Tracing the Mass during Low-Mass Star Formation, IV: Observations and Modeling of the Submillimeter Continuum Emission from Class I Protostars

We present results from the observations and modeling of seventeen Class I cores with the Submillimetre Common Users Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope (JCMT). By modeling the transfer of radiation through the envelope for nine cores, we find, for a power law distribution n(r)=n_f(r/r_f)^-p, the average and standard deviation p=1.6 +/- 0.4 and a median of p=1.8. However, the inclusion of a disk or other point-like component can cause the derived p to be shallower by as much as 0.5. In addition, we test the Shu collapse model for our sources and discuss the application of simpler analyses that derive a density power law distribution directly from the slope of the intensity radial profile. The total mass of the envelope in our sample has a range from 0.04 to 5.0 M_sun, but these masses disagree with the virial masses derived from molecular line observations. Finally, we discuss the nature of these sources in light of various evolutionary indicators and find that T_bol and L_obs/L_smm are often inconsistent in distinguishing Class 0 from Class I cores.