Dust continuum emission and the upper limit fluxes of sub-millimeter water lines of the protoplanetary disk around HD 163296 observed by ALMA

In this paper, we analyse the upper limit fluxes of sub-millimeter ortho-H$_{2}$$^{16}$O 321 GHz, para-H$_{2}$$^{18}$O 322 GHz, and HDO 335 GHz lines from the protoplanetary disk around the Herbig Ae star HD 163296, using the Atacama Large Millimeter/Submillimeter Array (ALMA). These water lines are considered to be the best candidate sub-millimeter lines to locate the position of the H$_{2}$O snowline, on the basis of our previous model calculations. We compare the upper limit fluxes with the values calculated by our models with dust emission included, and we constrain the line emitting region and the dust opacity from the observations. We conclude that, if the outer edge of the region with high water vapor abundance and if the position of the water snowline are beyond 8 au also, the mm dust opacity will have a value larger than 2.0 cm$^{2}$ g$^{-1}$. In addition, the position of the water snowline will be inside 20 au, if the mm dust opacity is 2.0 cm$^{2}$ g$^{-1}$. Future observations of the dust continuum emission at higher angular resolution and sub-millimeter water lines with longer observation time are required to clarify the detailed structures and the position of the H$_{2}$O snowline in the disk midplane.