2003ApJ...592..255L

We present modeling results for 6 of the 11 deeply embedded systems from our subarcsecond λ=2.7 mm continuum interferometric survey. The modeling, performed in the u-v plane, assumes dust properties, allows for a power-law density profile, uses a self-consistent, luminosity-conserving temperature profile, and has an embedded point source to represent a circumstellar disk. Even though we have the highest spatial resolution to date at these wavelengths, only the highest signal-to-noise ratio systems can adequately constrain the simple self-similar collapse models. Of the six sources modeled, all were fitted with a density power-law index of 2.0; however, in half of the systems, those with the highest signal-to-noise ratio, a density power-law index of 1.5 can be rejected at the 95% confidence level. Further, we modeled the systems using the pure Larson-Penston (LP) and Shu solutions, with only age and sound speed as parameters. Overall, the LP solution provides a better fit to the data, in both likelihood and providing the observed luminosity, but the ages of the systems required by the fits are surprisingly low (1000-2000 yr). We suggest that either there is some overall time scaling of the self-similar solutions that invalidates the age estimates or, more likely, we are at the limit of the usefulness of these models. With our observations we have begun to reach the stage at which models need to incorporate more of the fundamental physics of the collapse process, probably including magnetic fields and/or turbulence. In addition to constraining collapse solutions, our modeling allows the separation of large-scale emission from compact emission, enabling the probing of the circumstellar disk component embedded within the protostellar envelope. Typically, 85% or more of the total emission is from the extended circumstellar envelope component. Using HL Tauri as a standard candle, the range of circumstellar disk masses allowed in our models is 0.0-0.12 M_☉; our Class 0 systems do not have disks that are significantly more massive than those in Class I/II systems. This implies that the disk in Class 0 systems must quickly and efficiently process ∼1 M_☉of material from the envelope onto the protostar.