Using [C I] to probe the interstellar medium in z ∼ 2.5 sub-millimeter galaxies

We present new [C i](1-0) and (CO)-C-12(4-3) Plateau de Bure Interferometer observations of five sub-millimeter galaxies (SMGs) and combine these with all available [C i](1-0) literature detections in SMGs to probe the gas distribution within a sample of 14 systems. We explore the [C i](1-0) properties of the SMG population, particularly investigating the ratio of the [C i](1-0) luminosity to various (CO)-C-12 transition and far-infrared luminosities. We find that the SMGs with new observations extend the spread of L[Ci](1-0)/L-FIR to much higher values than found before, with our complete sample providing a good representation of the diverse z > 2 SMG population. We compare the line ratios to the outputs of photodissociation region (PDR) models to constrain the physical conditions in the interstellar medium (ISM) of the SMGs, finding an average density of << log (n/cm(-3))>> = 4.3 +/- 0.2 and an average radiation field (in terms of the local field value, G(0)) of << log (G(0))>> = 3.9 +/- 0.4. Overall, we find the SMGs are most comparable to local ultraluminous infrared galaxies (ULIRGs) in G(0) and n; however, a significant tail of 5 of the 14 SMGs are likely best compared to less compact, local starburst galaxies, providing new evidence that many SMGs have extended star formation distributions and are therefore not simply scaled up versions of local ULIRGs. We derive the ISM properties of a sample of quasars also finding that they have higher densities and radiation fields on average than the SMGs, consistent with the more extreme local ULIRGs, and reinforcing their interpretation as transition objects. We explore the limitations of using simple PDR models to understand [C i], which may be concomitant with the bulk H-2 mass rather than PDR distributed. We therefore also assess [C i] as a tracer of H-2, finding that for our sample SMGs, the H-2 masses derived from [C i] are often consistent with those determined from low excitation (CO)-C-12. We conclude that [C i] observations provide a useful tool to probe the bulk gas and gas processes occurring within merging SMGs, however more detailed, resolved observations are required to fully exploit [C i] as a diagnostic.