A global two-layer radiative transfer model for axisymmetric, shadowed protoplanetary disks

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 below "shadowed" surfaces receiving no direct starlight. Thanks to the assumed axisymmetry, the reprocessed starlight flux is given in one-dimensional integral form that can be computed at a low cost. Furthermore, our model evolves the midplane temperature using a time-dependent energy equation and can therefore treat thermal instabilities. We apply our global two-layer model to disks with a planetary induced gap and confirm that the model reproduces the disks' temperature profiles obtained from more computationally expensive Monte Carlo radiative transfer calculations to an accuracy of less than 20%. We also apply the model to study the long-term behavior of the thermal wave instability in irradiated disks. Being simple and computationally efficient, the global two-layer model will be suitable for studying the interplay between disks' thermal evolution and dust evolution.