High-redshift SMBHs can grow from stellar-mass seeds via chaotic accretion

Extremely massive black holes, with masses $M_{\rm BH} > 10^9 M_\odot$, have been observed at ever higher redshifts. These results create ever tighter constraints on the formation and growth mechanisms of early black holes. Here we show that even the most extreme black hole known, P\=oniu\=a'ena, can grow from a $10 M_\odot$ seed black hole via Eddington-limited luminous accretion, provided that accretion proceeds almost continuously, but is composed of a large number of episodes with individually-uncorrelated initial directions. This chaotic accretion scenario ensures that the growing black hole spins slowly, with the dimensionless spin parameter $a \lesssim 0.2$, so its radiative efficiency is also low, $\epsilon \simeq 0.06$. If accretion is even partially aligned, with $20-40\%$ of accretion events happening in the same direction, the black hole spin and radiative efficiency are much higher, leading to significantly slower growth. We suggest that the chaotic accretion scenario can be completely falsified only if a $10^9 M_\odot$ black hole is discovered at $z \geq 9.1$, approximately $150$~Myr before P\=oniu\=a'ena. The space density of extreme quasars suggests that only a very small fraction, roughly one in $4 \times 10^7$, of seed black holes need to encounter favourable growth conditions to produce the observed extreme quasars. Other seed black holes grow much less efficiently, mainly due to lower duty cycles, so are much more difficult to detect.