  We present a near-infrared (NIR) spectrum of WISE J1042+1641, an extremely
red dust-obscured galaxy (DOG), which has been observed with the LIRIS on the
4.2m William Hershel Telescope. This object was selected as a hyper-luminous
DOG candidate at z ~ 2 by combining the optical and IR photometric data based
on the SDSS and 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(L_IR/L_sun) = 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 M_BH = 10^10.92 M_sun based
on the broad Halpha line: the host stellar mass is derived as M_star = 10^13.55
M_sun 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 Hubble Space
Telescope. Its magnification factor has also been estimated with some
uncertainty (i.e., mu = 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
M_BH/M_star 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, and our Swift X-ray observation also supports that
this source is an absorbed AGN with an intrinsic column density of N_H = 4.9 x
10^23 cm^-2. These results imply that WISE J1042+1641 is in a blow-out phase at
the end of the buried rapid black hole growth.
