Effects of Spin on Constraining the Seeds and Growth of ≳10⁹M_⊙ Supermassive Black Holes in z > 6.5 Quasars

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.