Observational Signatures of Planets in Protoplanetary Disks: Temperature Structures in Spiral Arms
High-resolution imaging of protoplanetary disks has unveiled a rich diversity of spiral structure, some of which may arise from disk-planet interaction. Using 3D hydrodynamics with β cooling to a vertically stratified background, as well as radiative-transfer modeling, we investigate the temperature rise in planet-driven spirals. In rapidly cooling disks, the temperature rise is dominated by a contribution from stellar irradiation, 0.3%–3% inside the planet radius but always < 0.5% outside. When cooling time equals or exceeds dynamical time, however, this is overwhelmed by hydrodynamic PdV work, which introduces a ~10%–20% perturbation within a factor of ~2 from the planet’s orbital radius. We devise an empirical fit of the spiral amplitude Δ(T)=(M{sub p}/M{sub th}){sup c}(f{sub PdV}e{sup -t{sub a}{sub r}{sub m}/t{sub c}}+f{sub rad}) to take into account both effects. Where cooling is slow, we find also that temperature perturbations from buoyancy spirals—a strictly 3D, nonisothermal phenomenon—become nearly as strong as those from Lindblad spirals, which are amenable to 2D and isothermal studies. Our findings may help explain observed thermal features in disks like TW Hydrae and CQ Tauri, and underscore that 3D effects have a qualitatively important effect on disk structure.