Effect of Different Angular Momentum Transport mechanisms on the Distribution of Water in Protoplanetary Disks

The snow line in a protoplanetary disk demarcates regions with H$_2$O ice from regions with H$_2$O vapor. Where a planet forms relative to this location determines how much water and other volatiles it forms with. Giant planet formation may be triggered at the water snow line if vapor diffuses outward and is cold-trapped beyond the snow line faster than icy particles can drift inward. In this study we investigate the distribution of water across the snow line, considering three different radial profiles of the turbulence parameter $\alpha(r)$, corresponding to three different angular momentum transport mechanisms. We consider the radial transport of water vapor and icy particles by diffusion, advection, and drift. We show that even for similar values of $\alpha$, the gradient of $\alpha$(r) across the snow line significantly changes the snow line location, the sharpness of the volatile gradient across the snow line, and the final water/rock ratio in planetary bodies. A profile of radially decreasing $\alpha$, consistent with transport by hydrodynamic instabilities plus magnetic disk winds, appears consistent with the distribution of water in the solar nebula, with monotonically-increasing radial water content and a diverse population of asteroids with different water content. We argue that $\Sigma(r)$ and water abundance $N_{\rm H_2O}(r)/N_{\rm H_2}(r)$ are likely diagnostic of $\alpha(r)$ and thus the mechanism for angular momentum transport in inner disks.