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Super-Earths are by far the most dominant type of exoplanet, yet theirformation is still not well understood. In particular, planet formation modelspredict that many of them should have accreted enough gas to become gas giants.Here we examine the role of the protoplanetary disk in the cooling andcontraction of the protoplanetary envelope. In particular, we investigate theeffects of 1) the thermal state of the disk as set by the relative size ofheating by accretion or irradiation, and whether its energy is transported byradiation or convection, and 2) advection of entropy into the outer envelope bydisk flows that penetrate the Hill sphere, as found in 3D global simulations.We find that, at 5 and 1 AU, this flow at the level reported in thenon-isothermal simulations where it penetrates only to ~ 0.3 times the Hillradius has little effect on the cooling rate since most of the envelope mass isconcentrated close to the core, and far from the flow. On the other hand, at0.1 AU, the envelope quickly becomes fully-radiative, nearly isothermal, andthus cannot cool down, stalling gas accretion. This effect is significantlymore pronounced in convective disks, leading to envelope mass orders ofmagnitude lower. Entropy advection at 0.1 AU in either radiative or convectivedisks could therefore explain why super-Earths failed to undergo runawayaccretion. These results highlight the importance of the conditions and energytransport in the protoplanetary disk for the accretion of planetary envelopes.

The Imprint of the Protoplanetary Disk in the Accretion of Super-Earth Envelopes