Molecular line radiative transfer in protoplanetary disks: Monte Carlo simulations versus approximate methods
We analyze the line radiative transfer in protoplanetary disks using several approximate methods and a well-tested Accelerated Monte Carlo code. A low-mass flaring disk model with uniform as well as stratified molecular abundances is adopted. Radiative transfer in low and high rotational lines of CO, C18O, HCO+, DCO+, HCN, CS, and H2CO is simulated. The corresponding excitation temperatures, synthetic spectra, and channel maps are derived and compared to the results of the Monte Carlo calculations. A simple scheme that describes the conditions of the line excitation for a chosen molecular transition is elaborated. We find that the simple LTE approach can safely be applied for the low molecular transitions only, while it significantly overestimates the intensities of the upper lines. In contrast, the Full Escape Probability (FEP) approximation can safely be used for the upper transitions ($J_{\rm up} \ga 3$) but it is not appropriate for the lowest transitions because of the maser effect. In general, the molecular lines in protoplanetary disks are partly subthermally excited and require more sophisticated approximate line radiative transfer methods. We analyze a number of approximate methods, namely, LVG, VEP (Vertical Escape Probability) and VOR (Vertical One Ray) and discuss their algorithms in detail. In addition, two modifications to the canonical Monte Carlo algorithm that allow a significant speed up of the line radiative transfer modeling in rotating configurations by a factor of 10--50 are described.