  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 one-sigma 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 (less than half a solar mass) 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.
