On the Location of the Snow Line in a Protoplanetary Disk

In a protoplanetary disk, the inner edge of the region where the temperature falls below the condensation temperature of water is referred to as the 'snow line'. Outside the snow line, water ice increases the surface density of solids by a factor of 4. The mass of the fastest growing planetesimal (the 'isolation mass') scales as the surface density to the 3/2 power. It is thought that ice-enhanced surface densities are required to make the cores of the gas giants (Jupiter and Saturn) before the disk gas dissipates. Observations of the Solar System's asteroid belt suggest that the snow line occurred near 2.7 AU. In this paper we revisit the theoretical determination of the snow line. In a minimum-mass disk characterized by conventional opacities and a mass accretion rate of 10^-8 solar masses per year, the snow line lies at 1.6-1.8 AU, just past the orbit of Mars. The minimum-mass disk, with a mass of 0.02 solar, has a life time of 2 million years with the assumed accretion rate. Moving the snow line past 2.7 AU requires that we increase the disk opacity, accretion rate, and/or disk mass by factors ranging up to an order of magnitude above our assumed baseline values.