We have carried out radiative transfer calculations of infalling, dusty
envelopes surrounding embedded protostars to understand the observed properties
of the recently identified ``Class 0'' sources. To match the far-infrared peaks
in the spectral energy distributions of objects such as the prototype Class 0
source VLA 1623, pure collapse models require mass infall rates
\sim10^{-4}\msunyr−1. The radial intensity distributions predicted by
such infall models are inconsistent with observations of VLA 1623 at sub-mm
wavelengths, in agreement with the results of Andre et al. (1993) who found a
density profile of ρ∝r−1/2 rather than the expected ρ∝r−3/2 gradient. To resolve this conflict, while still invoking
infall to produce the outflow source at the center of VLA 1623, we suggest that
the observed sub-mm intensity distribution is the sum of two components: an
inner infall zone, plus an outer, more nearly constant-density region. This
explanation of the observations requires that roughly half the total mass
observed within 2000 AU radius of the source lies in a region external to the
infall zone. The column densities for this external region are comparable to
those found in the larger Oph A cloud within which VLA 1623 is embedded. The
extreme environments of Class 0 sources lead us to suggest an alternative or
additional interpretation of these objects: rather than simply concluding with
Andre et al. that Class 0 objects only represent the earliest phases of
protostellar collapse, and ultimately evolve into older ``Class I'' protostars,
we suggest that many Class 0 sources could be the protostars of very dense
regions. (Shortened)Comment: 22 pages, including 3 PostScript figures, accepted for publication in
The Astrophysical Journa