Turbulence destroys thermal lobes around Mars-sized planetary embryos

Abstract

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. The aim of this work is to investigate how turbulence driven by the MRI instability affects the thermal lobes formed around a planetary embryo, and to analyze the resulting torque acting on the embryo. We evaluate the thermal torques exerted on a planetary embryo of mass $M_p=0.33M_{Mars}$ and on a planetary core with mass $M_{p}=1M_{\oplus}$, each embedded in a turbulent gaseous protoplanetary disk, by means of high-resolution 3D magnetohydrodynamics simulations that include thermal diffusion and an initially toroidal magnetic field. The magnetic field strength is characterized by the $β$-plasma parameter with $β\in\{50,1000\}$. 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. 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 $0.03M_{\oplus}\lesssim M_{p}\lesssim 1M_{\oplus}$ experience stochastic migration, as expected in turbulent disks. 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.

Figures (6)

• Figure 1: Perturbation of density arising from heat release obtained by subtracting a hot run ($L=L_c$) and a cold run ($L=0$) for the case $\beta=50$ at $t=1$ orbit. The perturbation is integrated over colatitude and normalized to $\gamma(\gamma-1)L/\chi c_s^2$. The purple solid line indicates the corotation radius.
• Figure 2: Temporal evolution of $\alpha$, defined by Eq. (\ref{['eq:alpha']}), for the runs with $L=L_c$ and $\beta=50$ (left panel) and $\beta=1000$ (right panel).
• Figure 3: Quality factor averaged over space and time. The orange dotted line shows the eight-cell limit. The vertical gray lines delineate the buffer zones.
• Figure 4: Gas density (logarithmic scale) at the midplane at $t=11$ orbits. The zoomed regions correspond to an area similar to that shown in Fig. \ref{['fig:lobes']} around the planetary embryo. In these regions, no low-density structures resembling hot lobes are observed. The purple solid lines indicate the corotation radii. The yellow dashed and green dotted lines mark the locations of the magnetic resonances for $\beta=50$ and $\beta=1000$, respectively. The white plus symbol denotes the position of the planetary embryo.
• Figure 5: Temporal evolution of the total torque $\Gamma$ (in units of $\Gamma_0/\gamma$) on the planetary embryo.