Observations and modelling of CO and [CI] in protoplanetary disks First detections of [CI] and constraints on the carbon abundance

Context. The gas-solid budget of carbon in protoplanetary disks is related to the composition of the cores and atmospheres of the planets forming in them. The principal gas-phase carbon carriers CO, C-0, and C+ can now be observed regularly in disks. Aims. The gas-phase carbon abundance in disks has thus far not been well characterized observationally. We obtain new constraints on the [C]/[H] ratio in a large sample of disks, and compile an overview of the strength of [CI] and warm CO emission. Methods. We carried out a survey of the CO 6-5 line and the [CI] 1-0 and 2-1 lines towards 37 disks with the APEX telescope, and supplemented it with [CII] data from the literature. The data are interpreted using a grid of models produced with the DALI disk code. We also investigate how well the gas-phase carbon abundance can be determined in light of parameter uncertainties. Results. The CO6-5 line is detected in 13 out of 33 sources, [CI] 1-0 in 6 out of 12, and [CI] 2-1 in 1 out of 33. With separate deep integrations, the first unambiguous detections of the [CI] 1-0 line in disks are obtained, in TW Hya and HD 100546. Conclusions. Gas-phase carbon abundance reductions of a factor of 5-10 or more can be identified robustly based on CO and [CI] detections, assuming reasonable constraints on other parameters. The atomic carbon detection towards TW Hya confirms a factor of 100 reduction of [C]/[H](gas) in that disk, while the data are consistent with an ISM-like carbon abundance for HD 100546. In addition, BP Tau, T Cha, HD 139614, HD 141569, and HD 100453 are either carbon-depleted or gas-poor disks. The low [CI] 2-1 detection rates in the survey mostly reflect insufficient sensitivity for T Tauri disks. The Herbig Ae/Be disks with CO and [CII] upper limits below the models are debris-disk-like systems. An increase in sensitivity of roughly order of magnitude compared to our survey is required to obtain useful constraints on the gas-phase [C]/[H] ratio in most of the targeted systems.