On the Snow Line in Dusty Protoplanetary Disks

C. Hayashi prescribed a "minimum-mass solar nebula," which contained just enough material to make the planets. This prescription, which has been widely used in constructing scenarios for planet formation, proposed that ice will condense when the temperature falls below 170 K (the "snow line"). In Hayashi's model, that occurred at 2.7 AU. It is usually assumed that the cores of the giant planets (e.g., Jupiter) form beyond the snow line. The snow line, in Hayashi's model, is where the temperature of a black body that absorbed direct sunlight and reradiated as much as it absorbed would be 170 K. Since Hayashi, there have been a series of more detailed models of the absorption by dust of the stellar radiation and of accretional heating, which alter the location of the snow line. We have attempted a "self-consistent" model of a T Tauri disk in the sense that we used dust properties and calculated surface temperatures that matched observed disks. We then calculated the midplane temperature for those disks, with no accretional heating or with small (≤10^-8 M_☉ yr^-1) accretion rates. (Larger accretion rates can push the snow line out to beyond 4 AU but do not match the observed disks.) Our models bring the snow line in to the neighborhood of 1 AU—not far enough to explain the close planetary companions to other stars, but much closer than in recent starting lines for orbit migration scenarios.