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

Abstract

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).