Upper left: contours of χ² versus temperature and H₂ density for several different H₂O column densities (the different colors), with the minimum reduced χ² ~ 4. The contours show where (solid lines) and 1.5 (dashed lines), which roughly indicate the acceptable parameter space. The contours shown here are calculated to fits of lines with E′ > 400 K. The asterisks show the parameters of the sub-thermal model presented here (H12) and the high density envelope-disk accretion shock model (W07). Upper right and lower panels: contours of total number of H₂O molecules (upper right), radius (AU) of a circular emission area for H₂O emission (lower left), and length scale (log pc) of H₂O emission (lower right) compared with the best fit contours of n(H₂) and N(H₂O) for T = 1500 K. The asterisks indicate the parameters adopted for this paper. In the lower right panel, the solid line at 0.1 pc shows the conservative upper limit to the length scale of the emission. The parameters adopted for this paper are located in the lower right of the acceptable parameter space so that the length scale for the emission is small.