The temperature structure determines the location of the snow line, where water ice sublimates. Recent studies have shown that the temperature structure of magnetically accreting disks varies with the size and spatial distribution of small dust grains controlling the disk's ionization fraction and opacity. However, the growth and motion of the grains depend on the background temperature, implying that the coevolution of the dust and temperature should determine how the snow line migrates.
In this study, we explore the coevolution of dust and temperature structure in magnetically accreting protoplanetary disks. The temperature is determined by the balance between Joule heating and radiative cooling, which depend on the disk's ionization fraction and opacity. We compute the evolution of the disk's ionization structure and opacity considering the grain’s growth, fragmentation, and radial drift. The stickiness of silicate and icy grains inside and outside the snow line are taken as free parameters.
We find that the migration timescale of the snow line is mainly controlled by the stickiness of icy grains. When icy grains can stick up to 1 and 10 m/s, the snow line moves inside 1 au within 2 and 1 Myr after star formation, respectively. As the stickiness of ice is increased, the grains in the outer disk region grow to larger sizes and drift inward more rapidly, leading to faster depletion of the solids in the disk. The faster depletion of solids causes a faster decrease in the disk opacity and results in faster inward migration of the snow line. However, the higher inward dust flux also causes an enhancement of solids interior to the snow line if silicates are less sticky than ice. In this case, rocky planetesimals may form at 1 au through the gravitational and/or streaming instabilities in the first 1 Myr of planet formation.