Formation of Multiple Dynamical Classes in the Kuiper Belt via Disk Dissipation

TL;DR

This study develops a global planet-formation model that couples dust evolution, streaming-instability–driven planetesimal formation, N-body dynamics, pebble and gas accretion, disk-structure–driven gap opening, and internal photoevaporation to simulate the final stages of disk evolution. The authors show that disk dissipation can yield multiple dynamical classes of outer-system minor bodies—scattered, resonant, and dynamically cold—without requiring excessive pebble-driven growth, by balancing dust availability and dynamical stirring from giant planets. A key insight is that the competition between planetesimal formation and pebble accretion can determine whether a Kuiper Belt–like belt forms; faster photoevaporation or early core formation tends to suppress belt formation, while slower dispersal can preserve dust and enable belt assembly. The framework, parameterized by $L_X$, $M_{disk}$, and $\kappa$, provides a pathway to interpret the outer solar system’s architecture and informs exoplanetary debris-disk systems, though long-term evolution and broader parameter sweeps remain needed to assess universality.

Abstract

Planetesimal formation likely lasted for millions of years in the solar nebula, and the cold classicals in the Kuiper Belt are suggested to be the direct products of streaming instability. The presence of minor planetary bodies in the outer solar system and the exo-Kuiper belts provide key constraints to planet formation models. In this work, we connected dust drift and coagulation, planetesimal formation, N-body gravity, pebble accretion, planet migration, planetary core accretion, gap opening, and internal photoevaporation in one modeling framework. We demonstrate that multiple classes of minor planets, or planetesimals, can form during disk dissipation and remain afterwards, including a scattered group, a resonant group, and a dynamically cold group. Significant growth by pebble accretion was prevented by both dynamical heating due to the giant planet in the system and rapid dispersal of the disk toward the end of its lifetime. We also conducted a parameter study which showed that this is not a universal case, where the outcome is determined by the competition for dust between planetesimal formation and pebble accretion. Combining this scenario with sequential planet formation, this model provides a promising pathway toward an outer solar system formation model.

Figures (5)

• Figure 1: Eight key timestamps of one of the fiducial simulations. In each panel, the snapshot at the denoted time is shown. The solid and dashed lines, respectively, show the gas surface density $\Sigma_{\mathrm{g}}$ and dust surface density $\Sigma_{\mathrm{d}}$ with respect to the distance from the star $r$. The eccentricity $e$ and semimajor axis $r$ of the $N$-body particles are shown by the black dots, for mass $m\leq0.1M_\oplus$, and, otherwise, blue circles with the linear sizes proportional to $m^{1/3}$ and the provided scale. Upon the formation of massive planets, selected locations of mean motion commensurability with respect to the outermost one are also denoted in the top axis. And, the gray line in $r-e$ traces the orbits that just cross the outermost planet's apastron.
• Figure 2: Origins of mass of the $N$-body particles at the end of the fiducial simulation. 'Planetesimal' refers to the mass from the initial planetesimal formation and subsequent planetesimal accretions, 'Pebble' refers to the mass accreted from the dust in the disk and 'Gas' refers to the mass accreted from the gas in the disk. For bodies above $0.1M_\oplus$, the individual compositions are shown with the semimajor axis $r$ shown on the horizontal axis. For the remaining 3,283 minor bodies ($\leq0.1M_\oplus$), the sum of their compositions are shown instead, which is noted by '$\leq0.1M_\oplus$' on the horizontal axis.
• Figure 3: Distribution of planetesimal mass $m$ at formation in distance from the star $r$ (top), at the end of the fiducial simulation in Fig. \ref{['fig:frames']} (middle), and that in eccentricity $e$ at the end of the same simulation (bottom). The colors denote the formation time. The mass bins are log-uniform in the horizontal axis. Only the mass from planetesimal formation is considered while pebble accretion and planetesimal accretion are not shown here.
• Figure 4: Results of all random simulations. Each sub-figure presents the results from the simulation with the denoted set of parameters: a) fiducial parameters; b) lower stellar X-ray luminosities $L_\mathrm{X}=5\times10^{29}\mathrm{\ erg\ s}^{-1}$; c)$L_\mathrm{X}=2\times10^{29}\mathrm{\ erg\ s}^{-1}$; d) doubled disk mass $M_\mathrm{disk}=0.05 M_\odot$; e) halved gas envelope opacity $\kappa=0.01 \ \mathrm{cm}^2\ \mathrm{g}^{-1}$. In each sub-figure, the top panel shows the semimajor axis $r$ and eccentricity $e$ of the particles for each random simulation, respectively. Similar to Fig. \ref{['fig:frames']}, the eccentricity $e$ and semimajor axis $r$ of the $N$-body particles are shown by the black dots, for mass $m\leq0.1M_\oplus$, and, otherwise, colored circles with the linear sizes proportional to $m^{1/3}$ and the provided scale. The bottom panel shows the radial distribution of the planetesimal mass at formation, with the colors corresponding to the random simulations in the top panel. The simulation denoted by the color blue in sub-figure a) corresponds to the one presented in Fig. \ref{['fig:frames']} & \ref{['fig:plts_hist']}.
• Figure 5: Comparison of the fiducial simulation result with the observed Kuiper Belt objects retrieved from the Minor Planet Center on 2025 May 17. The two sets of data are overlayed in a manner that the horizontal axis shows the period ratio with respect to the outermost giant planet of 145.8 $M_\oplus$ (blue circle) in our simulation and Neptune (red circle), respectively. The color map presents the number density of Kuiper Belt objects, and the blue dots present the result of our fiducial simulation as shown in the last frame of Fig. \ref{['fig:frames']}. The linear sizes of the circles are proportional to $m^{1/3}$. The blue and red lines trace the orbits that just cross outermost giant planet's apastron and Neptune's aphelion, respectively. Our result reproduced the major dynamical groups: the scattered group, the resonant group, and the dynamically cold group.