Analytical Formulas of Molecular Ion Abundances and N2H+ Ring in Protoplanetary Disks

Abstract

We investigate the chemistry of ion molecules in protoplanetary disks, motivated by the detection of N${}_2$H${}^{+}$ ring around TW Hya. While the ring inner radius coincides with the CO snow line, it is not apparent why N${}_2$H${}^{+}$ 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 N${}_2$H${}^{+}$ 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 N${}_2$H${}^{+}$ 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 formulas, which are derived by analyzing the full-network model. The N${}_2$H${}^{+}$ ring is reproduced by the no-sink model, as well. The 2D (R-Z) distribution of N${}_2$H${}^{+}$, however, is different among the full-network model and no-sink model. The column density of N${}_2$H${}^{+}$ in the no-sink model depends sensitively on the desorption rate of CO and N${}_2$, and the flux of cosmic ray. We also found that N${}_2$H${}^{+}$ abundance can peak at the temperature slightly below the CO sublimation, even if the desorption energies of CO and N${}_2$ are the same.

arXiv commentaccepted to ApJ

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