The First Spatially Resolved Detection of ¹³CN in a Protoplanetary Disk and Evidence for Complex Carbon Isotope Fractionation

Recent measurements of carbon isotope ratios in both protoplanetary disks and exoplanet atmospheres have suggested a possible transfer of significant carbon isotope fractionation from disks to planets. For a clearer understanding of the isotopic link between disks and planets, it is important to measure the carbon isotope ratios in various species. In this paper, we present a detection of the (CN)-C-13 N = 2 - 1 hyperfine lines in the TW Hya disk with the Atacama Large Millimeter/submillimeter Array. This is the first spatially resolved detection of (CN)-C-13 in disks, which enables us to measure the spatially resolved (CN)-C-12/(CN)-C-13 ratio for the first time. We conducted nonlocal thermal equilibrium modeling of the (CN)-C-13 lines in conjunction with previously observed (CN)-C-12 lines to derive the kinetic temperature, H2 volume density, and column densities of (CN)-C-12 and (CN)-C-13. The H2 volume density is found to range between (4 - 10) x 10(7) cm(-3), suggesting that CN molecules mainly reside in the disk's upper layer. The (CN)-C-12/(CN)-C-13 ratio is measured to be 70(-6)(+9) at 30 < r < 80 au from the central star, which is similar to the C-12/C-13 ratio in the interstellar medium. However, this value differs from the previously reported values found for other carbon-bearing molecules (CO and HCN) in the TW Hya disk. This could be self-consistently explained by different emission layer heights for different molecules combined with preferential sequestration of C-12 into the solid phase toward the disk midplane. This study reveals the complexity of the carbon isotope fractionation operating in disks.