Carbon Isotope and Isotopomer Fractionation in Cold Dense Cloud Cores

We construct the gas-grain chemical network model which includes carbon isotopes (12C and 13C) with an emphasis on isotopomer-exchange reactions. Temporal variations of molecular abundances, the carbon isotope ratios (12CX/13CX) and the isotopomer ratios (12C13CX/13C12CX) of CCH and CCS in cold dense cloud cores are investigated by numerical calculations. We confirm that the isotope ratios of molecules, both in the gas phase and grain surfaces, are significantly different depending on whether the molecule is formed from the carbon atom (ion) or the CO molecule. Molecules formed from carbon atoms have the CX/13CX ratios greater than the elemental abundance ratio of [12C/13C]. On the other hand, molecules formed from CO molecules have the CX/13CX ratios smaller than the [12C/13C] ratio. We reproduce the observed C13CH/13CCH ratio in TMC-1, if the isotopomer exchange reaction, 13CCH + H <-> C13CH + H + 8.1 K, proceeds with the forward rate coefficient kf > 10^-11 cm3 s-1. However, the C13CS/13CCS ratio is lower than that observed in TMC-1. We then assume the isotopomer exchange reaction catalyzed by the H atom, 13CCS + H <-> C13CS + H + 17.4 K. In the model with this reaction, we reproduce the observed C13CS/13CCS, CCS/C13CS and CCS/13CCS ratio simultaneously.