Models of pure gas-phase chemistry in well-shielded regions of molecular clouds predict relatively high levels of molecular oxygen, O2, and water, H2O. Contrary to expectation, the space missions SWAS and Odin found only very small amounts of water vapour and essentially no O2 in the dense star-forming interstellar medium. Only toward rho Oph A did Odin detect a weak line of O2 at 119 GHz in a beam size of 10 arcmin. A larger telescope aperture such as that of the Herschel Space Observatory is required to resolve the O2 emission and to pinpoint its origin. We use the Heterodyne Instrument for the Far Infrared aboard Herschel to obtain high resolution O2 spectra toward selected positions in rho Oph A. These data are analysed using standard techniques for O2 excitation and compared to recent PDR-like chemical cloud models. The 487.2GHz line was clearly detected toward all three observed positions in rho Oph A. In addition, an oversampled map of the 773.8GHz transition revealed the detection of the line in only half of the observed area. Based on their ratios, the temperature of the O2 emitting gas appears to vary quite substantially, with warm gas (> 50 K) adjacent to a much colder region, where temperatures are below 30 K. The exploited models predict O2 column densities to be sensitive to the prevailing dust temperatures, but rather insensitive to the temperatures of the gas. In agreement with these model, the observationally determined O2 column densities seem not to depend strongly on the derived gas temperatures, but fall into the range N(O2) = (3 to >6)e15/cm^2. Beam averaged O2 abundances are about 5e-8 relative to H2. Combining the HIFI data with earlier Odin observations yields a source size at 119 GHz of about 4 - 5 arcmin, encompassing the entire rho Oph A core.
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