We present a radiative transfer model, which is applicable to the study of submillimetre spectral line observations of protostellar envelopes. The model uses an exact, non-LTE, spherically symmetric radiative transfer `Stenholm method, which numerically solves the radiative transfer problem by the process of `Lambda-iteration. We also present submillimetre spectral line data of the Class 0 protostars NGC1333-IRAS2 and Serpens SMM4. We examine the physical constraints which can be used to limit the number and range of parameters used in protostellar envelope models, and identify the turbulent velocity and tracer molecule abundance as the principle sources of uncertainty in the radiative transfer modelling. We explore the trends in the appearance of the predicted line profiles as key parameters in the models are varied. We find that the separation of the two peaks of a typical infall profile is dependent not on the evolutionary status of the collapsing protostar, but on the turbulent velocity dispersion in the envelope. We also find that the line shapes can be significantly altered by rotation. Fits are found for the observed line profiles of IRAS2 and SMM4 using plausible infall model parameters. The density and velocity profiles in our best fit models are inconsistent with a singular isothermal sphere model. We find better agreement with a form of collapse which assumes non-static initial conditions. We also find some evidence that the infall velocities are retarded from free-fall towards the centre of the cloud, probably by rotation, and that the envelope of SMM4 is rotationally flattened.
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