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The Redshift and Metallicity of the Host Galaxy of Dark GRB 080325 at z=1.78

We present near-infrared spectroscopy of the host galaxy of dark GRB 080325 using Subaru/MOIRCS. The obtained spectrum provides a clear detection of H$α$ emission and marginal [NII]$λ$6584. The host is a massive (M$_{*}\sim10^{11}$M$_{\odot}$), dusty ($A_{V}\sim 1.2$) star-forming galaxy at z=1.78. The star formation rate calculated from the H$α$ luminosity (35.6-47.0 M$_{\odot}$ yr$^{-1}$) is typical among GRB host galaxies (and star-forming galaxies generally) at z $>$1; however, the specific star formation rate is lower than normal star-forming galaxies at redshift $\sim$ 1.6, in contrast to the high specific star formation rates measured for many of other GRB hosts. The metallicity of the host is estimated to be 12+log(O/H)$_{\rm KK04}$$=$8.88. We emphasize that this is one of the most massive distant host galaxies for which metallcity is measured with emission-line diagnostics. The metallicity is fairly high among GRB hosts. However, this is still lower than the metallicity of normal star-forming galaxies of the same mass at z$\sim$1.6. The metallicity offset from normal star-forming galaxies is close to a typical value of other GRB hosts and indicates that GRB host galaxies are uniformly biased toward low metalicity over a wide range of redshift and stellar mass. The low-metallicity nature of the GRB 080325 host is likely not attributable to the fundamental metallicity relation of star-forming galaxies beacuse it is a metal-poor outlier from the relation and has a low sSFR. Thus we conclude that metallicity is important to the mechanism that produced this GRB.