ATLASGAL-selected massive clumps in the inner Galaxy X. Observations of atomic carbon at 492 GHz

Context. While high-mass stars are key drivers of the evolution of galaxies, how they form and interact with the surrounding gas is still not fully understood. To shed light on this overarching issue, we have been performing a multitelescope campaign to observe carbon species in similar to 100 massive clumps ("Top100") identified by the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL). Our targets constitute a representative sample of high-mass star-forming regions with a wide range of masses (similar to 20-10(4) M-circle dot), bolometric luminosities (similar to 60-10(6) L-circle dot), and evolutionary stages (70 mu m weak, infrared weak, infrared bright, and H II region sources). Aims. We aim to probe the physical conditions of [C I]-traced gas in the Top100 sample based on Atacama Pathfinder EXperiment (APEX) [C I] 492 GHz observations. This is the first of a series of papers presenting results from our [C II] and [C I] campaign. Methods. To determine physical properties such as the temperature, density, and column density, we combined the obtained [C I] 492 GHz spectra with APEX observations of [C I] 809 GHz and (CO)-C-13(2-1), as well as with other multiwavelength data, and employed both local thermodynamic equilibrium (LTE) and non-LTE methods. Results. Our 98 sources are clearly detected in [C I] 492 GHz emission, and the observed integrated intensities and line widths tend to increase toward evolved stages of star formation. In addition to these "main" components that are associated with the Top100 sample, 41 emission and two absorption features are identified by their velocities toward 28 and two lines of sight, respectively, as "secondary" components. The secondary components have systematically smaller integrated intensities and line widths than the main components. We found that [C I] 492 GHz and (CO)-C-13(2-1) are well correlated with the (CO)-C-13(2-1)-to-[C I] 492 GHz integrated intensity ratio varying from 0.2 to 5.3. In addition, we derived the H-2-to-[C I] conversion factor, X(C I), by dividing 870 um-based H-2 column densities by the observed [C I] 492 GHz integrated intensities and found that X(C I) (in units of cm(-2) (K km s(-1))(-1)) ranges from 2.3 x 10(20) to 1.3 x 10(22) with a median of 1.7 x 10(21). In contrast to the strong correlation with (CO)-C-13(2-1), [C I] 492 GHz has a scattered relation with the 870 mu m-traced molecular gas. Finally, we performed LTE and non-LTE analyses of the [C I] 492 GHz and 809 GHz data for a subset of the Top100 sample and inferred that [C I] emission likely originates from warm (kinetic temperature greater than or similar to 60 K), optically thin (opacity <0.5), and highly pressurized (thermal pressure similar to(2-5000) x 10(5) K cm(-3)) regions. Conclusions. Our [C I] 492 GHz survey demonstrates that [C I] 492 GHz is prevalent in the inner Galaxy and traces not only massive clumps, but also non-star-forming relatively diffuse gas. The strong correlation between [C I] 492 GHz and (CO)-C-13(2-1) indicates that they probe similar conditions, and the observed variations in the intensity ratio of the two transitions likely reflect local conditions of the interstellar medium. The scattered relation between [C I] 492 GHz and the 870 mu m-based molecular gas, on the other hand, implies that [C I] 492 GHz and (CO)-C-13(2-1) probe warm molecular gas that surrounds denser and colder clumps traced by 870 mu m emission.