" would lead to a small binary effective spin parameter $χ_{\rm eff} \ sim 0 $甚至用于大型内在的BH旋转。我们根据初始条件的函数计算以封闭形式的绝热性偏差。由于共振旋转 - 轨道相互作用，我们还将准确的限制在何时破裂。我们考虑恒星质量和超级质量BH三级伴侣，并提供了简单的处方，用于分析合并BH二进制文件的最终自旋轨道未对准角。
Black-hole (BH) binary mergers driven by gravitational perturbations of tertiary companions constitute an important class of dynamical formation channels for compact binaries detected by LIGO/VIRGO. Recent works have examined numerically the combined orbital and spin dynamics of BH binaries that undergo large Lidov-Kozai (LK) eccentricity oscillations induced by a highly inclined companion and merge via gravitational wave radiation. However, the extreme eccentricity variations make such systems difficult to characterize analytically. In this paper, we develop an analytical formalism for understanding the spin dynamics of binary BHs undergoing LK-induced mergers. We show that, under certain conditions, the eccentricity oscillations of the binary can be averaged over to determine the long-term behavior of the BH spin in a smooth way. In particular, we demonstrate that the final spin-orbit misalignment angle $θ_{\rm sl}$ is often related to the binary's primordial spin orientation through an approximate adiabatic invariant. Our theory explains the "$90^\circ$ attractor" (as found in recent numerical studies) for the evolution of $θ_{\rm sl}$ when the initial BH spin is aligned with the orbital axis and the octupole LK effects are negligible -- such a "$90^\circ$ attractor" would lead to a small binary effective spin parameter $χ_{\rm eff}\sim 0$ even for large intrinsic BH spins. We calculate the deviation from adiabaticity in closed form as a function of the initial conditions. We also place accurate constraints on when this adiabatic invariant breaks down due to resonant spin-orbit interactions. We consider both stellar-mass and supermassive BH tertiary companions, and provide simple prescriptions for determining analytically the final spin-orbit misalignment angles of the merging BH binaries.
