We present modeling results for six of the eleven deeply embedded systems from our sub-arcsecond \lambda = 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 systems can adequately constrain the simple self-similar collapse models .
Of the six sources modeled , all six were fit with a density power-law index of 2.0 ; however , in half of the systems , those with the highest signal-to-noise , 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 , both in likelihood and providing the observed luminosity , but the age of the systems required by the fits are surprising low ( 1000-2000 yrs ) .
We suggest that either there is some overall time scaling of the self-similar solutions that invalidate 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 where 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 to 0.12 M _ { \sun } ; 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 \sim 1 M _ { \sun } of material from the envelope onto the protostar .