Understand
Using linear perturbation theory, we investigate the torque exerted on a low-mass planet embedded in a gaseous protoplanetary disc with finite thermal diffusivity.
- When the planet does not release energy into the ambient disc, the main effect of thermal diffusion is the softening of the enthalpy peak near the planet, which results in the appearance of two cold and dense lobes on either side of the orbit, of size smaller than the thickness of the disc.
- The lobes exert torques of opposite sign on the planet, each comparable in magnitude to the one-sided Lindblad torque.
- When the planet is offset from corotation, the lobes are asymmetric and the planet experiences a net torque, the `cold' thermal torque, which has a magnitude that depends on the relative value of the distance to corotation to the size of the lobes $\sim\sqrt{\chi/\Omega_p}$, $\chi$ being the thermal diffusivity and $\Omega_p$ the orbital frequency.