Ratio of black hole to galaxy mass of an extremely red dust-obscured galaxy at <i>z</i> = 2.52

<jats:p>We present a near-infrared (NIR) spectrum of WISE J104222.11+164115.3, an extremely red dust-obscured galaxy (DOG), which has been observed with the Long-slit Intermediate Resolution Infrared Spectrograph (LIRIS) on the 4.2m <jats:italic>William Hershel</jats:italic> Telescope. This object was selected as a hyper-luminous DOG candidate at <jats:italic>z</jats:italic> ∼ 2 by combining the optical and IR photometric data based on the Sloan Digital Sky Survey (SDSS) and Wide-field Infrared Survey Explorer (WISE), although its redshift had not yet been confirmed. Based on the LIRIS observation, we confirmed its redshift of 2.521 and total IR luminosity of log(<jats:italic>L</jats:italic><jats:sub>IR</jats:sub>/<jats:italic>L</jats:italic><jats:sub>⊙</jats:sub>) = 14.57, which satisfies the criterion for an extremely luminous IR galaxy (ELIRG). Moreover, we indicate that this object seems to have an extremely massive black hole with <jats:italic>M</jats:italic><jats:sub>BH</jats:sub> = 10<jats:sup>10.92</jats:sup> <jats:italic>M</jats:italic><jats:sub>⊙</jats:sub> based on the broad H<jats:italic>α</jats:italic> line: the host stellar mass is derived as <jats:italic>M</jats:italic><jats:sub>⋆</jats:sub> = 10<jats:sup>13.55</jats:sup> <jats:italic>M</jats:italic><jats:sub>⊙</jats:sub> by a fit of the spectral energy distribution. Very recently, it has been reported that this object is an anomalous gravitationally lensed quasar based on near-IR high-resolution imaging data obtained with the <jats:italic>Hubble</jats:italic> Space Telescope. Its magnification factor has also been estimated with some uncertainty (i.e., <jats:italic>μ</jats:italic> = 53−122). We investigate the ratio of the black hole to galaxy mass, which is less strongly affected by a lensing magnification factor, instead of the absolute values of the luminosities and masses. We find that the <jats:italic>M</jats:italic><jats:sub>BH</jats:sub>/<jats:italic>M</jats:italic><jats:sub>⋆</jats:sub> ratio (i.e., 0.0140–0.0204) is significantly higher than the local relation, following a sequence of unobscured quasars instead of obscured objects (e.g., submillimeter galaxies) at the same redshift. Moreover, the LIRIS spectrum shows strongly blueshifted oxygen lines with an outflowing velocity of ∼1100 km s<jats:sup>−1</jats:sup>, and our <jats:italic>Swift</jats:italic> X-ray observation also supports that this source is an absorbed AGN with an intrinsic column density of <jats:italic>N</jats:italic><jats:sub>H</jats:sub><jats:sup>int</jats:sup> = 4.9 × 10<jats:sup>23</jats:sup> cm<jats:sup>−2</jats:sup>. These results imply that WISE J104222.11+164115.3 is in a blow-out phase at the end of the buried rapid black hole growth.</jats:p>