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

TL;DR

This paper derives analytical formulas for molecular ion abundances in protoplanetary disks and explains the formation of the N$_2$H$^+$ ring around TW Hya through chemical modeling, considering sink effects and desorption processes.

Contribution

It introduces analytical formulas for molecular ion abundances and demonstrates their application in modeling N$_2$H$^+$ rings, highlighting the impact of sink effects and desorption rates.

Findings

N$_2$H$^+$ ring can be reproduced without sink effects.

Abundance peaks near the CO sublimation temperature.

Column density sensitive to cosmic ray flux and desorption rates.

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.