ANALYTICAL FORMULAE OF MOLECULAR ION ABUNDANCES AND THE N2H+ RING IN PROTOPLANETARY DISKS

We investigate the chemistry of ion molecules in protoplanetary disks, motivated by the detection of the N2H+ ring around TW Hya. While the ring inner radius coincides with the CO snow line, it is not apparent why N2H+ is abundant outside the CO snow line in spite of the similar sublimation temperatures of CO and N-2. Using the full gas-grain network model, we reproduced the N2H+ ring in a disk model with millimeter grains. The chemical conversion of CO and N-2 to less volatile species (sink effect hereinafter) is found to affect the N2H+ distribution. Since the efficiency of the sink depends on various parameters such as activation barriers of grain-surface reactions, which are not well constrained, we also constructed the no-sink model; the total (gas and ice) CO and N-2 abundances are set constant, and their gaseous abundances are given by the balance between adsorption and desorption. Abundances of molecular ions in the no-sink model are calculated by analytical formulae, which are derived by analyzing the full-network model. The N2H+ ring is reproduced by the no-sink model, as well. The 2D (R-Z) distribution of N2H+, however, is different among the full-network model and no-sink model. The column density of N2H+ in the no-sink model depends sensitively on the desorption rate of CO and N-2. and the cosmic-ray flux. We also found that N2H+ abundance can peak at the temperature slightly below the CO sublimation, even if the desorption energies of CO and N-2 are the same.