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arXiv 2509.08041astro-ph.GAastro-ph.COastro-ph.HE
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超大质量黑洞丰度的不确定性及其对引力波背景的影响

Uncertainties in the supermassive black hole abundance and implications for the GW background

Gabriela Sato-Polito, Matias Zaldarriaga

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19 pages, 13 figures
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AI总结：

本文通过多种质量代理测量超大质量黑洞质量函数，评估其不确定性对引力波背景预测的影响，发现不同代理间可部分协调，但系统修正和选择效应仍带来显著偏差。

摘要：

超大质量黑洞（SMBH）的现今质量函数是预测和理论解释由脉冲星计时阵列（PTAs）测得的引力波背景（GWB）最重要的可观测量。由于具有动力学推断SMBH质量的星系样本量有限，与黑洞质量相关的更易测量的星系性质$X$被用作标签（通过标度关系$M_{\ullet}-X$），这些标签可以在更大的星系目录中被计数，从而产生质量函数的测量结果。从局域质量函数估计GWB的振幅因此比一般测量标度关系和星系质量/光度函数更简单，原因有二：特征应变的贡献由狭窄的质量范围主导，且质量代理$X$总是被边缘化。虽然两个目录中$X$的一致误差无关紧要，但它们之间相对较小的偏差可以在预测的SMBH丰度中产生显著变化。在这项工作中，我们通过一组在它们之间具有多个冗余测量的目录，探索使用不同质量代理测量SMBH质量函数。这使我们能够研究导致最终黑洞丰度差异的内部不一致性，同时最小化由组合不同测量集引起的观测系统偏差。我们关注3个代理：速度弥散$σ$、K波段光度$L$，以及由基本平面定义的$L$和半径$R$的组合。我们表明，这三者都可以在一定程度上协调，但强调了标度关系目录与质量函数目录之间量化不足的系统修正的剩余依赖性，以及选择效应的潜在影响。

英文摘要：

The present-day mass function of supermassive black holes is the most important observable quantity for the prediction and theoretical interpretation of the gravitational wave background (GWB) measured by pulsar timing arrays (PTAs). Due to the limited sample size of galaxies with dynamically inferred SMBH masses, more readily measurable galaxy properties $X$ that correlate with the black hole mass are used as labels (via scaling relations $M_{\bullet}-X$), which can then be counted in a larger galaxy catalog to produce a measurement of the mass function. Estimating the amplitude of the GWB from the local mass function is therefore simpler than general measurements of scaling relations and galaxy mass/luminosity functions for two reasons: the contribution to the characteristic strain is dominated by a narrow range of masses, and the mass proxy $X$ is always marginalized over. While consistent errors in $X$ in both catalogs are irrelevant, relatively small biases between them can produce significant shifts in the predicted SMBH abundance. In this work, we explore measurements of the SMBH mass function using different mass proxies through a set of catalogs with a number of redundant measurements between them. This enables us to investigate internal inconsistencies that lead to discrepancies in the final black hole abundance, while minimizing observational systematic biases induced by combining disparate sets of measurements. We focus on 3 proxies: the velocity dispersion $σ$, K-band luminosity $L$, and a combination of $L$ and radius $R$ defined by the fundamental plane. We show that all three can be reconciled to some degree, but highlight the remaining dependence on poorly-quantified systematic corrections between the scaling relation catalogs and the mass function catalogs, as well as the potential impact of selection effects.

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