A Novel Way of Measuring the Gas Disk Mass of Protoplanetary Disks Using N₂H⁺and C¹⁸O

Measuring the gas mass of protoplanetary disks, the reservoir available for giant planet formation, has proven to be difficult. We currently lack a far-infrared observatory capable of observing HD, and the most common gas mass tracer, CO, suffers from a poorly constrained CO-to-H₂ ratio. Expanding on previous work, we investigate if N₂H⁺, a chemical tracer of CO-poor gas, can be used to observationally measure the CO-to-H₂ ratio and correct CO-based gas masses. Using disk structures obtained from the literature, we set up thermochemical models for three disks, TW Hya, DM Tau and GM Aur, to examine how well the CO-to-H₂ ratio and gas mass can be measured from N₂H+ and C¹⁸O line fluxes. Furthermore, we compare these gas masses to gas masses independently measured from archival HD observations. The N₂H⁺(3 − 2)/C¹⁸O(2 − 1) line ratio scales with the disk CO-to-H₂ ratio. Using these two lines, we measure 4.6 × 10⁻³ M_⊙ ≤ M_disk ≤ 1.1 × 10⁻¹ M_⊙ for TW Hya, 1.5 × 10⁻² M_⊙ ≤ M_disk ≤ 9.6 × 10⁻² M_⊙ for GM Aur and 3.1 × 10⁻² M_⊙ ≤ M_disk ≤ 9.6 × 10⁻²M_⊙ for DM Tau. These gas masses agree with values obtained from HD within their respective uncertainties. The uncertainty on the N₂H⁺ + C¹⁸O gas mass can be reduced by observationally constraining the cosmic-ray ionization rate in disks. These results demonstrate the potential of using the combination of N2H+ and C18O to measure gas masses of protoplanetary disks.