多模态质量与扩展自旋分布的原初黑洞蒸发：对有效相对论粒子数的宇宙学印记
Evaporation of Primordial Black Holes with Multimodal Mass and Extended Spin Distributions: Cosmological Imprints on the Effective Number of Relativistic Species
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中文总结 AI 辅助
该研究构建FRISHBEE代码实现多模态质量函数与扩展自旋分布，计算原初黑洞蒸发对有效相对论粒子数$\Delta N_{\rm eff}$的影响，发现质量分布和自旋会改变$\Delta N_{\rm eff}$，其可作为原初黑洞形成通道的判别依据。
中文摘要 AI 辅助
原初黑洞（PBHs）通过多种不同机制形成，每种机制都会留下特征质量函数，而单一质量处理可能会抹去这些特征。基于FRISBHEE代码，我们引入FRISHBEE，在多模态框架中实现了四种质量函数——对数正态（log-normal）、幂律（power-law）、临界坍缩（critical collapse）、度规预热（metric preheating），并通过高斯（Gaussian）和菲什巴赫（Fishbach）剖面模拟自旋。关键在于，各通道的权重源自原初坍缩概率而非拟合，将质量函数与功率谱振幅关联起来——这是暴胀模型构建与宇宙微波背景（CMB）可观测性之间的联系。我们针对原初大爆炸核合成（pre-BBN）窗口内初始质量$M_{\rm PBH}^{\rm in}=10^{7}$克求解弗里德曼-玻尔兹曼方程，计算了五种分布、三种自旋构型和三种权重下的$\Delta N_{\rm eff}$。扩展质量函数使$\Delta N_{\rm eff}$相对于单色基准提高了约1.03倍（临界坍缩）至约1.84倍（对数正态），在质量窗口$\{10^{5},10^{7},10^{8}\}$克范围内保持了$LN > MM > PL > MP > CC$的层级关系。近极值自旋（$a_{\star}=0.99$）和自旋-2暗辐射会反转这一趋势：宽分布中超辐射自旋损失比单色群体更快平均，使得单色近似高估了$\Delta N_{\rm eff}$。针对CMB-S4和西蒙斯天文台（灵敏度分别为$\sigma\simeq 0.06$和$0.05$），单色基准对于标量暗辐射（sDR $=0$）不可探测，而对数正态、幂律和多模态分布达到约1.6至1.7$\sigma$；对于自旋-2暗辐射，信号下降一个数量级以上，均不可探测。因此，形成通道决定了霍金信号的幅度和观测可及性，确立$\Delta N_{\rm eff}$作为单通道与多通道PBH形成场景的判别依据。
英文摘要
Primordial black holes (PBHs) form through several distinct mechanisms, each imprinting a characteristic mass function that a single-mass treatment risks erasing. Building on the FRISBHEE code, we introduce FRISHBEE, implementing four mass functions--log-normal, power-law, critical collapse, metric preheating--in a multimodal framework, with spin modeled via Gaussian and Fishbach profiles. Crucially, each channel's weight is derived from the primordial collapse probability rather than fitted, tying the mass function to the power-spectrum amplitude--a link between inflationary model-building and CMB observables. Solving the Friedmann-Boltzmann equations for $M_{\rm PBH}^{\rm in}=10^{7}$~g in the pre-BBN window, we compute $ΔN_{\rm eff}$ for five distributions, three spin configurations, and three weightings. Extended mass functions enhance $ΔN_{\rm eff}$ over the monochromatic benchmark by factors of $\sim\!1.03$ (critical collapse) to $\sim\!1.84$ (log-normal), preserving the hierarchy $LN > MM > PL > MP > CC$ across the mass window $\{10^{5},10^{7},10^{8}\}$~g. Near-extremal spin ($a_{\star}=0.99$) and spin-2 dark radiation invert this trend: superradiant spin loss averages away faster in broad distributions than in a monochromatic population, letting the monochromatic approximation overestimate $ΔN_{\rm eff}$. Against CMB-S4 and Simons Observatory sensitivities ($σ\simeq 0.06$ and $0.05$), the monochromatic benchmark is undetectable for scalar dark radiation (sDR $=0$), while log-normal, power-law, and multimodal distributions reach $\sim\!1.6$--$1.7σ$; for spin-2 dark radiation the signal drops over an order of magnitude, with none detectable. The formation channel thus governs the magnitude and observational accessibility of the Hawking signal, establishing $ΔN_{\rm eff}$ as a discriminant between single- and multi-channel PBH formation scenarios.
发表机构
- Energy, Environment, and Applications (LP2EA), Polydisciplinary Faculty, Laboratory of Physics, Cadi Ayyad University（卡迪阿亚德大学多学科学院物理实验室能源、环境与应用研究组）
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