Concurrent Accretion and Migration of Giant Planets in their Natal Disks with Consistent Accretion Torque (II): Parameter Survey and Condition for Outward Migration

Abstract

Migration typically occurs during the formation of planets and is closely linked to the planetary formation process. In classical theories of non-accreting planetary migration, both type I and type II migration typically result in inward migration, which is hard to align with the architecture of the planetary systems.In this work, we conduct systematic, high-resolution 3D/2D numerical hydrodynamic simulations to investigate the migration of an accreting planet. Under different disk conditions, we compared the dynamical evolution of planets with different planet-to-star mass ratios. We find that accretion of planets can significantly diminish the inward migration tendency of planets, or even change the migration direction. The migration of low-/high-mass planets is classified as Type I/II inward migration, respectively, while intermediate-mass planets, which have the strongest accretion, show an outward migration trend. We confirm that the outward migration is mainly attributed to the positive torque from the azimuthal asymmetric structures around the accreting planet, similar to Li et al. (2024). The termination of planetary mass growth is thus synonymous with the transition from outward to inward migration. For the high viscosity $α=0.04$ and disk aspect ratio height $h_0=0.05$ cases, the mass ratio range for planetary outward migration is $1\times10^{-4}\lesssim q\lesssim4\times10^{-3}$. For the low viscosity case with $α=0.001$, and/or the low disk aspect ratio cases $h_0=0.03$, the mass ratio range for the outward migration will shift toward the lower end. Our parameter survey reveals that a simple gap opening parameter determines the outward migration condition; details of the analytical interpretation are presented in Ida et al. (2025).

Figures (7)

• Figure 1: The first row shows the evolution of planetary accretion rate $\dot{m}_{\rm p}$. The middle and third row show the semi-major axis evolution $\dot{a}_{\rm p}/a_{\rm p}$ due to the gravitational and accretion torque and their sum. Different columns correspond to models with different mass ratio $q$. The dashed line in first row shows the disk accretion rate $\dot{m}_{\rm d}$ from outer boundary. The blue and green line in middle row show the migration rate $\dot{a}_{\rm p}/a_{\rm p}$ contributed by gravitational and accretion torque, respectively. The orange dashed line represents the gravitational torque in which the sinkhole part $(\delta r<r_{\rm a})$ has been excluded.
• Figure 2: Spatial distribution of gravitational torque on planet for $q=2\times10^{-3}$(model mp2e3). The upper left panel shows the torque around the planet in Cartesian Coordinate. The red and blue part represent positive and negative torque, respectively. In order to unveil the asymmetry between the leading horseshoe (upper) and trailing horseshoe (lower) region, we "fold" and sum them in the upper right panel, i.e., $\Gamma(r,\phi)+\Gamma(r,-\phi)$. The lower left panel shows the azimuthally averaged torque distribution in the $r-z$ coordinate. The lower right panel shows the cumulative radial torque distribution integrated within three different height $z$. The total torque can be obtained from the value of $r=r_{\rm out}$. The vertical dashed line correspond to the region of Hill radius $R_{\rm H}$. The planet is located in $x=r_0, y=0, R=r_0, z=0$. It can be seen that the positive torque mostly comes from the co-orbital region, and the negative torque from the outer spiral arm.
• Figure 3: Same as Figure \ref{['fig:torque_mp2e3']}, but for the mass ratio $q=5\times10^{-5}$. We only shows the torque near the planet ($0.8<r<1.2$) in lower right panel since the torque contribution from the region far away from the planet location is negligible.
• Figure 4: Same as Figure \ref{['fig:torque_mp2e3']}, but for the mass ratio $q=8\times10^{-3}$. The asymmetry between the leading and trailing sides around planet is not so pronounced, and the upper right panel shows an alternating pattern of positive and negative values. The figure shows a larger space to highlight the Lindblad torque that become significant at this mass ratio.
• Figure 5: The distribution of normalized surface density for model mp2e3 (upper panel) and mp8e3 (lower panel), where we fold the distribution in the trailing side of planet to the leading side, i.e., $(\Sigma_{\rm lead}-\Sigma_{\rm trail})/\Sigma_0$. The contour lines mark the values of 0.05 and 0.2, with dashed lines for negative value and solid lines for positive value.