Radiative-transfer effects and the interpretation of interstellar molecular cloud observations. I. Basic physics of line formation

Various radiative-transfer effects which can be important in the interpretation of molecular cloud observations are examined. The concept of relaxation length (tau/sub r/) is introduced to describe the physics of line formation. The relaxation length is determined by photon loss mechanisms such as thermalization, line interlocking, absorption by continuous opacity, and escape due to velocity gradients. The effects of different nonthermal velocity fields on the emergent line profiles are also studied. In the presence of both turbulence and systematic velocity gradients, the crucial parameter defining the emergent profile is the ratio (α) of systematic to turbulent velocities in the region of line formation. For α>3, the emergent profiles, which are asymmetric, are dominated by optical depth effects. The precise form of the systematic velocity law plays only a minor role in defining the line shapes, although the asymmetries in the profile and surface brightness can be used to determine the direction of gas motions. For α>10, the profiles are dominated by geometrical effects determined by the form of the velocity law, although portions of the profile formed in regions of small α are still affected by optical depth effects. Besides cloud geometry, fluctuations in density and temperature can alter the line width and peak intensity substantially (even for similar optical depths) and prevent self-absorption in optically thick lines in turbulent models, while surface heating does not always prevent self-absorption in optically thick lines in turbulent models, while surface heating does not always prevent self-absorption. The gas temperature distribution depends sensitively on the density distribution and the form of the heating mechanism. Finally, the nature and effects of radiation field anisotropy are briefly examined