Planet Migration in Protoplanetary Disks with Rims

TL;DR

The paper examines how intrinsic ring-gap structures in protoplanetary disks, produced by viscosity transitions (dead zones), influence the migration of embedded planets. Using 2D hydrodynamic simulations with an α-disk rim, it finds that Jupiter-mass planets tend to migrate away from density bumps and deeper gaps, while super-Earths tend to be trapped near density bumps due to predominantly corotation torques; in disks with gaps, Jupiter can be trapped at the gap center and further modify the gap. The study connects observational ring features to planet demographics, predicting Jupiters are more likely in dark rings and super-Earths in bright rings, with migration timescales on the order of a few thousand years at 1 AU for MMSN-like disks. Its findings underscore the importance of disk structure in shaping planetary architectures and caution against inferring planet locations solely from gap morphology; the results are scale-free and can be applied to a range of disk models, though the work is limited by fixed orbits and single-planet setups.

Abstract

Complex structures, including sharp edges, rings and gaps, have been commonly observed in protoplanetary disks with or without planetary candidates. Here we consider the possibility that they are the intrinsic consequences of angular momentum transfer mechanisms, and investigate how they may influence the dynamical evolution of embedded planets. With the aid of numerical hydrodynamic simulations, we show that gas giants have a tendency to migrate away from sharp edges, whereas super-Earths embedded in the annuli tend to be retained. This implies that, observationally, Jupiters are preferentially detected in dark rings (gaps), whereas super-Earths tend to be found in bright rings (density bumps). Moreover, planets' tidal torque provide, not necessarily predominant, feedback on the surface density profile. This tendency implies that Jupiter's gap-opening process deepens and widens the density gap associated with the dark ring, while super-Earths can be halted by steep surface density gradient near the disk or ring boundaries. 13Hence, we expect there would be a desert for super-Earths in the surface density gap.

Figures (7)

• Figure 1: Schematic of dead zone structure (panel a), planetary migration directions (panel b), and torque distribution relative to dead zone boundaries (panels c and d). In panel (a) is a conceptual graph of the disk and dead zone. The gray region in the figure denotes the dead zone (with initial $\alpha_{\rm dead} = 10^{-4}$ for Jupiter and $\alpha_{\rm dead} = 10^{-3}$ for super-Earth) , while the remaining disk regions have initial $\alpha_{\rm active} = 10^{-2}$.
• Figure 2: The azimuthally averaged surface density profiles and $\alpha^{-1}$ profile of the dead zone ($\alpha_{\rm dead}=10^{-4}$) in the absence of planets. The red dashed curve represents the gas surface density profile after 1000 orbits while the blue solid line corresponds to $1/\alpha$. By applying a dead zone in the $\alpha$ profile, we obtain an annular surface density bump in the resulting gas surface density. The surface density peak aligns with the region of reduced $\alpha$ in the dead zone.
• Figure 3: Radial surface density (averaged) profiles and radial torque (sum) profiles for the models with a Jupiter mass planet. Different panels correspond to different runs (enclosed by the purple 'L' shaped structures) as shown in the panel(c) of Fig. \ref{['fig:torque_scatter']}. The simulation parameters are set with $M_{\mathrm{p}} = M_{\mathrm{J}}$. The inner and outer dead-zone boundaries $r_{\mathrm{dz\_in}}$ and $r_{\mathrm{dz\_out}}$ are indicated in each panel. For the left column (top to bottom): the top panel employs $r_{\mathrm{dz\_in}} = 0.8\,r_0$, $r_{\mathrm{dz\_out}} = 1.3\,r_0$; the middle panel uses $r_{\mathrm{dz\_in}} = 0.8\,r_0$, $r_{\mathrm{dz\_out}} = 1.4\,r_0$; and the bottom panel is specified as $r_{\mathrm{dz\_in}} = 0.7\,r_0$, $r_{\mathrm{dz\_out}} = 1.4\,r_0$. For the right column (top to bottom): the top panel adopts $r_{\mathrm{dz\_in}} = 0.7\,r_0$, $r_{\mathrm{dz\_out}} = 1.2\,r_0$; the middle panel has $r_{\mathrm{dz\_in}} = 0.6\,r_0$, $r_{\mathrm{dz\_out}} = 1.2\,r_0$; and the bottom panel corresponds to $r_{\mathrm{dz\_in}} = 0.6\,r_0$, $r_{\mathrm{dz\_out}} = 1.3\,r_0$. The red solid curves trace the simulated surface density distribution $\Sigma(r)$, while orange solid lines indicate the initial surface density slope $\Sigma_0(r)$ for reference. The dead zone is marked by gray dotted lines. The blue solid curve represents the radial cumulative torque, which is azimuthally integrated.
• Figure 4: Theoretical calculation of the torque for super-Earth. Here, we set $M_{\rm p} = 10M_{\oplus}$. We compute the theoretical torque values for the models enclosed by the green rectangle in Fig. \ref{['fig:torque_scatter']}(d). All these models have a dead zone width of $0.7r_0$, and the inner boundary of the dead zone $r_{\rm dz\_in}$ is shown on the horizontal axis of the figure. The blue diamond-dashed line represents the Lindblad torque, and the red square-dashed line denotes the corotation torque. The black dot-solid line shows the sum of the two obtained from analytical calculation, representing the total torque. The purple x-solid line corresponds to the total torque directly computed from Eq. \ref{['eq:Ttot_sim']}.
• Figure 5: Pseudocolor maps of surface density and vortensity distribution. The left panels corresponds to the case with a vortex, while the right panels shows the case without a vortex. The inset in the middle shows a magnified view around the planet, with white streamlines depicting the velocity field. These correspond to the two locations marked by pentagram symbols in the lower-left and upper-right corners of Fig.\ref{['fig:torque_scatter']}(c), respectively. In the left panel, an asymmetric ring structure is visible outside the annular surface density bump, highlighting the presence of a vortex.