Radiation thermo-chemical models of protoplanetary discs IV. Modelling CO ro-vibrational emission from Herbig Ae discs

Context. The carbon monoxide (CO) ro-vibrational emission from discs around Herbig Ae stars and T Tauri stars with strong ultraviolet emissions suggests that fluorescence pumping from the ground X¹Σ⁺ to the electronic A¹Π state of CO should be taken into account in disc models.
Aims. We wish to understand the excitation mechanism of CO ro-vibrational emission seen in Herbig Ae discs, in particular in transitions involving highly excited rotational and vibrational levels.
Methods. We implemented a CO model molecule that includes up to 50 rotational levels within nine vibrational levels for the ground and A-excited states in the radiative-photochemical code ProDiMo. We took CO collisions with hydrogen molecules (H₂), hydrogen atoms (H), helium (He), and electrons into account. We estimated the missing collision rates using standard scaling laws and discussed their limitations. We tested the effectiveness of ultraviolet (UV) fluorescence pumping for the population of high-vibrational levels (v = 1-9, J = 1-50) for four Herbig Ae disc models (disc mass M_disc = 10^-2 , 10^-4 and inner radius R_disc = 1, 20 AU). We tested the effect of infrared (IR) pumping on the CO vibrational temperature and the rotational population in the ground vibrational level.
Results. UV fluorescence and IR pumping impact on the population of ro-vibrational v > 1 levels. The v = 1 rotational levels are populated at rotational temperatures between the radiation temperature around 4.6 μm and the gas kinetic temperature. The UV pumping efficiency increases with decreasing disc mass. The consequence is that the vibrational temperatures T_vib, which measure the relative populations between the vibrational levels, are higher than the disc gas kinetic temperatures (suprathermal population of the vibrational levels). The effect is more important for low-density gases because of lower collisional de-excitations.The UV pumping is more efficient for low-mass (M_disc <10^-3 M_⊙) than high-mass (M_disc <10^-3 M_⊙) discs. Rotational temperatures from fundamental transitions derived using optically thick ¹²CO v = 1-0 lines do not reflect the gas kinetic temperature. Uncertainties in the rate coefficients within an order of magnitude result in variations in the CO line fluxes up to 20%. CO pure rotational levels with energies lower than 1000 K are populated in local thermodynamic equilibrium but are sensitive to a number of vibrational levels included in the model. The ¹²CO pure rotational lines are highly optically thick for transition from levels up to E_upper = 2000 K. The model line fluxes are comparable with the observed line fluxes from typical Herbig Ae low-and high-mass discs.