Interior dynamics of envelopes around disk-embedded planets

Center for Star and Planet Formation, GLOBE Institute, University of Copenhagen, Øster Voldgade 5-7, 1350 Copenhagen, Denmark

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Received: 7 October 2025
Accepted: 16 January 2026

Abstract

In the core accretion scenario, forming planets start to acquire gaseous envelopes while accreting solids. Conventional 1D models assume envelopes to be static and isolated. However, recent 3D simulations demonstrate dynamic gas exchange from the envelope to the surrounding disk. This process is controlled by the balance between heating, through the accretion of solids, and cooling, which is regulated by poorly known opacities. In this work we systemically investigated a wide range of cooling and heating rates using 3D hydrodynamical simulations. We identify three distinct cooling regimes. Fast-cooling envelopes (β ≲ 1, with β the cooling time in units of orbital time) are nearly isothermal and have inner radiative layers that are shielded from recycling flows. In contrast, slow cooling envelopes (β ≳ 10³) become fully convective. In the intermediate regime (1 ≲ β ≲ 300), envelopes are characterized by a three-layer structure, comprising an inner convective, a middle radiative, and an outer recycling layer. The development of this radiative layer traps small dust and vapor released from sublimated species. In contrast, fully convective envelopes efficiently exchange material from the inner to the outer envelope. Such fully convective envelopes are likely to emerge in the inner parts of protoplanetary disks (≲ 1 au) where cooling times are long, implying that inner-disk super-Earths may see their growth stalled and be volatile-depleted.