Modeling Studies III. Sub-millimeter H$$_{2}$$ $$^{16}$$O and H$$_{2}$$ $$^{18}$$O Lines

In this chapter, we extend the results presented in our former papers [41, 42] on using ortho-\(\mathrm {H_2}\) \(^{16}\mathrm {O}\) line profiles to constrain the location of the \(\mathrm {H_2O}\) snowline in T Tauri and Herbig Ae disks, to include sub-millimeter para-\(\mathrm {H_2}\) \(^{16}\mathrm {O}\) and ortho- and para-\(\mathrm {H_2}\) \(^{18}\mathrm {O}\) lines. Since the number densities of the ortho- and para-H\(_{2}\) \(^{18}\)O molecules are about 1/560 times smaller than their \(^{16}\)O analogues, they trace deeper into the disk than the ortho-H\(_{2}\) \(^{16}\)O lines (down to \(z=0\)), and lines with relatively smaller upper state energies (\(\sim \)a few 100 K) can also locate the \(\mathrm {H_2O}\) snowline positions. Thus these H\(_{2}\) \(^{18}\)O lines are potentially better probes of the H\(_{2}\)O snowline positions at the disk midplane, depending on the dust optical depth. The values of the Einstein A coefficients of sub-millimeter candidate water lines tend to be lower (typically \(10^{-4}\) s\(^{-1}\)) than infrared candidate water lines. Thus in the sub-millimeter candidate water line cases, the local intensity from the outer optically thin region in the disk is around \(10^{4}\) times smaller than that in the infrared candidate water line cases. Therefore, in the sub-millimeter lines, especially H\(_{2}\) \(^{18}\)O and para-H\(_{2}\) \(^{16}\)O lines with relatively lower upper state energies (\(\sim \)a few 100 K) can also locate the position of the \(\mathrm {H_2O}\) snowline. We also investigate the possibility of future observations with ALMA to identify the water snowline position. There are several candidate water lines that trace the hot water vapor inside the \(\mathrm {H_2O}\) snowline in ALMA Bands 5–10. Most contents of this chapter is based on our refereed paper that has been published (Notsu et al. 2018, ApJ, 855, 62).