CO mass upper limits in the Fomalhaut ring - The importance of NLTE excitation in debris discs and future prospects with ALMA

In recent years, gas has been observed in an increasing number of debris discs, though its nature remains to be determined. Here, we analyse CO molecular excitation in optically thin debris discs, and search Atacama Large Millimeter/submillimeter Array (ALMA) Cycle-0 data for CO J = 3-2 emission in the Fomalhaut ring. No significant line emission is observed; we set a 3σ upper limit on the integrated line flux of 0.16 Jy km s^-1. We show a significant dependence of the CO excitation on the density of collisional partners n, on the gas kinetic temperature T_k and on the ambient radiation field J, suggesting that assumptions widely used for protoplanetary discs (e.g. local thermodynamic equilibrium, LTE) do not necessarily apply to their lowdensity debris counterparts. When applied to the Fomalhaut ring, we consider a primordial origin scenario where H₂ dominates collisional excitation of CO, and a secondary origin scenario dominated by e^- and H₂O. In either scenario, we obtain a strict upper limit on the CO mass of 4.9 × 10^-4 M_⊕. This arises in the non-LTE regime, where the excitation of the molecule is determined solely by the well-known radiation field. In the secondary scenario, assuming any CO present to be in steady state allows us to set an upper limit of ~55 per cent on the CO/H₂O ice ratio in the parent planetesimals. This could drop to ~3 per cent if LTE applies, covering the range observed in Solar system comets (0.4-30 per cent). Finally, in light of our analysis, we present prospects for CO detection and characterization in debris discs with ALMA.