Formation of cold giant planets around late M dwarfs via core accretion and the fate of inner rocky worlds

TL;DR

This study addresses whether cold giant planets can form at 1–3 au around very low-mass stars via core accretion and under what conditions inner rocky worlds can survive. Using N-body simulations with pebble and gas accretion and a migration scheme that yields outward movement for planet–star mass ratios above a threshold, the authors explore a compact, low-viscosity disk where α_t=α_g=1e-4 and a disk lifetime of ~10 Myr. They find that a ~5 M_E core can form quickly through collisions and pebble accretion, reaching runaway gas accretion to Saturn–Jupiter masses within a few Myr, with outward migration transporting the planet to ~2–3 au by disk dispersal; inner rocky planets can survive if they reach the inner cavity early enough. The results show that cold giants around the smallest stars do not require extreme dust masses, highlighting a feasible formation pathway and implications for the occurrence and architecture of planetary systems around late M dwarfs.

Abstract

Modeling the formation of cold giant planets around M dwarfs is difficult because their disks may not contain enough solids to form massive cores and because forming giants are expected to migrate inward through disk interactions. It is also unclear whether inner rocky planets can survive in systems hosting a cold giant, with implications for the habitability of close-in worlds. We investigated the conditions that allow giant planets to form at 1-3 au around a 0.1 M$_\odot$ star and explored when a close-in rocky planet can survive. We perform N-body simulations in which embryos grow through pebble and gas accretion in a disk with a local turbulent viscosity of $α_t = 10^{-4}$. Planet-disk interactions are included using a prescription that triggers outward migration when the planet-to-star mass ratio ($q$) exceeds 0.002. We find that a cold giant can form even in a disk with an initial pebble mass of 6 M$_\oplus$ if the disk gas mass is 10$\%$ of the stellar mass. This requires a compact 20 au disk with a dense inner region set by $α_g = 10^{-4}$, the assembly of a $\sim$5 M$_\oplus$ core within 1 Myr, and a disk lifetime of 10 Myr. A close-in rocky planet can survive if it reaches the inner cavity before the outer body becomes a giant. Thus, giant planet formation around very low-mass stars does not require high dust masses as previously thought. A combination of planet-planet collisions, efficient pebble accretion, and a long disk lifetime plays a key role in enabling the formation of cold giant planets with masses between those of Saturn and Jupiter.

Figures (4)

• Figure 1: Evolutionary pathway of cold giant planet formation. Top: Evolution of the planetary mass (black line) across different growth regimes: the pebble-accretion–dominated phase (orange area), limited by the isolation mass (dotted orange line); the phase dominated by planet–planet collisions (pink area), with the critical mass required to trigger runaway gas accretion indicated (dotted pink line); and the gas-accretion–dominated phase (green area), during which the planet grows until it reaches its final mass (dotted green line) before disk dispersal (dash-dotted black line). Bottom: Evolution of the semi-major axis (black line) across the different migration regimes: type I migration (light blue area), transition regime where migration slows (gray area), and outward migration (orange area).
• Figure 2: Evolution of the planetary mass, semi-major axis, eccentricity, and inclination of the planetary seeds (gray lines) in systems where a single giant planet forms (top row), and where a close-in rocky planet forms together with a cold giant planet (bottom row). We show the evolution of the giant planet (black line) and the evolutions the other planets that survived in the system (colored lines) before the more massive planet became a giant planet. The inner edge of the disk, $r_{\rm{in}}$, is indicated (horizontal dashed black line). The location of the innermost planet (pink line) is marked with an arrow for comparison with the inner edge of the disk. The gas aspect ratio, $h_{\rm{gas}}$ (dotted black lines), and the pebble aspect ratio, $h_{\rm{peb}}$ (dotted-dashed black lines), are also overplotted, evaluated at $a=0.02$ au and $a=2$ au.
• Figure 3: Gas accretion rates as a function of planetary mass. The curves show the Kelvin–Helmholtz contraction regime (blue line), the Hill regime (orange line), and disk-limited accretion (green line). The effective accretion rate onto the planet, defined as the minimum of the three regimes, is shown (dashed black line). The critical planetary masses at which the accretion rate reaches $10^{-5}$ M$_\oplus$yr$^{-1}$ are highlighted (dotted gray lines).
• Figure 4: Normalized torques as a function of planetary mass and semi-major axis, assuming circular and coplanar orbits. The different migration regimes are indicated, separating inward from outward migration. The mass required to open a gap in the disk (dashed white line), the planet-to-star mass ratio ($q$) of $0.002$, and the gas depth criterion $K=10^{4}$ are over-plotted (dashed black lines).