The past decade has seen significant progress in understanding galaxy formation and evolution using large-scale cosmological simulations. While these simulations produce galaxies in overall good agreement with observations, they employ different sub-grid models for galaxies and supermassive black holes (BHs). We investigate the impact of the sub-grid models on the BH mass properties of the Illustris, TNG100, TNG300, Horizon-AGN, EAGLE, and SIMBA simulations, focusing on the MBH − M⋆ relation and the BH mass function. All simulations predict tight MBH − M⋆ relations, and struggle to produce BHs of $M_{\rm BH}\leqslant 10^{7.5}\, \rm M_{\odot }$ in galaxies of $M_{\star }\sim 10^{10.5}\!-\!10^{11.5}\, \rm M_{\odot }$. While the time evolution of the mean MBH − M⋆ relation is mild ($\rm \Delta M_{\rm BH}\leqslant 1\, dex$ for 0 $\leqslant z \leqslant$ 5) for all the simulations, its linearity (shape) and normalization varies from simulation to simulation. The strength of SN feedback has a large impact on the linearity and time evolution for $M_{\star }\leqslant 10^{10.5}\, \rm M_{\odot }$. We find that the low-mass end is a good discriminant of the simulation models, and highlights the need for new observational constraints. At the high-mass end, strong AGN feedback can suppress the time evolution of the relation normalization. Compared with observations of the local Universe, we find an excess of BHs with $M_{\rm BH}\geqslant 10^{9}\, \rm M_{\odot }$ in most of the simulations. The BH mass function is dominated by efficiently accreting BHs ($\log _{10}\, f_{\rm Edd}\geqslant -2$) at high redshifts, and transitions progressively from the high-mass to the low-mass end to be governed by inactive BHs. The transition time and the contribution of active BHs are different among the simulations, and can be used to evaluate models against observations.

中文翻译：

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宇宙学模拟中的超大质量黑洞 I：MBH − M⋆ 关系和黑洞质量函数

在过去的十年中，使用大规模宇宙学模拟在理解星系形成和演化方面取得了重大进展。虽然这些模拟产生的星系总体上与观测结果非常吻合，但它们对星系和超大质量黑洞 (BH) 采用了不同的亚网格模型。我们研究了子网格模型对 Illustris、TNG100、TNG300、Horizo​​n-AGN、EAGLE 和 SIMBA 模拟的 BH 质量属性的影响，重点关注 MBH - M⋆ 关系和 BH 质量函数。所有模拟都预测紧密的 MBH - M⋆ 关系，并且难以在 $M_{\star }\ 的星系中产生 $M_{\rm BH}\leqslant 10^{7.5}\, \rm M_{\odot }$ 的 BH sim 10^{10.5}\!-\!10^{11.5}\, \rm M_{\odot }$。虽然平均 MBH - M⋆ 关系的时间演化是温和的 ($\rm \Delta M_{\rm BH}\leqslant 1\, dex$ for 0 $\leqslant z \leqslant$ 5) 对于所有模拟，其线性（形状）和归一化因模拟而异。SN 反馈的强度对 $M_{\star }\leqslant 10^{10.5}\, \rm M_{\odot }$ 的线性和时间演化有很大影响。我们发现低质量端是模拟模型的一个很好的判别器，并强调了对新观测约束的需求。在高质量端，强烈的 AGN 反馈可以抑制关系归一化的时间演化。与对局部宇宙的观察相比，我们发现在大多数模拟中，$M_{\rm BH}\geqslant 10^{9}\, \rm M_{\odot }$ 的 BH 过多。BH 质量函数主要是在高红移时有效地吸积 BH ($\log _{10}\, f_{\rm Edd}\geqslant -2$)，并逐渐从高质量端过渡到低质量端，由不活跃的 BH 控制。模拟之间的过渡时间和活跃 BH 的贡献不同，可用于根据观察评估模型。