Tracing pebble drift and trapping using radial carbon depletion profiles in protoplanetary disks

The composition of planets may be largely determined by the chemical processing and accretion of icy pebbles in protoplanetary disks. Recent observations of protoplanetary disks hint at wide-spread depletion of gaseous carbon. The missing volatile carbon is likely frozen in CO and/or CO$_2$ ice on grains and locked into the disk through pebble trapping in pressure bumps or planetesimals. We present the results of the first successful ACA (Atacama Compact Array) [C I] $J$ = 1-0 mini-survey of seven protoplanetary disks. Using tailored azimuthally symmetric DALI (Dust And LInes) thermo-chemical disk models, supported by the [C I] $J$ = 1-0 and resolved CO isotopologue data, we determine the system-averaged elemental volatile carbon abundance in the outer disk of three sources. Six out of seven sources are detected in [C I] $J$ = 1-0 with ACA, four of which show a distinct disk component. Based on the modeling we find severe cold gaseous carbon depletion in the outer disk of DL Tau and moderate depletion in the outer disks of DR Tau and DO Tau. Combining the outer and inner disk carbon abundances, we demonstrate definitive evidence for radial drift in the disk of DL Tau, where the existence of multiple dust rings points to either short lived or leaky dust traps. We find dust locking in the compact and smooth disks of DO Tau and DR Tau, hinting at unresolved dust substructure. Comparing our results with stars of different ages and luminosities, we identify an observational evolutionary trend in gaseous carbon depletion that is consistent with dynamical models of CO depletion processes. Transport efficiency of solids in protoplanetary disks can significantly differ from what we expect based on the current resolved substructure in the continuum observations. This has important implications for our understanding of the impact of radial drift and pebble accretion on planetary compositions.