Clumpy cloud models for CS and C$^{34

In this article we present an analysis of CS and C(34) S spectra observed in southern massive star forming cores. The results are based on radiative transfer calculations performed with the Monte Carlo method using three dimensional clumpy cloud models. The density distributions of the model clouds are either fractal or consist of a hierarchy of spherical clumps. We have searched for models that would simultaneously reproduce all the observed CS and C(34) S spectra. In most cases satisfactory fits could be found with models having constant kinetic temperatures. The models tend to have very low volume filling factors, typically fla 0.2. The radial density dependences of the original models were n ~ r(-beta ) with beta la 1.0. Although this provided in general a good correspondence with the observations the CS(7--6) emission was underestimated. Better fits were obtained with models having steeper radial density distributions and with models with kinetic temperature increasing inwards. The abundance ratio between the two isotopes was not treated as a free variable, but the results are consistent with an average ratio of ~ 10. The results from the Monte Carlo modelling were compared with LTE analysis and with LVG models. The LTE mass estimates are clearly lower than the values from the clumpy cloud models. However, even the mass estimates from different clumpy models can be different by a factor of two. Assuming an abundance ratio R=10 for the two CS isotopes the column densities calculated with LVG models are in good agreement with the Monte Carlo results. The LVG models could not, however, reproduce the observed CS line ratios as well as the clumpy cloud models.