We present deep near-infrared spectroscopy of six quasars at 6.1 \leq z \leq 6.7 with VLT/X-Shooter and Gemini-N/GNIRS .
Our objects , originally discovered through a wide-field optical survey with the Hyper Suprime-Cam ( HSC ) Subaru Strategic Program ( HSC-SSP ) , have the lowest luminosities ( -25.5 \leq M _ { \mathrm { 1450 } } \leq - 23.1 mag ) of the z > 5.8 quasars with measured black hole masses .
From single-epoch mass measurements based on Mg ii \lambda 2798 , we find a wide range in black hole masses , from M _ { \mathrm { BH } } = 10 ^ { 7.6 } to 10 ^ { 9.3 } M _ { \odot } .
The Eddington ratios L _ { \mathrm { bol } } / L _ { \mathrm { Edd } } range from 0.16 to 1.1 , but the majority of the HSC quasars are powered by M _ { \mathrm { BH } } \sim 10 ^ { 9 } M _ { \odot } SMBHs accreting at sub-Eddington rates .
The Eddington ratio distribution of the HSC quasars is inclined to lower accretion rates than those of , who measured the black hole masses for similarly faint z \sim 6 quasars .
This suggests that the global Eddington ratio distribution is wider than has previously been thought .
The presence of M _ { \mathrm { BH } } \sim 10 ^ { 9 } M _ { \odot } SMBHs at z \sim 6 can not be explained with constant sub-Eddington accretion from stellar remnant seed black holes .
Therefore , we may be witnessing the first build-up of the most massive black holes in the first billion years of the universe , the accretion activity of which is transforming from active growth to a quiescent phase .
Measurements of a larger complete sample of z \gtrsim 6 low-luminosity quasars , as well as deeper observations with future facilities will enable us to better understand the early SMBH growth in the reionization epoch .