AI 中文总结
该研究探讨标量场坍缩临界行为的离散自相似性对原初黑洞质量函数的印记，发现其会产生对数周期特征，宽谱会消除该子结构，为相关现象学提供连接桥梁。
AI 中文摘要
我们研究标量场坍缩临界行为中的离散自相似性（DSS）如何印记在原初黑洞（PBH）质量函数上。利用宇宙学模拟中发现的DSS调制临界标度律，我们在运动学（kination）时期将近阈值质量映射传播到归一化的PBH质量函数中。我们比较了高斯窗函数、k空间顶帽窗函数、实空间顶帽窗函数，以及乘以运动学转移函数的实空间顶帽窗函数。我们发现，即使对于无限窄的原初谱，引力坍缩的临界行为也会产生不可约的最小宽度，随后DSS会调制该临界标度轮廓，在质量中产生近似对数周期特征。在固定视界质量下，DSS调制临界质量映射的连续相等相位点满足ΔlnM_PBH=γP_ln。因此，在窄谱极限下，最终质量函数中的对应结构应满足Δlnm≃γP_ln，对于基准Choptuik DSS参数γ和P_ln，即m_{n+1}/m_n≃5.6。对于宽原初谱，视界质量上的卷积会使DSS模式失相并逐渐消除临界子结构。我们对质量函数进行归一化，以便主要研究轮廓形状和DSS子结构的存活情况，而非绝对PBH丰度。这些结果为宇宙学DSS坍缩模拟与包括天体观测在内的PBH现象学提供了桥梁。
英文摘要
We study how discrete self-similarity (DSS) in the critical behavior of scalar-field collapse is imprinted on primordial-black-hole (PBH) mass functions. Using the DSS-modulated critical scaling law found in cosmological simulations, we propagate the near-threshold mass map into normalized PBH mass functions during a {kination} era. We compare Gaussian window function, $k$-space top-hat window function, and real-space top-hat window function, together with a real-space top-hat window function multiplied by a kination transfer function. We find that critical behavior in gravitational collapse produces an irreducible minimum width even for an infinitesimally narrow primordial spectrum. DSS then modulates this critical-scaling profile, generating approximately log-periodic features in mass. At fixed horizon mass, successive equal-phase points of the DSS-modulated critical mass map satisfy $Δ\ln M_{\rm PBH}=γP_{\rm ln}$. Consequently, in the narrow-spectrum limit, the corresponding structures in the final mass function are expected to satisfy $Δ\ln m\simeqγP_{\rm ln}$, or $m_{n+1}/m_n\simeq5.6$, for the fiducial Choptuik DSS parameters $γ$ and $P_{\rm ln}$. For broad primordial spectra, the convolution over horizon masses dephases the DSS pattern and progressively washes out the critical substructure. We normalize the mass functions so that we may primarily study the profile shape and the survival of DSS substructure, rather than the absolute PBH abundance. These results provide a bridge between cosmological DSS collapse simulations and PBH phenomenology including population observables.
Comments17 pages, 4 figures. Comments are welcome
