分层黑洞并合的自相似质量谱
Self-Similar Mass Spectra of Hierarchical Black Hole Mergers
- University of California, Santa Cruz（加州大学圣克鲁兹分校）
- Santa Cruz Institute for Particle Physics（圣克鲁兹粒子物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究将分层黑洞并合建模为凝聚过程，推导其晚期自相似质量谱，发现多数双星形成通道可致失控增长，而三体通道呈缓慢自相似增长，且辐射能量显著影响谱形与总质量。
AI中文摘要：
反复并合的黑洞在其质量分布中记录了这段历史。我们将分层并合视为一个凝聚问题，其中单个核函数编码了并合率如何依赖于所涉及的质量和宇宙时间，并推导出这类族群趋近的晚期谱。该框架产生了封闭的标度律、一个精确可解的基准，以及通过一个单一指数对并合环境进行分类，该指数衡量并合对质量较大参与者的促进或抑制程度。将其应用于原初黑洞时，需要谨慎地将已发表的并合率转化为核函数形式；正确完成后，四个标准双星形成通道中有三个映射到超线性核函数，因此是失控增长的候选者，在这种增长中，最重的天体会占主导地位，且不存在稳定的质量守恒谱；然而，确立物理凝胶化需要完整的依赖于族群的核函数及其有限的凝聚历史，这两点我们在此均未解决。只有早期的三体通道映射到非凝胶区域，并允许缓慢的自相似增长。对十三个抑制性、非凝胶核函数的数值解表明，谱的形状并非仅由标度指数决定，并且考虑每次并合辐射的能量会显著改变高质量截断，并消耗族群的总黑洞质量。
英文摘要：
Black holes that merge repeatedly carry a record of that history in their mass distribution. We treat hierarchical merging as a coagulation problem, in which a single kernel encodes how the merger rate depends on the masses involved and on cosmic time, and we derive the late-time spectra that such populations approach. The framework yields closed scaling laws, an exactly solvable benchmark, and a classification of merger environments by a single exponent measuring how strongly mergers favor or suppress massive participants. Applying it to primordial black holes requires care in translating published merger rates into kernel form; done correctly, three of the four standard binary-formation channels map onto superlinear kernels and are therefore candidates for runaway growth, in which the heaviest objects would dominate and no steady mass-conserving spectrum exists; establishing physical gelation, however, requires the full population-dependent kernel and its finite coagulation history, neither of which we settle here. Only the early three-body channel maps into the nongelling regime and admits slow self-similar growth. Numerical solutions across thirteen suppressive, nongelling kernels show that the shape of the spectrum is not fixed by the scaling exponent alone, and that accounting for the energy radiated at each merger measurably changes the high-mass cutoff and drains the population's total black-hole mass.
