We investigate the properties of the interstellar medium, star formation, and the current-day stellar population in the strongly-lensed star-forming galaxy H-ATLAS J091043.1-000321 (SDP.11), at z = 1.7830, using new Herschel and ALMA observations of far-infrared fine-structure lines of carbon, oxygen and nitrogen. We report detections of the [O III] 52 um, [N III] 57 um, and [O I] 63 um lines from Herschel/PACS, and present high-resolution imaging of the [C II] 158 um line, and underlying continuum, using ALMA. We resolve the [C II] line emission into two spatially-offset Einstein rings, tracing the red- and blue-velocity components of the line, in the ALMA/Band-9 observations at 0.2 resolution. The values seen in the [C II]/FIR ratio map, as low as ~ 0.02% at the peak of the dust continuum, are similar to those of local ULIRGs, suggesting an intense starburst in this source. This is consistent with the high intrinsic FIR luminosity (~ 3 x 10^12 Lo), ~ 16 Myr gas depletion timescale, and < 8 Myr timescale since the last starburst episode, estimated from the hardness of the UV radiation field. By applying gravitational lensing models to the visibilities in the uv-plane, we find that the lensing magnification factor varies by a factor of two across SDP.11, affecting the observed line profiles. After correcting for the effects of differential lensing, a symmetric line profile is recovered, suggesting that the starburst present here may not be the result of a major merger, as is the case for local ULIRGs, but instead could be powered by star-formation activity spread across a 3-5 kpc rotating disk.
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