Understanding the thermal structure of protoplanetary disks is crucial for modeling planet formation and interpreting disk observations. We present a new two-layer radiative transfer model for computing the thermal structure of axisymmetric irradiated disks. Unlike the standard two-layer model, our model accounts for the radial as well as vertical transfer of the starlight reprocessed at the disk surface. The model thus allows us to compute the temperature of regions below "shadowed" surfaces receiving no direct starlight. Thanks to the assumed axisymmetry, the reprocessed starlight flux is given in a one- dimensional integral form that can be computed at a low cost. Our model evolves the midplane temperature using a time-dependent energy equation, allowing us to study thermal instabilities. The latest version of our numerical code also implements dust evolution (growth, fragmentation, radial drift, and radial diffusion) and takes into account its effect on the disk’s opacity and temperature evolution.
We apply our global two-layer model to study the couple evolution of the dust and thermal structure around the snow line. Previous studies predicted that when icy grains are stickier than silicates, a pileup of small silicate grains inside the snow line produces a cold shadowed region outside the snow line. Our coupled simulations show that this disk structure is stable and a wide shadowed region can be sustained for a wide range of parameter space. We also discuss planet formation and migration in the shadowed region.