Effects of clumping on temperature I: externally heated clouds

We present a study of radiative transfer in dusty, clumpy star-forming regions. A series of self-consistent, three-dimensional, continuum radiative transfer models are constructed for a grid of models parameterized by central luminosity, filling factor, clump radius, and face-averaged optical depth. The temperature distribution within the clouds is studied as a function of this parameterization. Among our results, we find that: (a) the effective optical depth in clumpy regions is less than in equivalent homogeneous regions of the same average optical depth, leading to a deeper penetration of heating radiation in clumpy clouds, and temperatures higher by over 60 per cent; (b)penetration of radiation is driven by the fraction of open sky (FOS) – which is a measure of the fraction of solid angle along which no clumps exist; (c) FOS increases as clump radius increases and as filling factor decreases; (d) for values of FOS > 0.6 − 0.8 the sky is sufficiently “open” that the temperature distribution is relatively insensitive to FOS; (e) the physical process by which radiation penetrates is preferentially through streaming of radiation between clumps as opposed to diffusion through clumps; (f) filling factor always dominates the determination of the temperature distribution for large optical depths, and for small clump radii at smaller optical depths; (g) at lower face-averaged optical depths, the temperature distribution is most sensitive to filling factors of 1 10 per cent, in accordance with many observations; (h) direct shadowing by clumps can be important for distances approximately one clump radius behind a clump.