Migration of Earth-size planets in 3D radiative discs

In this paper, we address the migration of small mass planets in 3D radiative disks. Indeed, migration of small planets is known to be too fast inwards in locally isothermal conditions. However, thermal effects could reverse its direction, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. This effect has been seen for masses larger than 5 Earth masses, but the minimum mass for this to happen has never been probed numerically, although it is of crucial importance for planet formation scenarios. We have extended the hydro-dynamical code FARGO to 3D, with thermal diffusion. With this code, we perform simulations of embedded planets down to 2 Earth masses. For a set of discs parameters for which outward migration has been shown in the range of $[5, 35]$ Earth masses, we find that the transition to inward migration occurs for masses in the range $[3, 5]$ Earth masses. The transition appears to be due to an unexpected phenomenon: the formation of an asymmetric cold and dense finger of gas driven by circulation and libration streamlines. We recover this phenomenon in 2D simulations where we control the cooling effects of the gas through a simple modeling of the energy equation.