Constraining the physical structure of the inner few 100 AU scales of
  deeply embedded low-mass protostars
  (Abridged) The physical structure of deeply-embedded low-mass protostars
(Class 0) on scales of less than 300 AU is still poorly constrained.
Determining this is crucial for understanding the physical and chemical
evolution from cores to disks. In this study two models of the emission, a
Gaussian disk intensity distribution and a parametrized power-law disk model,
are fitted to sub-arcsecond resolution interferometric continuum observations
of five Class 0 sources, including one source with a confirmed Keplerian disk.
For reference, a spherically symmetric single power-law envelope is fitted to
the larger scale ($\sim$1000 AU) emission and investigated further for one of
the sources on smaller scales. A thin disk model can approximate the emission
and physical structure in the inner few 100 AU scales of the studied
deeply-embedded low-mass protostars and paves the way for analysis of a larger
sample with ALMA. While the disk radii agree with previous estimates the masses
are different for some of the sources studied. Assuming a typical temperature
distribution, the fractional amount of mass in the disk above 100 K varies in
between 7% to 30%. Kinematic data are needed to determine the presence of any
Keplerian disk. Using previous observations of p-H$_2^{18}$O, we estimate the
relative gas phase water abundances roughly an order of magnitude higher than
previously inferred when both warm and cold H$_2$ was used as reference. A
spherically symmetric single power-law envelope model fails to simultaneously
reproduce both the small and large scale emission.
