Numerical methods for non-LTE line radiative transfer:: Performance and convergence characteristics

Comparison is made between a number of independent computer programs for radiative transfer in molecular rotational lines. The test models are spherically symmetric circumstellar envelopes with a given density and temperature profile. The first two test models have a simple power law density distribution, constant temperature and a fictive 2-level molecule, while the other two test models consist of an inside-out collapsing envelope observed in rotational transitions of HCO+. For the 2-level molecule test problems all codes agree well to within 0.2%, comparable to the accuracy of the individual codes, for low optical depth and up to 2% for high optical depths (tau = 4800). The problem of the collapsing cloud in HCO+ has a larger spread in results, ranging up to 12% for the J = 4 population. The spread is largest at the radius where the transition from collisional to radiative excitation occurs. The resulting line profiles for the HCO+ J = 4-3 transition agree to within 10%, i.e., within the calibration accuracy of most current telescopes. The comparison project and the results described in this paper provide a benchmark for future code development, and give an indication of the typical accuracy of present day calculations of molecular line transfer.