The "Red Radio Ring": Ionised and Molecular Gas in a Starburst/Active Galactic Nucleus at $z \sim 2.55$.

We report the detection of the far-infrared (FIR) fine-structure line of singly ionised nitrogen, \Nplusa, within the peak epoch of galaxy assembly, from a strongly lensed galaxy, hereafter ``The Red Radio Ring''; the RRR, at z = 2.55. We combine new observations of the ground-state and mid-J transitions of CO (J$_{\rm up} =$ 1,5,8), and the FIR spectral energy distribution (SED), to explore the multi-phase interstellar medium (ISM) properties of the RRR. All line profiles suggest that the HII regions, traced by \Nplusa, and the (diffuse and dense) molecular gas, traced by the CO, are co-spatial when averaged over kpc-sized regions. Using its mid-IR-to-millimetre (mm) SED, we derive a non-negligible dust attenuation of the \Nplusa line emission. Assuming a uniform dust screen approximation results a mean molecular gas column density $> 10^{24}$\, cm$^{-2}$, with a molecular gas-to-dust mass ratio of 100. It is clear that dust attenuation corrections should be accounted for when studying FIR fine-structure lines in such systems. The attenuation corrected ratio of $L_{\rm NII205} / L_{\rm IR(8-1000\mu m)} = 2.7 \times 10^{-4}$ is consistent with the dispersion of local and $z >$ 4 SFGs. We find that the lower-limit, \Nplusa -based star-formation rate (SFR) is less than the IR-derived SFR by a factor of four. Finally, the dust SED, CO line SED and $L_{\rm NII205}$ line-to-IR luminosity ratio of the RRR is consistent with a starburst-powered ISM.