Fast spectral line calculations with the escape probability method and tests using synthetic observations of interstellar clouds

Context. Radiative transfer (RT) effects need to be taken into account when analysing spectral line observations. When the data are not sufficient for detailed modelling, simpler methods are needed. The escape probability formalism (EPF) is one such tool. Aims. We wish to quantify the model errors in the EPF analysis of interstellar clouds and cores. Methods. We introduce PEP, a parallel programme for calculating fast EPF parameters quickly. We modelled a full RT to generate synthetic observations for various cloud models. We examined these with the PEP programme, comparing these results to the actual beam-averaged kinetic temperatures, column densities, and volume densities. Results. PEP enables the calculation of even millions of parameter combinations in a matter of seconds. However, the simple assumptions of EPF can lead to significant errors. In these tests, the errors were typically within a factor of 2, but could (in some cases) rise to one full order of magnitude. The model errors are thus similar or even larger than the statistical errors caused by the typical observational noise. Due to degeneracies, the parameter combinations were shown to be better constrained than the individual parameters. The model errors could be reduced by using full radiative transfer modelling. However, in the absence of full knowledge of the source structure, the errors are difficult to quantify. We also present a method for approximate handling of hyperfine structure lines in EPF calculations. Conclusions. Both the observational statistical errors and the model errors need to be considered when estimating the reliability of EPF results. Full RT modelling is needed to better understand the true uncertainties.