发表机构
ETH Zürich; Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid（苏黎世联邦理工学院; 马德里自治大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对原初黑洞团自旋产生与宇宙学存续的矛盾，本研究提出致密核心+延展暗晕的结构模型，通过N体模拟揭示其引力波特征，为引力波观测解读提供新框架。
AI 中文摘要
原初黑洞（PBHs）被认为诞生时基本无自旋，且如果原初曲率涨落具有非高斯尾部，它们会呈现强成团性。因此，在PBH族群中测量到的任何自旋都必然是动力学产生的。我们使用经修改的\textsc{nbody6++gpu}程序开展直接N体模拟（该程序经调整可处理近抛物线动力学俘获并合事件），量化了初始无自旋的PBH团在何种条件下会产生当前引力波观测可探测的自旋、质量及随机背景特征。我们发现了一个尖锐的矛盾：要在30-50倍太阳质量（$M_\bullet$）的范围内产生均方根自旋$χ_{\rm rms}\thicksim0.1 - 0.2$，需要初始Plummer半径约为$10^{-5}\rm pc$，而要在宇宙学时间尺度上存续则需要秒差距尺度的团。如果PBH形成时拥有一个嵌在延展暗晕中的致密、短寿命核心，这一矛盾就能自然得到解决，因此我们将这两个区域作为独立模块进行模拟。核心模块包含4000个PBH，Plummer半径为$3\times10^{-6} - 10^{-4}\rm pc$，会在数天到数年内发生坍缩，产生一阵并合爆发，这些并合的轨道呈强非圆性（$e\to1$）且无量纲轨道角动量较低，因此残余黑洞的自旋系统性地低于准圆情形下的数值$χ\backsimeq0.7$。从其形成红移后，核心并合事件会产生一个随机背景，峰值位于LISA可探测的$10^{-6}$--$10^{-4}\rm Hz$频段。该图景预言了可观测量之间的明确分工：自旋由原初坍缩决定，可探测并合由长期演化的暗晕决定，且存在双成分随机背景；尤其值得注意的是，自旋和质量数据都支持在约50倍太阳质量处截断的原初质量函数。
英文摘要
Primordial black holes (PBHs) are expected to be born essentially non-spinning and, if the primordial curvature fluctuations possess non-Gaussian tails, strongly clustered. Any spin measured in a PBH population must therefore be dynamically generated. Using direct $N$-body simulations with \textsc{nbody6++gpu}, modified to treat nearly parabolic dynamical-capture mergers, we quantify the conditions under which an initially non-spinning PBH cluster develops the spin, mass and stochastic-background signatures that gravitational-wave observations are now sensitive to. We find a sharp tension: producing a root-mean-square spin $χ_{\rm rms}\sim0.1 - 0.2$ in the $30 - 50\,M_\odot$ range requires initial Plummer radii of order $10^{-5}\,{\rm pc}$, whereas survival over cosmological times requires parsec-scale clusters. This tension is resolved naturally if PBHs form with a compact, short-lived core embedded in an extended halo, and we therefore simulate the two regimes as independent blocks. The core block ($4000$ PBHs, Plummer radii $3\times10^{-6} - 10^{-4}\,{\rm pc}$) collapses in days to years, producing a burst of mergers whose orbits are strongly non-circular ($e\to1$) and of low dimensionless orbital angular momentum, so that remnant spins are systematically below the quasi-circular value $χ\simeq0.7$. Redshifted from their formation epoch, the core mergers deposit a stochastic background peaking in the $10^{-6}$--$10^{-4}\,{\rm Hz}$ band accessible to LISA. The picture predicts a specific division of labour between observables, spins set in the primordial collapse, detectable mergers set by the long-term halo, and a two-component stochastic background, and, in particular, that both the spin and the mass data favour a primordial mass function truncated near $50\,M_\odot$.
Comments18 pages, 14 figures
