2002ApJ...575..337S

Seven Class 0 sources mapped with SCUBA at 850 and 450 µm are modeled using a one-dimensional radiative transfer code. The modeling takes into account heating from an internal protostar, heating from the interstellar radiation field (ISRF), realistic beam effects, and chopping to model the normalized intensity profile and spectral energy distribution. Power-law density models, n(r)∝r^–p, fit all of the sources; best-fit values are mostly p=1.8±0.1, but two sources with aspherical emission contours have lower values (p∼1.1). Including all sources, <p≥1.63±0.33. Based on studies of the sensitivity of the best-fit p to variations in other input parameters, uncertainties in p for an envelope model are Δp=±0.2. If an unresolved source (e.g., a disk) contributes 70% of the flux at the peak, p is lowered in this extreme case and Δp=^+0.2_–0.6. The models allow a determination of the internal luminosity (<L_int≥4.0 L_☉) of the central protostar as well as a characteristic dust temperature for mass determination (<T_iso≥13.8±2.4 K). We find that heating from the ISRF strongly affects the shape of the dust temperature profile and the normalized intensity profile, but it does not contribute strongly to the overall bolometric luminosity of Class 0 sources. There is little evidence for variation in the dust opacity as a function of distance from the central source. The data are well fitted by dust opacities for coagulated dust grains with ice mantles (Ossenkopf & Henning). The density profile from an inside-out collapse model (Shu) does not fit the data well, unless the infall radius is set so small as to make the density nearly a power law.