Turbulence destroys thermal lobes around Mars-sized planetary embryos

¹ Charles University, Faculty of Mathematics and Physics, Astronomical Institute, V Holešovičkách 747/2, 180 00, Prague 8, Czech Republic
² Instituto de Astronomía, Universidad Nacional Autónoma de México, Apt. Postal 70-264, C.P. 04510, Mexico City, Mexico

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 1 January 2026
Accepted: 19 March 2026

Abstract

Context. The release of heat by a planetary embryo modifies the local density perturbations, forming thermal lobes in its vicinity, and thereby altering the torque exerted by the disk on the embryo. In laminar disks, these thermal torques can dominate the disk-embryo interaction, rendering the classical Lindblad and corotation torques largely subdominant.

Aims. The aim of this work is to investigate how turbulence driven by the magnetorotational instability affects the thermal lobes that formed around a planetary embryo, and to analyze the resulting torque acting on the embryo.

Methods. We evaluate the thermal torques exerted on a planetary embryo of mass M_p = 0.33 M_♂ (where is the mass of Mars) and on a planetary core with mass M_p = 1 M_⊕, with each embedded in a turbulent gaseous protoplanetary disk, by means of highresolution three-dimensional magnetohydrodynamics simulations that include thermal diffusion and an initially toroidal magnetic field. The magnetic field strength is characterized by the plasma ß plasma parameter with ß ∈ {50, 1000}. We consider two values for the luminosity of the planetary embryo: L = 0 (cold thermal lobes) and L = L_c (hot thermal lobes), where L_c represents the critical luminosity. For the 0.33 L_♂ embryo, L_c = 7.8 × 10²⁵ergs s⁻¹ when it orbits a Sun-like star at a distance r_p = 5.2 au.

Results. We find that, even in the presence of a weak magnetic field and irrespective of the luminosity, for both planetary masses, the development of turbulence in the disk (which takes between 1.5 to 3 orbital periods) completely disrupts the thermal lobes. As a result, the torque acting on both the planetary embryo and the Earth-mass core displays a strongly oscillatory behavior. This suggests that planets with masses in the range 0.03 M_⊕ ≲ M_p ≲ 1 M_⊕ experience stochastic migration, as expected in turbulent disks.

Conclusions. Thermal torques become inefficient in turbulent regions of protoplanetary disks, such as outside the dead zone, in both the inner and outer disk regions where the magnetorotational instability operates.