A Catastrophic Failure to Build a Massive Galaxy around a Supermassive Black Hole at z = 3.84

<jats:title>Abstract</jats:title> <jats:p>We present observations of the stellar and molecular gas mass of SDSS J163909+282447.1, a luminous quasar at <jats:italic>z</jats:italic> = 3.84 with an extreme mass for a supermassive black hole (SMBH; <jats:italic>M</jats:italic> <jats:sub>BH</jats:sub> = 2.5 × 10<jats:sup>10</jats:sup> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>). The local SMBH mass–galaxy mass relation predicts a massive host galaxy with <jats:italic>M</jats:italic> <jats:sub>stellar</jats:sub> ≳ 10<jats:sup>12</jats:sup> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> 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, <jats:italic>M</jats:italic> <jats:sub>stellar</jats:sub> < 6.3 × 10<jats:sup>10</jats:sup> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>, 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 <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{{{\rm{H}}}_{2}}\sim 4.5\times {10}^{9}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjab2cd3ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> and a dynamical mass within a radius of 0.45 ± 0.2 kpc of <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{\mathrm{dyn}}={4}_{-4}^{+10}\times {10}^{10}$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjab2cd3ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>. 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 <jats:italic>M</jats:italic> <jats:sub>stellar</jats:sub> ≲ 1.5 × 10<jats:sup>10</jats:sup> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>, 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.</jats:p>