# Oscillatory migration of accreting protoplanets driven by a 3D distortion of the gas flow

## TL;DR

This study uses 3D radiation hydrodynamic simulations to show that temperature-dependent opacities cause oscillatory migration of accreting protoplanets due to flow instabilities and asymmetries in the gas flow.

## Contribution

It reveals how non-uniform opacities induce flow instabilities that lead to oscillatory torques and migration patterns in protoplanets, extending previous steady-state models.

## Key findings

- Heating torque causes flow perturbations and asymmetries.
- Flow instabilities lead to oscillatory protoplanet migration.
- Oscillations result in alternating inward and outward movement.

## Abstract

Context. The dynamics of a low-mass protoplanet accreting solids is influenced by the heating torque, which was found to suppress inward migration in protoplanetary disks with constant opacities. Aims. We investigate the differences of the heating torque between disks with constant and temperature-dependent opacities. Methods. Interactions of a super-Earth-sized protoplanet with the gas disk are explored using 3D radiation hydrodynamic simulations. Results. Accretion heating of the protoplanet creates a hot underdense region in the surrounding gas, leading to misalignment of the local density and pressure gradients. As a result, the 3D gas flow is perturbed and some of the streamlines form a retrograde spiral rising above the protoplanet. In the constant-opacity disk, the perturbed flow reaches a steady state and the underdense gas responsible for the heating torque remains distributed in accordance with previous studies. If the opacity is non-uniform, however, the differences in the disk structure can lead to more vigorous streamline distortion and eventually to a flow instability. The underdense gas develops a one-sided asymmetry which circulates around the protoplanet in a retrograde fashion. The heating torque thus strongly oscillates in time and does not on average counteract inward migration. Conclusions. The torque variations make the radial drift of the protoplanet oscillatory, consisting of short intervals of alternating rapid inward and outward migration. We speculate that transitions between the positive and oscillatory heating torque may occur in specific disk regions susceptible to vertical convection, resulting in the convergent migration of multiple planetary embryos.