We report the detection of CO 5-4, 3-2, and 1-0 emission in the strongly lensed, Herschel/SPIRE-selected submillimeter galaxy (SMG) HLSW-01 at z=2.9574+/-0.0001, using the Plateau de Bure Interferometer, the Combined Array for Research in Millimeter-wave Astronomy, and the Green Bank Telescope. The observations spatially resolve the molecular gas into four lensed images with a maximum separation of ~9", and reveal the internal gas dynamics in this system. We derive lensing-corrected CO line luminosities of L'(CO 1-0) = (4.17+/-0.41), L'(CO 3-2) = (3.96+/-0.20) and L'(CO 5-4) = (3.45+/-0.20) x 10^10 (mu_L/10.9)^-1 Kkm/s pc^2, corresponding to luminosity ratios of r_31 = 0.95+/-0.10, r_53 = 0.87+/-0.06, and r_51 = 0.83+/-0.09. This suggests a total molecular gas mass of Mgas = 3.3 x 10^10 (alpha_CO/0.8) (mu_L/10.9)^-1 Msun. The gas mass, gas mass fraction, gas depletion timescale, star formation efficiency, and specific star formation rate are typical for an SMG. The velocity structure of the gas reservoir suggests that the brightest two lensed images are dynamically resolved projections of the same dust-obscured region in the galaxy that are kinematically offset from the unresolved fainter images. The resolved kinematics appear consistent with the complex velocity structure observed in major, `wet' (i.e., gas-rich) mergers. Major mergers are commonly observed in SMGs, and are likely to be responsible for fueling their intense starbursts at high gas consumption rates. This study demonstrates the level of detail to which galaxies in the early universe can be studied by utilizing the increase in effective spatial resolution and sensitivity provided by gravitational lensing.Comment: 7 pages, 5 figures, to appear in ApJL (accepted April 19, 2011
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