The Snow Line in Viscous Disks around Low-mass Stars: Implications for Water Delivery to Terrestrial Planets in the Habitable Zone

The water-ice or snow line is one of the key properties of protoplanetary disks that determines the water content of terrestrial planets in the habitable zone. Its location is determined by the properties of the star, the mass accretion rate through the disk, and the size distribution of dust suspended in the disk. We calculate the snow-line location from recent observations of mass accretion rates and as a function of stellar mass. By taking the observed dispersion in mass accretion rates as a measure of the dispersion in initial disk mass, we find that stars of a given mass will exhibit a range of snow-line locations. At a given age and stellar mass, the observed dispersion in mass accretion rates of 0.4 dex naturally leads to a dispersion in snow-line locations of ~0.2 dex. For ISM-like dust sizes, the 1σ snow-line location among solar-mass stars of the same age ranges from ~2 to ~5 AU. For more realistic dust opacities that include larger grains, the snow line is located up to two times closer to the star. We use these locations and the outcome of N-body simulations to predict the amount of water delivered to terrestrial planets that formed in situ in the habitable zone. We find that the dispersion in snow-line locations leads to a large range in water content. For ISM-like dust sizes, a significant fraction of habitable-zone terrestrial planets around Sun-like stars remain dry, and no water is delivered to the habitable zones of low-mass M stars (