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We analyze the line radiative transfer in protoplanetary disks using severalapproximate methods and a well-tested Accelerated Monte Carlo code. A low-massflaring disk model with uniform as well as stratified molecular abundances isadopted. Radiative transfer in low and high rotational lines of CO, C18O, HCO+,DCO+, HCN, CS, and H2CO is simulated. The corresponding excitationtemperatures, synthetic spectra, and channel maps are derived and compared tothe results of the Monte Carlo calculations. A simple scheme that describes theconditions of the line excitation for a chosen molecular transition iselaborated. We find that the simple LTE approach can safely be applied for thelow molecular transitions only, while it significantly overestimates theintensities 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 masereffect. In general, the molecular lines in protoplanetary disks are partlysubthermally excited and require more sophisticated approximate line radiativetransfer methods. We analyze a number of approximate methods, namely, LVG, VEP(Vertical Escape Probability) and VOR (Vertical One Ray) and discuss theiralgorithms in detail. In addition, two modifications to the canonical MonteCarlo algorithm that allow a significant speed up of the line radiativetransfer modeling in rotating configurations by a factor of 10--50 aredescribed.

Molecular line radiative transfer in protoplanetary disks: Monte Carlo simulations versus approximate methods