Carbon Isotope Fractionation of Complex Organic Molecules in Star-forming Cores

Recent high-resolution and sensitivity ALMA observations have unveiled the carbon isotope ratios (¹²C/¹³C) of Complex Organic Molecules (COMs) in a low-mass protostellar source. To understand the ¹²C/¹³C ratios of COMs, we investigated the carbon isotope fractionation of COMs from prestellar cores to protostellar cores with a gas-grain chemical network model. We confirmed that the ¹²C/¹³C ratios of small molecules are bimodal in the prestellar phase: CO and species formed from CO (e.g., CH₃OH) are slightly enriched in ¹³C compared to the local ISM (by ~ 10 $%$), while those from C and C⁺ are depleted in ¹³C owing to isotope exchange reactions. COMs are mainly formed on the grain surface and in the hot gas ($>$ 100 K) in the protostellar phase. The ¹²C/¹³C ratios of COMs depend on which molecules the COMs are formed from. In our base model, some COMs in the hot gas are depleted in ¹³C compared to the observations. Thus, We additionally incorporate reactions between gaseous atomic C and H₂O ice or CO ice on the grain surface to form H₂CO ice or {C2O} ice, as suggested by recent laboratory studies. The direct C-atom addition reactions open pathways to form {^13C}-enriched COMs from atomic C and CO ice. We find that these direct C-atom addition reactions mitigate ¹³C-depletion of COMs, and the model with the direct C-atom addition reactions better reproduces the observations than our base model. We also discuss the impact of the cosmic ray ionization rate on the ¹²C/¹³C ratio of COMs.