Tracing the Mass during Low-Mass Star Formation. III. Models of the Submillimeter Dust Continuum Emission from Class 0 Protostars

Seven Class 0 sources mapped with SCUBA at 850 and 450 micron are modeled using a one dimensional radiative transfer code. The modeling takes into account heating from an internal protostar, heating from the 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 \Delta p = +/- 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 \Delta p = ^{+0.2}_{-0.6}. The models allow a determination of the internal luminosity (<L_{int}> = 4.0 \lsun) 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 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 1994). The density profile from an inside-out collapse model (Shu 1977) does not fit the data well, unless the infall radius is set so small as to make the density nearly a power-law.