Title: The importance of thermal couples on the migration of growing planets by accretion of pebbles

Authors: OM Guilera, MM Miller Bertolami, F. Masset, J. Cuadra, J. Venturini, deputy Ronco

Institution of the first author: Instituto de Astrofísica de La Plata, CONICET-UNLP, La Plata, Argentina

Paper Status: Accepted at MNRAS [open access]

If you were the universe and you had to prepare a rock ball, what would you use? Usually when we try to make a popcorn ball, we stick sticky popcorn until the whole mass becomes sufficiently massive and spherical. But if you were the universe, you wouldn’t have things big enough to stick together, so you would need to use what you have: tiny particles and gas. This is how rock cores form from the accretion of small particles of negligible gravitational mass (we call them pebbles) on large gravitational bodies. Large gravitational bodies, also known as planetesimals, protoplanets, and planets, are all massive enough that their gravity attracts pebbles. Gas drag and gravity play an important role in the pebble accretion process.

However, during its formation, a planet also exchanges angular momentum and torque with a protoplanetary disk. This exchange moves the planet, or as we call it, emigrate from its initial position. In today’s article, the authors discuss the migration of planets that grow by accretion of pebbles.

When a planet and a disk interact, a certain total (net) torque causes a planet to migrate. This total couple consists of several couples, and the authors of today’s article focus on the thermal torque. It is the couple due to the fact that a planet is a luminous object, which releases heat in the surrounding disc. The authors of the article study the importance of this thermal couple in the planetary migration and show that the migration and the final masses of the planets can be different depending on whether the thermal couple is included or not.

Indoor or outdoor?

Figure 1 shows the evolution of the semi-major axis (horizontal) and the mass (vertical) of a planet. The semi-major axis shows how a planet migrates: if the line goes to the right, then the planet migrates outward (its semi-major axis lengthens), if the line goes to the left, then the planet migrates towards the interior (its semi-major axis – the major axis becomes shorter). Looking at the lines in Figure 1, you can also see how the planetary mass is increasing – well, the planet is forming!

One of the important results is that if the thermal torque is not included, the red lines show that for planets initially located beyond 2 AU (region of the ice line), the planets grow faster towards larger central masses and, when they reach the ice line, they “eat” the solids in the ice line and migrate inward. The concept of the ice line takes on all its importance here, as this is the region where the properties of the dust change. For models where the thermal torque is considered (the black lines), the planets that are located closer (the first two black lines on the left) first migrate inward but then quickly begin to migrate outward. due to thermal torque, then, after getting closer to the ice line, they migrate inward again! For the planets initially located beyond the ice line (with the exception of the two outermost), and the one located just inside, 2 AU, they migrate significantly outward due to the thermal couple. Then the outward migration is reversed and the planets migrate inward. However, although the migration of the planets is quite different, the final masses and the semi-major axes end up being similar, despite taking into account thermal torques.

What if we gave the planets more food?

Figure 2 shows the formation trajectory of a planet in a more massive disk. Looking at the black curves, they show the simulations which take thermal couples into account. Most of these black curves show inward migration until the planets reach the inner edge of the disk (

To study what happens not only if the disk is more massive but also has more solids, the authors run further simulations (see Figure 3). The authors performed a set of tests with a fixed initial metallicity of the disc – now the disc has three times the solids. For the case where the thermal couple is considered, the planets migrate efficiently outward up to about 20 AU, at which time their migration is reversed. For the case where the thermal couple is not taken into account, the migration is strictly towards the interior.

The thermal torque is an important contribution to the total torque on a migrating planet, especially if the planet is growing by accretion of pebbles. As this work has shown, it can change the mass, semi-major axis, and composition of a planet. The work also shows that the thermal torque is particularly important for solid and high metallicity discs, because it completely reverses the direction of migration. The study of the migration of the planets is important for the formation of the planets, because the planets do not stay too long in their position!

Astrobite edited by: Jason Hinkle

Featured Image Credit: Singing planets

About Sabina Sagynbayeva

I am a graduate student at Stony Brook University and my main area of ​​research is the formation of planets. I am currently working on planetary migration using hydrodynamic simulations. I am also interested in protoplanetary disks, but almost any subject related to planets fascinates me! In addition to doing research, I am also a singer-songwriter. I LOVE writing songs, and you can find them on any streaming platform.