New migration patterns in high planet-star mass ratio systems in disks with low viscosity

TL;DR

This study addresses how high planet–star mass ratio planets migrate in low-viscosity disks (α=$10^{-4}$) and derives analytical prescriptions that apply across stellar masses from Sun-like to M dwarfs. Using 2D isothermal hydrodynamic simulations with FARGO3D across $q$ in [$10^{-3}$, $2\times10^{-2}$], it maps torques, migration directions, and eccentricity evolution, uncovering a robust migration reversal near $q\approx 0.002$ and outward migration for larger $q$ when $e<0.2$, with higher eccentricities capable of stalling migration. The authors present new torque fits and a density-dependent framework that links migration timescales to observed giant-planet demographics, showing faster inward migration in the inner disk and longer timescales farther out, with notable differences between FGK hosts and M dwarfs. The results imply outward migration is a viable pathway to form super-Jupiter planets around Sun-like stars and Neptune-mass planets around very low-mass stars, improving theoretical interpretations of exoplanet populations and guiding future observations.

Abstract

Migration of giant planets remains a complex topic. While significant progress has been made for high-viscosity disks, the migration of planets with large planet-star mass ratios in low-viscosity environments is still not fully understood. We study the migration of such planets in disks with $α= 10^{-4}$ and derive analytical prescriptions applicable across stellar masses, from Sun-like stars to M dwarfs. Using hydrodynamical simulations with FARGO3D, we explored planets with mass ratios $10^{-3} < q < 2 \times 10^{-2}$ under different disk conditions, varying gas surface density, scale height, and density slope. Our results show a migration reversal at $ q \approx 0.002$, with outward migration for $ q > 0.002$. For planets undergoing outward migration, the migration speed depends on the unperturbed local gas density. In most cases, outward migration is sustained by a positive torque related to planetary eccentricities below $ e < 0.2$. However, for certain disk parameters, planets with $ q > 0.01$ reach higher eccentricities ($0.2 < e < 0.45$), leading to stalled migration. Our findings suggest that outward migration is a viable mechanism for massive planets in low-viscosity disks, which has implications for the formation and distribution of super-Jupiter planets around Sun-like stars and planets more massive than Neptune around very low-mass stars. Given the challenges in detecting such planets, improving our theoretical understanding of their migration is essential for interpreting exoplanet demographics and guiding future observational efforts.

Figures (9)

• Figure 1: Top panels: Evolution of the normalized torque, along with the smoothing function, over the integration (left) for a planet with $q=0.003$ in a low-viscosity disk ($\alpha=10^{-4}$) with $\Sigma_0=10^{-4}$, and $h=0.05$. Distribution of the azimuthally averaged gas-disk density around the planet's initial location at three different integration times (right). Bottom panels: Evolution of the semi-major axis (left) and eccentricity (right) of the planet during the integration. The vertical lines mark the times when the torque changes sign, indicating a reversal in the direction of the planet's migration. Time is expressed in units of $t_0$, the orbital period of the planet at $r=r_0$.
• Figure 2: Left: Normalized positives (red dots), negatives (blue and pink for $q \leq 1 \times 10^{-3}$), and close to zero (black) torques as a function of a wide range of the $K$-parameter, including the previously studied domain by K18 (white background) and the new domain explored in this work (cream background), assuming $\alpha=10^{-4}$, $h_0=0.05$, $s=0.5$, and $\Sigma_0=10^{-4}$. The fitting proposed by K18 in the $K$-range of their study (solid blue line) together with the potential extension in the new regime (dotted blue line) is given in Eq. \ref{['eq:K2018-fit']}. Torques exerted onto planets in orbits with $e>0.2$ are highlighted (green circles). Four different migration regimes are marked indicating inward migration, a halt in migration, outward migration, and migration stalls (dotted gray lines). Right: Evolution of the semi-major axis (top) and the eccentricity of the six planets that experience either outward migration or a halt in migration: $q=1.5 \times 10^{-3}$ (dotted black line), $q=2 \times 10^{-3}$ (dashed-dotted red line), $q=3 \times 10^{-3}$ (dashed red line), $q=5 \times 10^{-3}$ (solid red line), $q=1 \times 10^{-2}$ (solid blue line) and $q=2 \times 10^{-2}$ (solid black line). The value of eccentricity $e=0.2$ that gives the change in the torques sign is overplotted (gray dotted line). The simulation for the planet with $q=0.01$ was extended to allow eccentricity to settle.
• Figure 3: Normalized torques vs the K-parameter range proposed in this study for the mass ratio $5 \times 10^{-4} < q < 2 \times 10^{-2}$ a) with fixed $\alpha=10^{-4}$ and $\Sigma_0=10^{-4}$, varying $h_0$ or $s$; b) with fixed $\alpha=10^{-4}$, $h_0=0.05$, and $s=0.5$, varying $\Sigma_0$; c) by changing $h_0$, $s$ and $\Sigma_0$ to simulate realistic conditions along the disk; d) with fixed $\Sigma_0=10^{-4}$, $h_0=0.05$, and $s=0.5$, varying $\alpha$. Same color palette as in Figure \ref{['fig:standard-torques']}.
• Figure 4: Normalized torques for the different mass ratios associated with planets in low-viscosity disks ($\alpha=10^{-4}$) and with orbital eccentricities $e<0.2$. The transition between inward (blue symbols) and outward (red symbols) migration (shaded area) occurs for $q$ between 0.0015 and 0.002 (black dots), depending on the disk's physical parameters. Symbols and colors are the same as in Figure \ref{['fig:torques-casesofstudy']}. For cases with near-zero torque, values around $1 \times 10^{-5}$ were used for better visibility in the figure.
• Figure 5: Absolute values of the normalized torques for planets undergoing outward migration in low-viscosity disks ($\alpha=10^{-4}$) with $2\times10^{-3} < q < 2\times10^{-2}$ and $e<0.2$ (see Table \ref{['tab:cases-of-study2']}). Left: results from the simulations assuming a local density $\Sigma_0>10^{-5}$. Right: results from the simulations assuming $\Sigma_0<10^{-5}$. In each panel, the fitting function proposed in this work (dashed red lines-see Eq. \ref{['eq:newfit']}) along with a region within $\pm 2$ the standard deviation of the logarithmic residuals (red shadow area). Symbols and colors are as in Figure \ref{['fig:torques-casesofstudy']}.