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.