ALMA observations of atomic carbon in z ∼ 4 dusty star-forming galaxies

21 pages, 12 figures. Accepted for publication in MNRASInternational audienceWe 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 ∼ 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 × 10 10 M. 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 α CO ∼ 2.5 and a gas-to-dust ratio ∼ 200, or (b) an high carbon abundance X CI ∼ 7 × 10 −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