| Riassunto: | We present Herschel-Spectral and Photometric Imaging Receiver (SPIRE) Fourier transform spectrometer (FTS) and radio follow-up observations of two Herschel-Astrophysical Terahertz Large Area Survey (H-ATLAS)-detected strongly lensed distant galaxies. In one of the targeted galaxies H-ATLAS J090311.6+003906 (SDP.81), we detect [Oiii]88μm and [Cii]158μm lines at a signal-to-noise ratio of ~5. We do not have any positive line identification in the other fainter target H-ATLAS J091305.0-005343 (SDP.130). Currently, SDP.81 is the faintest submillimetre galaxy with positive line detections with the FTS, with continuum flux just below 200mJy in the 200-600μm wavelength range. The derived redshift of SDP.81 from the two detections isz= 3.043 ± 0.012, in agreement with ground-based CO measurements. This is the first detection byHerschelof the [Oiii]88μm line in a galaxy at redshift higher than 0.05. Comparing the observed lines and line ratios with a grid of photodissociation region (PDR) models with different physical conditions, we derive the PDR cloud densityn≈ 2000cm-3 and the far-ultraviolet ionizing radiation fieldG0≈ 200 (in units of the Habing field - the local Galactic interstellar radiation field of 1.6 × 10-6 W m-2). Using the CO-derived molecular mass and the PDR properties, we estimate the effective radius of the emitting region to be 500-700pc. These characteristics are typical for star-forming, high-redshift galaxies. The radio observations indicate that SDP.81 deviates significantly from the local far-infrared/radio (FIR/radio) correlation, which hints that some fraction of the radio emission is coming from an active galactic nucleus (AGN). The constraints on the source size from millimetre-wave observations put a very conservative upper limit of the possible AGN contribution to less than 33 per cent. These indications, together with the high [Oiii]/FIR ratio and the upper limit of [Oi]63μm/[Cii]158μm, suggest that some fraction of the ionizing radiation is likely to originate from the AGN. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.
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