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arXiv 2501.09786astro-ph.COastro-ph.HE
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基于脉冲星计时阵测量的超大质量黑洞演化：并合与吸积增长的启示

Evolution of SMBHs in light of PTA measurements: implications for growth by mergers and accretion

Gabriela Sato-Polito, Matias Zaldarriaga, Eliot Quataert

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14 pages, 8 figures
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AI总结：

本研究结合脉冲星计时阵探测的引力波背景、类星体光度函数与局地黑洞质量函数约束，分析超大质量黑洞的并合与吸积增长模式，发现三者存在观测张力，并指出高并合率下大质量黑洞具有显著自旋。

摘要：

我们研究了同时考虑吸积与并合两种机制的超大质量黑洞（SMBH）增长过程。其中吸积过程的观测约束来自类星体光度函数（QLF），并合过程的约束来自脉冲星计时阵（PTA）近期探测到的引力波背景（GWB），而现今黑洞质量函数的测量结果则作为边界条件。引力波背景的信号主要由质量大于约10^9倍太阳质量的最大质量黑洞贡献。\n我们证明这类黑洞的演化可简化为两阶段过程：在红移z≤1时，并合是质量增长的主导机制；而在1.4≤z≤2区间，吸积作用达到峰值。观测到的引力波背景幅度较大，表明宇宙中存在数量可观的黑洞并合事件。我们指出，这一结果普遍意味着类星体的平均爱丁顿比要高于并合可忽略不计的假设场景。\n在不存在并合的情况下，将局地黑洞丰度测量与类星体光度函数匹配，可得到辐射效率ε_r=0.12、爱丁顿比λ=0.2的结果。当存在并合时，初始质量为M_i的前身黑洞会通过并合增长至最终总质量M_f，且并合过程增加的质量与类星体种群的平均爱丁顿比存在直接关联，满足M_f/M_i~λ/0.2的关系。\n由此，观测到的引力波背景、类星体性质与黑洞质量函数之间存在张力：与类星体推断的爱丁顿比及ε_r~0.1相符的质量函数估计值会低估引力波背景强度；多体并合或等质量并合可以提升引力波背景水平，但会导致爱丁顿比偏高。如果局地质量函数处于当前测量范围的高值端，引力波背景更易得到解释，但这需要ε_r~10^-2的低辐射效率，而这一效率值不符合标准发光吸积模型的预期。此外，引力波背景暗示的高并合率也强烈表明，局地宇宙中质量最大的一批黑洞因并合带来的轨道角动量会具有显著的自旋，自旋参数a可能约为0.5。

英文摘要：

We study the growth of supermassive black holes accounting for both accretion and mergers. The former is informed by observations of the quasar luminosity function (QLF) and the latter by the gravitational wave-background (GWB) recently detected by PTAs, while estimates of the present-day black hole mass function provide a boundary condition. The GWB is dominated by the most massive black holes ($\gtrsim10^{9}M_{\odot}$). We show that their evolution can be simplified into a two-step process: mergers dominate at $z\leq1$, while accretion peaks at $1.4\leq z\leq2$. The large amplitude of the observed GWB suggests a significant number of mergers. We show that this generically implies a higher average Eddington ratio for quasars relative to a scenario in which mergers are negligible. In the absence of mergers, matching local estimates of BH abundance to the QLF implies a radiative efficiency $ε_r=0.12$ and Eddington ratio $λ=0.2$. With mergers, a progenitor of mass $M_i$ is boosted to a final total mass $M_f$ and there is a direct relation between the mass gained in mergers and the average Eddington ratio of the quasar population, given by $M_f/M_i\simλ/0.2$. There is thus a tension between the observed GWB, quasar properties, and the BH mass function: estimates of the mass function consistent with Eddington ratios inferred in quasars and $ε_r\sim0.1$ underpredict the GWB; multiple/equal mass mergers can boost the GWB, but lead to a high Eddington ratio. If the local mass function is on the high end of current estimates, the GWB is more readily explained, but requires low efficiencies $ε_r\sim10^{-2}$ not expected in standard luminous accretion models. The significant merger rate implied by the GWB also strongly suggests that the most massive BHs in the local universe have significant spin due to the orbital angular momentum from mergers, perhaps $a\sim0.5$.

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