The [CII]/[NII] ratio in 3 < z < 6 sub-millimetre galaxies from the
  South Pole Telescope survey
  We present Atacama Compact Array and Atacama Pathfinder Experiment
observations of the [N II] 205 $\mu$m fine-structure line in 40 sub-millimetre
galaxies lying at redshifts z = 3 to 6, drawn from the 2500 deg$^2$ South Pole
Telescope survey. This represents the largest uniformly selected sample of
high-redshift [N II] 205 $\mu$m measurements to date. 29 sources also have [C
II] 158 $\mu$m line observations allowing a characterization of the
distribution of the [C II] to [N II] luminosity ratio for the first time at
high-redshift. The sample exhibits a median L$_{[C II]}$ /L$_{[N II]}$
$\approx$ 11 and interquartile range of 5.0 to 24.7. These ratios are similar
to those observed in local (U)LIRGs, possibly indicating similarities in their
interstellar medium. At the extremes, we find individual sub-millimetre
galaxies with L$_{[C II]}$ /L$_{[N II]}$ low enough to suggest a smaller
contribution from neutral gas than ionized gas to the [C II] flux and high
enough to suggest strongly photon or X-ray region dominated flux. These results
highlight a large range in this line luminosity ratio for sub-millimetre
galaxies, which may be caused by variations in gas density, the relative
abundances of carbon and nitrogen, ionization parameter, metallicity, and a
variation in the fractional abundance of ionized and neutral interstellar
medium.
