Deciphering the formation of supermassive black holes (SMBHs) is a key science goal for upcoming observational facilities. In many theoretical channels proposed so far, the seed formation depends crucially on local gas conditions. We systematically characterize the impact of a range of gas-based black hole seeding prescriptions on SMBH populations using cosmological simulations. Seeds of mass $M_{\mathrm{seed}}\sim 10^3\!-\!10^{6}~\mathrm{M}_{\odot }\, h^{-1}$ are placed in haloes that exceed critical thresholds for star-forming, metal-poor gas mass and halo mass (defined as $\tilde{M}_{\mathrm{sf,mp}}$ and $\tilde{M}_{\mathrm{h}}$, respectively, in units of Mseed). We quantify the impact of these parameters on the properties of z ≥ 7 SMBHs. Lower seed masses produce higher black hole merger rates (by factors of ∼10 and ∼1000 at z ∼ 7 and z ∼ 15, respectively). For fixed seed mass, we find that $\tilde{M}_{\mathrm{h}}$ has the strongest impact on the black hole population at high redshift (z ≳ 15, where a factor of 10 increase in $\tilde{M}_{\mathrm{h}}$ suppresses merger rates by ≳100). At lower redshift (z ≲ 15), we find that $\tilde{M}_{\mathrm{sf,mp}}$ has a larger impact on the black hole population. Increasing $\tilde{M}_{\mathrm{sf,mp}}$ from 5 to 150 suppresses the merger rates by factors of ∼8 at z ∼ 7–15. This suggests that the seeding criteria explored here could leave distinct imprints on LISA merger rates. In contrast, AGN luminosity functions are much less sensitive to seeding criteria, varying by factors ≲2–3 within our models. Such variations will be challenging to probe even with future sensitive instruments such as Lynx or JWST. Our study provides a useful benchmark for development of seed models for large-volume cosmological simulations.

中文翻译：

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基于气体的播种对 z ≥ 7 处超大质量黑洞种群的影响

破译超大质量黑洞 (SMBH) 的形成是即将到来的观测设施的一个关键科学目标。在迄今为止提出的许多理论渠道中，种子的形成主要取决于当地的气体条件。我们使用宇宙学模拟系统地描述了一系列基于气体的黑洞播种处方对 SMBH 种群的影响。质量为 $M_{\mathrm{seed}}\sim 10^3\!-\!10^{6}~\mathrm{M}_{\odot }\, h^{-1}$ 的种子放置在超过恒星形成、贫金属气体质量和晕质量临界阈值的晕（定义为 $\tilde{M}_{\mathrm{sf,mp}}$ 和 $\tilde{M}_{\mathrm{ h}}$，分别以 Mseed 为单位）。我们量化了这些参数对 z ≥ 7 SMBHs 特性的影响。较低的种子质量会产生较高的黑洞合并率（在 z ∼ 7 和 z ∼ 15 处增加 ∼10 和 ∼1000 的因子，分别）。对于固定的种子质量，我们发现 $\tilde{M}_{\mathrm{h}}$ 在高红移 (z ≳ 15, 其中 $\tilde 增加了 10 倍) 时对黑洞种群的影响最强{M}_{\mathrm{h}}$ 将合并率抑制 ≳100)。在较低的红移处（z ≲ 15），我们发现 $\tilde{M}_{\mathrm{sf,mp}}$ 对黑洞种群的影响更大。将 $\tilde{M}_{\mathrm{sf,mp}}$ 从 5 增加到 150，在 z ∼ 7-15 处将合并率抑制了 ∼8 倍。这表明这里探讨的种子标准可能会在 LISA 合并率上留下不同的印记。相比之下，AGN 光度函数对播种标准的敏感性要低得多，在我们的模型中因因子≲2-3 而异。即使使用未来的敏感仪器（如 Lynx 或 JWST）来探测这种变化也将具有挑战性。