Hydrodynamical Simulations of Planet Rebound Migration in Photo-evaporating Disks

TL;DR

The paper addresses how photoevaporation-induced inner cavities in protoplanetary disks affect planetary migration, introducing rebound outward migration as a viable mechanism near the expanding cavity edge. It employs 2D hydrodynamical simulations with a stellar X-ray photoevaporation profile (normalized to $\dot M_{PE}\approx1.6\times10^{-8}\,M_\odot\,\rm yr^{-1}$) and a viscous $\ u=\alpha c_s H$ disk to follow planets from Neptune- to Jupiter-mass placed at $r_0=10$ au. The key finding is that Neptune- and super-Earth-mass planets can experience sustained outward rebound driven by a strong positive corotation torque arising from an asymmetric inverse vortensity distribution at the cavity edge, while Saturn-mass planets do not rebound and Jupiter-mass planets may migrate outward due to disk eccentricity; the efficiency of rebound depends on the disk density profile, PE rate, and aspect ratio. This work confirms rebound migration as a robust outcome of inside-out disk clearing and highlights its potential role in shaping the observed diversity of exoplanet architectures, including non-resonant configurations.

Abstract

This study investigates the orbital migration of a planet located near the truncated edge of protoplanetary disks, induced by X-ray photo-evaporation originating from the central star. The combined effects of turbulent viscous accretion and stellar X-ray photo-evaporation give rise to the formation of a cavity in the central few astronomical units in disks. Once the cavity is formed, the outer disk experiences rapid mass loss and the cavity expands inside out. We have conducted 2D hydrodynamical simulations of planet-disk interaction for various planet masses and disk properties. Our simulations demonstrate that planets up to about Neptune masses experience a strong positive corotation torque along the cavity edge that leads to sustained outward migration -- a phenomenon previously termed {\it rebound} migration. Rebound migration is more favorable in disks with moderate stellar photo-evaporation rates of ${\sim}10^{-8} ~ \rm M_{\odot}\,yr^{-1}$. Saturn-mass planets only experience inward migration due to significant gas depletion in their co-orbital regions. In contrast, Jupiter-mass planets are found to undergo modest outward migration as they cause the residual disk to become eccentric. This work presents the first 2D hydrodynamical simulations that confirm the existence and viability of rebound outward migration during the inside-out clearing in protoplanetary disks.

Figures (8)

• Figure 1: Migration of a Neptune-mass planet (panel a) and disk surface density evolution (panel b) in simulation run-fid. In panel (a), the solid curve shows the time evolution of the planet's semi-major axis. The grey circle marks the planet position at the time shown in Figures \ref{['fig:sigN']} and \ref{['fig:vertN']}. The planet undergoes a reversal in migration direction (termed "rebound migration") as the inner photo-evaporative cavity expands inside-out. The video can be downloaded from: https://github.com/bbliu-astro/movies/blob/main/hydrodynamic_rebound/Neptune.gif.
• Figure 2: Surface density perturbation of $\Sigma/\overline{\Sigma}$ (panel a) and $\rm \log(\Sigma)$ (panel b), and specific torque density as a function of orbital distance (panel c) in run-fid for a Neptune-mass planet at $t{=}3.5 \times 10^4~P_0$. The location of the planet is marked by a grey circle. In panel (b) data is averaged over $20$ snapshots in $1~P_0$, the purple crosses indicate the wiggle torque positions, and the width between the vertical dashed lines is $\Delta r_{\rm with} {=} 2 \max(r_{\rm H}, r_{\rm hs})$. For visibility, the x-axis in panel c uses a linear scale up to 12 au and a logarithmic scale beyond that.
• Figure 3: Inverse vortensity ($\zeta$) close to the planet in the $r{-}\phi$ frame (panel a), surface density profile and corotation torque components (panel b) in run-fid for a Neptune-mass planet at $t{=}3.5\times 10^{4} ~P_0$. In both panels, the width between the vertical dashed lines is $2 \max(r_{\rm H}, r_{\rm hs})$. The asymmetric $\zeta$ distribution between the upper and lower parts of the horseshoe region results in a strong, positive corotation torque.
• Figure 4: Evolution of semi-major axis (top) and disk surface density (bottom) in simulations run-fid for a super-Earth planet of $3 ~M_{\oplus}$ (left), a Saturn-mass planet (middle) and a Jupiter-mass planet (right). In the upper panels the grey circles mark the planet's position used in Figure \ref{['fig:snapshot']}, and the cyan area in the top-right panel shows the radial extent between the planet's pericentre and apocentre. The video can be downloaded from: https://github.com/bbliu-astro/movies/blob/main/hydrodynamic_rebound/superEarth.gif.
• Figure 5: Surface density perturbation of $\Sigma/{\overline{\Sigma}}$ (left) and $\rm \log(\Sigma)$ (middle), and specific torque density as a function of orbital distance (right) in run-fid for a super-Earth planet of $3 \ M_{\oplus}$ (upper panels, $t{=}4 \times 10^{4}~P_0$), a Saturn-mass planet (middle panels, $t{=}1.4 \times 10^{4}~P_0$) and a Jupiter-mass planet (lower panels, $t{=}3.5 \times 10^{4}~P_0$). The location of the planet is marked by a grey circle. The data used to compute the torque density is averaged over $20$ snapshots in $1~P_0$, the purple crosses in the top and middle rows of panels indicate the wiggle torque positions, and the radial width between the vertical dashed lines is $\Delta r_{\rm with} {=} 2 \max(r_{\rm H}, r_{\rm hs})$. For visibility, the x-axes in the right panels use a linear scale up to 12 au and a in logarithmic scale beyond that.