The existence of ≳10⁹ M _⊙ supermassive black holes (SMBHs) at redshift z>6 raises the problem of how such SMBHs can grow up within the cosmic time (<1 Gyr) from small seed BHs. In this Letter, we use the observations of 14 quasars at z>6.5 with mass estimates to constrain their seeds and early growth, by self-consistently considering the spin evolution and the possibility of super-Eddington accretion. We find that spin plays an important role in the growth of early SMBHs, and the constraints on seed mass and super-Eddington accretion fraction strongly depend on the assumed accretion history. If the accretion is coherent with single (or a small number of) episode(s), leading to high spins for the majority of accretion time, then the SMBH growth is relatively slow; and if the accretion is chaotic with many episodes and in each episode the total accreted mass is much less than the SMBH mass, leading to moderate/low spins, then the growth is relatively fast. The constraints on the seed mass and super-Eddington accretion fraction are degenerate. A significant fraction (≳0.1%–1% in linear scale but ∼3–4 dex in logarithmic scale for 10³–10⁴ M _⊙ seeds) of super-Eddington accretion is required if the seed mass is not ≫10⁵ M _⊙, and the requirements of high seed mass and/or super-Eddington accretion fraction are moderately relaxed if the accretion is chaotic.

的≳10存在⁹ 中号 _⊙在红移黑洞（SMBHs）Ž > 6提出了这样SMBHs如何从小种子黑洞宇宙时间（<1 Gyr的）内长大的问题。在这封信中，我们使用z处14个类星体的观测值> 6.5，通过自洽一致地考虑自旋进化和超爱丁顿增生的可能性，通过大量估计来限制其种子和早期生长。我们发现自旋在早期SMBHs的生长中起着重要作用，并且对种子质量和超爱丁顿增生分数的限制在很大程度上取决于假定的增生历史。如果增生与单个（或少量）情节一致，导致大部分增生时间出现高自旋，则SMBH的增长相对较慢；并且如果增生是混乱的，并且每集的总增生质量远小于SMBH的增生质量，则导致中度/低速旋转，则增长相对较快。种子质量和超爱丁顿积累分数的约束退化。很大一部分（≳0。^3个-10 ⁴ 中号 _⊙如果种子质量不»10超爱丁顿积的种子）需要⁵ 中号 _⊙如果附着物是混乱的，并且高种子质量和/或超爱丁顿积部分的要求放宽适度。