ALMA observations of atomic carbon in z~4 dusty star-forming galaxies
  We present ALMA [CI]($1-0$) (rest frequency 492 GHz) observations for a
sample of 13 strongly-lensed dusty star-forming galaxies originally discovered
at 1.4mm in a blank-field survey by the South Pole Telescope. We compare these
new data with available [CI] observations from the literature, allowing a study
of the ISM properties of $\sim 30$ extreme dusty star-forming galaxies spanning
a redshift range $2 < z < 5$. Using the [CI] line as a tracer of the molecular
ISM, we find a mean molecular gas mass for SPT-DSFGs of $6.6 \times 10^{10}$
M$_{\odot}$. This is in tension with gas masses derived via low-$J$ $^{12}$CO
and dust masses; bringing the estimates into accordance requires either (a) an
elevated CO-to-H$_2$ conversion factor for our sample of $\alpha_{\rm CO} \sim
2.5$ and a gas-to-dust ratio $\sim200$, or (b) an high carbon abundance $X_{\rm
CI} \sim 7\times10^{-5}$. Using observations of a range of additional atomic
and molecular lines (including [CI], [CII], and multiple transitions of CO), we
use a modern Photodissociation Region code (3D-PDR) to assess the physical
conditions (including the density, UV radiation field strength, and gas
temperature) within the ISM of the DSFGs in our sample. We find that the ISM
within our DSFGs is characterised by dense gas permeated by strong UV fields.
We note that previous efforts to characterise PDR regions in DSFGs may have
significantly underestimated the density of the ISM. Combined, our analysis
suggests that the ISM of extreme dusty starbursts at high redshift consists of
dense, carbon-rich gas not directly comparable to the ISM of starbursts in the
local Universe.
