[论文解读] Compact Dark Objects in Neutron Star Mergers

Andreas Bauswein, Gang Guo+3 more|arXiv (Cornell University)|Dec 22, 2020

Pulsars and Gravitational Waves Research参考文献 83被引用 8

一句话总结

本文研究了在中子星并合残余物中绕行的致密暗物质（DM）天体所产生的长期引力波（GW）辐射。通过三维广义相对论模拟和测试粒子近似，结果表明，质量为0.01–0.1 M⊙的DM核心可产生频率在kHz量级、持续数秒至数年的GW信号，仅当DM质量足够大时才可探测到，且频率与中子星紧凑度及并合后流体GW模态成比例。

ABSTRACT

We estimate the long-lasting gravitational wave (GW) emission of compact dark objects following a binary neutron-star (NS) merger. We consider compact dark objects, which initially reside in the centers of NSs and which may consist of self-interacting dark matter (DM). By approximating the compact dark objects as test particles, we model the merging of NS binaries hosting DM components with three-dimensional relativistic simulations. Our simulation results suggest that the DM components remain gravitationally bound and orbit inside the merger remnant with orbital separations of typically a few km. The subsequent orbital motion of the DM components generates a GW signal with frequencies in the range of a few kHz. When considering a range of different binary masses and high-density equations of state (EoS), we find that the GW frequency of the orbiting DM components scales with the compactness of NSs. Similarly, we find relations between the DM GW frequency and the dominant postmerger GW frequency of the stellar fluid or the tidal deformability, which quantifies EoS effects during the binary inspiral. Hence, a measurement of these quantities can be used to specify the frequency range of the GW emission by DM. Under the assumption that GW back reaction is the only relevant dissipative process, the GW signal may last between seconds and years depending on the mass of the DM component. We estimate the detectability of the GW signals and find that DM components in NS mergers may only be detectable with existing and projected GW instruments if the dark objects are as massive as about 0.01 to 0.1 M_sun. We emphasize that the GW emission is limited by the lifetime of the remnant. A forming black hole will immediately swallow the DM objects because their orbits are smaller than the innermost stable circular orbit of the black hole.

研究动机与目标

• 探索双中子星并合后形成的致密暗物质天体产生长期引力波辐射的可能性。
• 利用广义相对论流体力学和测试粒子近似，模拟暗物质核心在并合残余物中的轨道动力学。
• 评估此类GW信号被当前及未来引力波天文台探测的可能性。
• 建立轨道DM的GW频率与可观测中子星性质（如紧凑度、潮汐可变形性及并合后流体GW模态）之间的标度关系。
• 研究在残余物坍缩为黑洞前，GW信号的持续时间，该过程将立即终止辐射。

提出的方法

• 使用三维广义相对论流体力学模拟双中子星并合，将DM视为测试粒子处理。
• 采用有效质量近似 μ(R) = M_DM / M(R) 来描述在球对称、非均匀介质中的轨道动力学。
• 求解轨道运动方程 d²u/dθ² + u = (1/L²)(4πρM²_DM)/u³，其中 u = 1/R，以描述在引力与GW反作用力共同作用下的非圆形轨道。
• 应用四极矩公式计算每圈的GW能量与角动量损失，并迭代更新轨道参数随时间的变化。
• 通过每N₀个周期重新计算能量与角动量损失，持续演化系统，直至累积损失超过初始能量的1%。
• 比较圆形与非圆形轨道的GW振幅与频率，以评估辐射效率。

实验结果

研究问题

• RQ1 中子星并合残余物中的致密暗物质天体能否产生长期引力波信号？
• RQ2 绕行暗物质核心的引力波辐射的频率与持续时间为何？
• RQ3 暗物质成分的GW频率如何随中子星紧凑度及并合后流体振荡而变化？
• RQ4 现有及未来引力波探测器对这类GW信号的探测阈值是什么？
• RQ5 与圆形轨道相比，轨道偏心率如何影响GW辐射效率？

主要发现

• 质量为0.01–0.1 M⊙的绕行暗物质核心可产生频率在数kHz范围内的引力波信号。
• 暗物质成分的GW频率与中子星紧凑度成比例，从而可对物态方程提供间接约束。
• 发现DM的GW频率与主导的并合后流体GW频率之间存在相关性，同时也与并合前潮汐可变形性相关。
• 在GW反作用力为主要耗散机制的假设下，GW信号可持续数秒至数年，具体取决于暗物质质量。
• 非圆形轨道的辐射效率低于等效圆形轨道，因有效包覆质量减少，导致振幅小2–3倍。
• 残余物的寿命限制了GW辐射，因黑洞形成后会立即吞噬暗物质天体，原因在于其轨道半径小于最内稳定圆轨道。