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

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 William Hershel Telescope. This object was selected as a hyper-luminous DOG candidate at z similar to 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(L-IR/L-circle dot) = 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-circle dot based on the broad H alpha line: the host stellar mass is derived as M-star = 10(13.55) M-circle dot 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 similar to 1100 km s(-1), and our Swift X-ray observation also supports that this source is an absorbed AGN with an intrinsic column density of N-H(int) = 4.9 x 10(23) cm(-2). 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.