The First Spatially-resolved Detection of ${}^{13}$CN in a Protoplanetary Disk and Evidence for Complex Carbon Isotope Fractionation

Abstract

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 ${}^{13}$CN $N=2-1$ hyperfine lines in the TW Hya disk with the Atacama Large Millimeter/submillimeter Array. This is the first spatially-resolved detection of ${}^{13}$CN in disks, which enables us to measure the spatially resolved ${}^{12}$CN/${}^{13}$CN ratio for the first time. We conducted non-local thermal equilibrium modeling of the ${}^{13}$CN lines in conjunction with previously observed ${}^{12}$CN lines to derive the kinetic temperature, ${\mathrm{H}}_2$ volume density, and column densities of ${}^{12}$CN and ${}^{13}$CN. The ${\mathrm{H}}_2$ volume density is found to range between $(4-10)\times 10^7\mathrm{c}{\mathrm{m}}^{-3}$, suggesting that CN molecules mainly reside in the disk upper layer. The ${}^{12}$CN/${}^{13}$CN ratio is measured to be $70_{-6}^{+9}$ at $30<r<80$ au from the central star, which is similar to the ${}^{12}\mathrm{C}{/}^{13}\mathrm{C}$ 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 ${}^{12}\mathrm{C}$ into the solid phase towards the disk midplane. This study reveals the complexity of the carbon isotope fractionation operating in disks.

16 pages, 7 figures, accepted for publication in ApJ