Measuring elemental abundance ratios in protoplanetary disks at millimeter wavelengths

During the million years of evolution, gas dust and ice in protoplanetary disks can be chemically reprocessed. There are evidences that the gas-phase carbon and oxygen abundances are sub-solar in disks belonging to nearby star forming regions. These findings have a major impact on the composition of the primary atmosphere of giant planets (but it may also be valid for super-Earths and sub-Neptunes) as they accrete their gaseous envelopes from the surrounding material in the disk. In this study, we performed a thermo-chemical modelling analysis with the aim at testing how reliable and robust are the estimates of elemental abundance ratios based on (sub-)millimeter observations of molecular lines. We created a grid of disk models for the following different elemental abundance ratios: C/O, N/O and S/O, and, we computed the line flux of a set of carbon-, nitrogen and sulphur-bearing species, namely CN, HCN, NO, C$_{2}$H, c--C$_{3}$H$_{2}$, H$_{2}$CO, HC$_{3}$N, CH$_{3}$CN, CS, SO, H$_{2}$S and H$_{2}$CS, that have been detected with present (sub-)millimeter facilities such as ALMA and NOEMA. We find that the line fluxes, once normalized to the flux of the $^{13}$CO $J=2-1$ line, are sensitive to the elemental abundance ratios. On the other hand, the stellar and disk physical parameters have only a minor effect of the line flux ratios. Our results demonstrate that a simultaneous analysis of multiple molecular transitions is a valid approach to constrain the elemental abundance ratio in protoplanetary disks.