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Direct imaging of the water snow line at the time of planet formation using two ALMA continuum bands

Molecular snow lines in protoplanetary disks have been studied theoretically for decades because of their importance in shaping planetary architectures and compositions. The water snow line lies in the planet formation region at < 10 AU, and so far its location has been estimated only indirectly from spatially-unresolved spectroscopy. This work presents a proof-of-concept method to directly image the water snow line in protoplanetary disks through its physical and chemical imprint in the local dust properties. We adopt a physical disk model that includes dust coagulation, fragmentation, drift, and a change in fragmentation velocities of a factor 10 between dry silicates and icy grains as found by laboratory work. We find that the presence of a water snow line leads to a sharp discontinuity in the radial profile of the dust emission spectral index α_mm, due to replenishment of small grains through fragmentation. We use the ALMA simulator to demonstrate that this effect can be observed in protoplanetary disks using spatially-resolved ALMA images in two continuum bands. We explore the model dependence on the disk viscosity and find that the spectral index reveals the water snow line for a wide range of conditions, with opposite trends when the emission is optically thin rather than thick. If the disk viscosity is low (α_visc < 10^-3) the snow line produces a ring-like structure with a minimum at α_mm ~ 2 in the optically thick regime, possibly similar to what has been measured with ALMA in the innermost region of the HL Tau disk.