THE SOBOLEV APPROXIMATION IN MOLECULAR CLOUDS

To derive the physical properties of a molecular cloud from line obser vations, one has to know or assume the molecular excitation conditions . The Sobolev approximation neglecting nonlocal radiative interactions is often used for a simple estimate. It is based on the existence of large velocity gradients throughout the cloud. We have investigated th e justification of the Sobolev approximation in situations where this condition is not strictly fulfilled. A semi-analytical extension of th e Sobolev approximation for the line radiative transfer problem in mol ecular clouds and outflows is developed. It is applied to test the ran ge of the validity of the ordinary Sobolev approximation and to solve problems beyond its limits. This linear approximation is able to treat configurations with moderate velocity gradients where the basic assum ption of the Sobolev approximation, taking constant physical parameter s within the radiative interaction region, is no longer justified. It turns out that the Sobolev approximation is quite accurate even far be yond the limits of its strict applicability. The computed energy densi ties deviate by less than a factor 2.5 in systems with a smooth, monot onic density and velocity structure. This maximum error is further red uced in regions with constant density gradients falling down to 20% fo r spherical homogeneous flows. For situations requiring high accuracie s of the line intensity computations, a simple way for the improvement of results obtained by the ordinary Sobolev approximation is demonstr ated. (C) 1997 Elsevier Science B.V.