Abstract

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 similar to 0.2 dex. For ISM-like dust sizes, the 1 sigma snow- line location among solar-mass stars of the same age ranges from similar to 2 to similar 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 ( 0.5 M circle dot) as in previous works. The closer-in snow line in disks with larger grains enables water delivery to the habitable zone for a significant fraction of M stars and all FGK stars. Considering their larger numbers and higher planet occurrence, M stars may host most of the water-rich terrestrial planets in the galaxy if these planets are able to hold on to their water in their subsequent evolution.