Ondřej Chrenko

3D gas flow around cold and hot protoplanets

In Chrenko & Lambrechts (2019), we investigated migration of low-mass protoplanets in radiative disks. Our aim was to check how the heating torque (Benítez-Llambay et al. 2015) differs between disks with constant and non-uniform opacities. In the process, we realised that the 3D gas flow around accreting luminous ('hot') protoplanets is significantly different compared to non-luminous ('cold') protoplanets. As shown in the figure on the left, the topology of the horseshoe region profoundly changes and a vertical outflow is established when the protoplanet has a substantial luminosity. The depicted simulation was performed with a constant value of the disk opacity. The distortion of the flow arises because of baroclinic and convective perturbations.

Simulations in Chrenko & Lambrechts (2019) were conducted with Fargo3D (Benítez-Llambay & Masset 2016) into which we implemented the energy equations for gas and radiation.

Flow instability in disks with temperature-dependent opacities

In disks with temperature-dependent opacities, the gas flow around accreting protoplanets can develop an instability. It arises in disks where the vertical temperature gradient is close to a super-adiabatic stratification. In such a situation, the gas flow never reaches a steady state because of vigorous convective displacements. The figure on the left shows how the (perturbed) gas distribution evolves in the orbital plane of the protoplanet. The overplotted streamlines (shown in the corotating reference frame) are clearly connected to the gas redistribution. The instability has an important impact on the magnitude of the heating torque. The heating torque no longer boosts outward migration and moreover, migration of the protoplanet becomes oscillatory, consisting of alternating inward and outward excursions.

Evolution of protoplanets growing by pebble accretion

According to recent developments in the planet formation theory, protoplanets form by accretion of small solid particles, known as pebbles, which move through the gaseous media and are decelerated by the aerodynamic drag. Owing to the vigorous material deposition, protoplanets grow rapidly, they become heated and radiate the excessive energy into their surroundings. At the same time, protoplanets migrate due to gravitational interactions with the surrounding disk. I study the evolution of newborn planetary systems while taking into account all the aforementioned phenomena simultaneously, thus providing a realistic feedback between all the system components. Hydrodynamic global-scale simulations are necessary for this purpose.

Two-fluid hydrodynamic code with pebble accretion

I have developed an extension of the 2D FARGO hydrocode. The additional features:

• Non-isothermal gas disk with the internal energy equation accounting for compressional heating, viscous friction, in-plane radiative diffusion, vertical radiation escape, stellar irradiation and accretion heating.
• Pebble disk treated as an Eulerian pressureless and inviscid fluid, coupled with the gas disk through the Epstein drag term. Massive bodies accrete from the pebble component self-consistently.
• Rebound package interface allowing for e.g. 3D high-order orbital integration with adaptive time-stepping (IAS15 integrator), collision search, etc.
• Gravitational planet-disk interaction calculated by means of a vertically-averaged potential assuming a simple vertical distribution of gas (and pebbles) over the corresponding scale height.

For a detailed code description, see Chrenko et al. (2017).
You can get your own copy of the code on this website!