Peak flux density of the HO 3_1,3–2_2,0 (203 GHz) as function of the stellar accretion rate. These models are based on the embedded disk models of Harsono et al. (2015) with a central luminosity of 1 L_⊙. The blue squares indicate the predicted water emission by taking into account water vapor inside the disk and envelope. The green circles show the expected water flux densities emitted only by the embedded disk. These models adopt a water vapor abundance of 10⁻⁴ in the regions where T_dust > 100 K and visual extinction A_v > 3 to avoid regions whose emission can be affected by outflowing gas. The predicted line flux densities are calculated via thermalized molecular emission (Eqs. (9) and (10) of Harsono et al. 2015) considering the water column density inside of 25 au radius. From these embedded disk models, the water emitting mass fraction is shown as function of the accretion rate in orange. The upper limit (1σ) for our observations is indicated by the horizontal purple dashed line. The full radiative transfer of water from a generic disk model (see text in Sect. 5.4, Bosman et al., in prep.) is indicated by the purple line to indicate the integrated water flux density for a typical disk in the absence of and accretion heating.