We present observations of the stellar and molecular gas mass of SDSS J163909+282447.1, a luminous quasar at z = 3.84 with an extreme mass for a supermassive black hole (SMBH; M BH = 2.5 × 1010 M o). The local SMBH mass-galaxy mass relation predicts a massive host galaxy with M stellar 1012 M o for this quasar. Based on sensitive near-infrared imaging with adaptive optics (AO) using Subaru, the stellar light from the host is undetected, thus resulting in an upper limit on the mass, M stellar < 6.3 × 1010 M o, a factor of 16 less than expected. The CO(4 - 3) observations at 0.″2 resolution using the Atacama Large Millimeter/submillimeter Array indicate a molecular gas mass from CO of M o and a dynamical mass within a radius of 0.45 ± 0.2 kpc of M o. With the SMBH accounting for ∼60% of the dynamical mass and considering the amount of molecular gas, we find an upper limit on the stellar mass to be M stellar ≲ 1.5 × 1010 M o, a value consistent with the limit from Subaru AO imaging. Based on these results, this SMBH has one of the largest host stellar mass deficits known given its SMBH mass; hence, it is unclear how to grow a SMBH/host galaxy to such a state since there is not enough molecular gas available to form a substantial amount of stellar mass to make up for the difference. Any physical model is likely to require an earlier phase of super-Eddington accretion onto the SMBH.
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