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 ¹³CN $N=2-1$ hyperfine lines in the TW Hya disk with the Atacama Large Millimeter/submillimeter Array. This is the first spatially-resolved detection of ¹³CN in disks, which enables us to measure the spatially resolved ¹²CN/¹³CN ratio for the first time. We conducted non-local thermal equilibrium modeling of the ¹³CN lines in conjunction with previously observed ¹²CN lines to derive the kinetic temperature, H₂ volume density, and column densities of ¹²CN and ¹³CN. The H₂ volume density is found to range between (4 - 10)×10⁷ \ cm⁻³, suggesting that CN molecules mainly reside in the disk upper layer. The ¹²CN/¹³CN ratio is measured to be 70⁺⁹₋₆ at $30 < r < 80$ au from the central star, which is similar to the ¹²C/¹³C 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 ¹²C into the solid phase towards the disk midplane. This study reveals the complexity of the carbon isotope fractionation operating in disks.