Evidence for Low Radiative Efficiency or Highly Obscured Growth of $z>7$ Quasars

The supermassive black holes (SMBHs) observed at the centers of all massive galaxies are believed to have grown via luminous accretion during quasar phases in the distant past. The fraction of inflowing rest mass energy emitted as light, the radiative efficiency, has been inferred to be 10\%, in agreement with expectations from thin disk accretion models. But the existence of billion solar-mass SMBHs powering quasars at $z > 7$ challenges this picture: provided they respect the Eddington limit, there is not enough time to grow $z>7$ SMBHs from stellar remnant seeds unless the radiative efficiency is below 10\%. Here we show that one can constrain the radiative efficiencies of the most distant quasars known using foreground neutral intergalactic gas as a cosmological-scale ionizing photon counter. From the Ly$\alpha$ absorption profiles of ULAS J1120+0641 ($z=7.09$) and ULAS J1342+0928 ($z=7.54$), we determine posterior median radiative efficiencies of 0.08\% and 0.1\%, respectively, and the combination of the two measurements rule out the canonical 10\% efficiency at 99.8\% credibility after marginalizing over the unknown obscured fraction. This low radiative efficiency implies rapid mass accretion for the earliest SMBHs, greatly easing the tension between the age of the Universe and the SMBH masses. However, our measured efficiency may instead reflect nearly complete obscuration by dusty gas in the quasar host galaxies over the vast majority of their SMBH growth. Assuming 10\% efficiency during unobscured phases, we find that the obscured fraction would be $>82\%$ at 95\% credibility, and imply a $25.7^{+49.6}_{-16.5}$ times larger obscured than unobscured luminous quasar population at $z>7$.