Turbulence destroys thermal lobes around Mars-sized planetary embryos

Technical Deep Dive: Turbulence destroys thermal lobes around Mars-sized planetary embryos

Problem & Context

• Thermal forces can drive the migration and growth of low-mass planets in protoplanetary disks. These include:
  • Heating torques: Caused by asymmetric hot gas lobes around a luminous planet
  • Cold thermal torques: Caused by asymmetric cold gas lobes around a non-luminous planet
• These thermal torques can dominate over the classical Lindblad and corotation torques, potentially slowing down or even reversing inward migration of growing planets.
• However, prior studies of thermal torques have assumed a laminar, unmagnetized disk. In reality, many regions of protoplanetary disks are expected to be turbulent, driven by the magnetorotational instability (MRI).

Methodology

• The authors conducted high-resolution 3D magnetohydrodynamic (MHD) simulations of a planetary embryo embedded in a stratified, thermally diffusive protoplanetary disk with a toroidal magnetic field.
• They simulated two cases: a cold embryo (L=0, cold thermal torque) and a hot, luminous embryo (L=Lc, heating torque).
• The strength of the magnetic field was parameterized by the plasma beta (β) parameter, with β=50 and β=1000 cases considered.
• They analyzed the development of turbulence, the disruption of thermal lobes, and the resulting torques on the planetary embryo.

Results

• Turbulence develops within 1.5-3 orbital periods, completely disrupting the thermal lobes around the planetary embryo.
• This is true regardless of the embryo's luminosity (L=0 or L=Lc) or the magnetic field strength (β=50 or β=1000).
• In the turbulent regime, the total torque on the planetary embryo displays a strongly oscillatory, stochastic behavior, rather than the coherent thermal torques seen in laminar disks.
• This stochastic torque regime applies to planetary masses in the range 0.03 M⊕ ≲ Mp ≲ 1 M⊕, as well as for Mp ≳ 3 M⊕.
• The authors found no evidence that magnetic resonances play a significant role in the turbulent disk.

Interpretation

• Thermal torques become inefficient in turbulent regions of protoplanetary disks, such as outside the dead zone where the MRI operates.
• Planets in the mass range 0.03 M⊕ ≲ Mp ≲ 1 M⊕ and Mp ≳ 3 M⊕ experience stochastic migration in these turbulent disk regions, rather than the coherent migration driven by thermal torques in laminar disks.

Limitations & Uncertainties

• The authors used a constant thermal diffusivity in their simulations, whereas in real disks it would vary with local conditions like density, temperature, and dust properties.
• They only simulated two specific planetary masses (0.33 M₃ and 1 M⊕). The behavior for other masses in the critical range is not directly addressed.

What Comes Next

• Future work should explore more realistic models with variable thermal diffusivity and an explicit treatment of dust, which can influence the local thermal properties.
• Simulations covering a broader range of planetary masses in the 0.03-1 M⊕ regime would help better characterize the transition to stochastic migration.

Sources:

• Turbulence destroys thermal lobes around Mars-sized planetary embryos