We discovered an H alpha absorption in a broad H alpha emission line of an unusual broad absorption line quasar, SDSS J083942.11+380526.3 at z=2.318, by near-infrared spectroscopy with the Cooled Infrared Spectrograph and Camera for OHS (CISCO) on the Subaru telescope. The Presence of non-stellar H alpha absorption is known only in the Seyfert galaxy NGC 4151 to date, thus our discovery is the first case for quasars. The H alpha absorption line is blueshifted by 520 km/s relative to the H alpha emission line, and its redshift almost coincides with those of UV low-ionization metal absorption lines. The width of the H alpha absorption (~ 340 km/s) is similar to those of the UV low-ionization absorption lines. These facts suggest that the H alpha and the low-ionization metal absorption lines are produced by the same low-ionization gas which has a substantial amount of neutral gas. The column density of the neutral hydrogen is estimated to be ~ 10^18 cm^-2 by assuming a gas temperature of 10,000 K from the analysis of the curve of growth. The continuum spectrum is reproduced by a reddened (E(B-V) ~ 0.15 mag for the SMC-like reddening law) composite quasar spectrum. Furthermore, the UV spectrum of SDSS J083942.11+380526.3 shows a remarkable similarity to that of NGC 4151 in its low state, suggesting the physical condition of the absorber in SDSS J083942.11+380526.3 is similar to that of NGC 4151 in the low state. As proposed for NGC 4151, SDSS J083942.11+380526.3 may be also seen through the close direction of the surface of the obscuring torus.
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