# Envelopes of embedded super-Earths II. Three-dimensional isothermal simulations

## TL;DR

This study uses three-dimensional isothermal hydrodynamic simulations to explore how the properties of gaseous envelopes around super-Earth cores depend on core mass and disc interactions, revealing complex flow patterns and recycling processes.

## Contribution

It provides new insights into the flow dynamics and envelope properties of embedded super-Earths across different core masses using detailed 3D simulations.

## Key findings

- High-mass cores experience supersonic polar inflows and shock-driven turbulence.
- Envelope properties are sensitive to the ratio of Bondi radius to core size.
- Gas recycling influences runaway gas accretion and atmosphere retention.

## Abstract

Massive planetary cores embedded in protoplanetary discs are believed to accrete extended atmospheres, providing a pathway to forming gas giants and gas-rich super-Earths. The properties of these atmospheres strongly depend on the nature of the coupling between the atmosphere and the surrounding disc. We examine the formation of gaseous envelopes around massive planetary cores via three-dimensional inviscid and isothermal hydrodynamic simulations. We focus the changes in the envelope properties as the core mass varies from low (sub-thermal) to high (super-thermal) values, a regime relevant to close-in super-Earths. We show that global envelope properties such as the amount of rotational support or turbulent mixing are mostly sensitive to the ratio of the Bondi radius of the core to its physical size. High-mass cores are fed by supersonic inflows arriving along the polar axis and shocking on the densest parts of the envelope, driving turbulence and mass accretion. Gas flows out of the core's Hill sphere in the equatorial plane, describing a global mass circulation through the envelope. The shell of shocked gas atop the core surface delimits regions of slow (inside) and fast (outside) material recycling by gas from the surrounding disc. While recycling hinders the runaway growth towards gas giants, the inner regions of protoplanetary atmospheres, more immune to mixing, may remain bound to the planet.