From planetesimals to planets with N-body simulations in the giant-planet formation region

Using GPU-accelerated N-body simulations with a new pebble accretion module, the authors demonstrate that wide-orbit giant planets can form from streaming-instability-derived planetesimals regardless of their initial radial distribution, as rapid dynamical scattering and pebble flux filtering drive core growth while naturally producing scattered discs and rare giant impacts within the first 100 Myr.

The Gist

Imagine the early universe as a giant, swirling cosmic kitchen. In the center sits a young star (like our Sun), and swirling around it is a massive disk of gas and dust. This is where planets are born.

For a long time, scientists have wondered: How do giant planets like Jupiter and Saturn actually form? Do they start as tiny pebbles that slowly stick together? Or do they start as large rocks that crash into each other?

This paper, written by Sebastian Lorek and Michiel Lambrechts, acts like a high-speed, super-computer movie of this process. They simulated the birth of giant planets in the "outer kitchen" (between 10 and 50 times the distance from the Sun to Earth) to see how tiny rocks turn into massive worlds.

Here is the story of their discovery, explained simply:

1. The Ingredients: Pebbles and Rocks

Think of the disk as a river of pebbles (tiny icy rocks) flowing inward toward the star.

• The Old Theory: Scientists used to think giant planets grew by smashing big rocks (planetesimals) together. But this is slow, like trying to build a castle by throwing bricks at each other. It often doesn't work fast enough before the gas disk disappears.
• The New Theory: The authors tested a different idea. They started with a mix of rocks of all sizes, created by a process called "streaming instability" (imagine a traffic jam of dust that suddenly collapses into boulders). Then, they let these rocks "eat" the flowing pebbles.

2. The Experiment: Two Different Start Lines

The researchers ran two types of simulations to see if where the rocks started mattered:

• The "Ring" Scenario: Imagine the rocks were all lined up in four distinct, narrow race tracks (rings) around the star.
• The "Uniform" Scenario: Imagine the rocks were spread out evenly like a thick fog across the whole area.

They also tested two "budgets": one with a small pile of rocks (1 Earth mass) and one with a huge pile (10 Earth masses).

3. The Process: The "Pebble Buffet"

As the simulation runs, the biggest rocks (the "seeds") start eating the pebbles.

• The Feast: The biggest seeds grow the fastest. They act like vacuum cleaners, sucking up the pebbles flowing past them.
• The Traffic Jam: As these seeds grow, they start to get rowdy. They bump into smaller rocks, flinging them around. This creates chaos.
• The "Isolation" Effect: Once a planet gets big enough (about the size of Earth), it creates a gap in the pebble river. It blocks the pebbles from reaching the smaller rocks behind it. It's like a big kid at a buffet who eats all the food, leaving nothing for the kids behind them.

4. The Results: What Happened?

Here are the surprising findings from their "cosmic kitchen":

• It Doesn't Matter Where You Start: Whether the rocks started in neat rings or spread out like fog, the result was almost the same. Within a few million years, the rocks scattered and mixed so thoroughly that they forgot their original positions. The final planet systems looked identical.
• The "Self-Regulating" Buffet: Even when they started with 10 times more rocks, they didn't end up with 10 times more giant planets. Why? Because the first few big planets grew so fast and blocked the pebble supply so effectively that the other rocks starved. The system naturally limited itself to forming just one or two giant gas planets and a few smaller "ice giants."
• The Great Migration: The giant planets didn't stay where they were born. They drifted inward, like leaves floating down a stream, settling into orbits between 3 and 10 AU (roughly where Jupiter and Saturn are in our solar system).
• The "Scattered Disc" Leftover: After the gas disk vanished, the giant planets started playing "cosmic pool." They knocked the leftover small rocks and embryos into wild, chaotic orbits far away from the star. This created a scattered disc—a messy, distant cloud of leftovers. This might explain why we see debris disks around other young stars today.
• No Giant Smashes: Surprisingly, the giant planets rarely smashed into each other in the first 100 million years. They mostly just grew by eating pebbles and drifted gently.

5. The Big Picture

This study tells us that giant planets are robust builders. They don't need perfect starting conditions to form. Whether the rocks start in neat lines or a chaotic mess, the physics of "eating pebbles" and "blocking the flow" naturally leads to a system with a couple of giant planets and a messy, scattered ring of leftovers.

The Takeaway:
Think of planet formation not as a delicate construction project, but as a chaotic, self-correcting buffet. The biggest eaters grow fast, block the food for the others, and in the end, they create a stable family of planets with a chaotic, scattered neighborhood of leftovers. This helps explain why our Solar System (and many others) looks the way it does today.

Technical Summary

Here is a detailed technical summary of the paper "From planetesimals to planets with N-body simulations in the giant-planet formation region" by Lorek and Lambrechts (2026).

1. Problem Statement

The formation of wide-orbit giant planets (10–50 AU) remains a complex problem in astrophysics. While the core accretion scenario is well-established, the transition from the initial population of planetesimals to massive planetary embryos is poorly constrained. Key uncertainties include:

• Initial Conditions: The spatial distribution (uniform vs. ring-like) and mass distribution of planetesimals formed via streaming instability are not fully known.
• Efficiency: It is unclear how efficiently pebbles are converted into planetesimals and how the remaining pebble flux is consumed by growing cores.
• Numerical Challenges: Previous studies often assumed the existence of pre-formed planetary embryos to reduce computational costs, skipping the critical phase where planetesimals grow into embryos. Simulating the full population of planetesimals (ranging from ~200 km to ~0.1 $M_{\oplus}$) alongside pebble accretion and migration is computationally prohibitive for standard CPU-based N-body codes.
• Dynamical Evolution: The interplay between pebble accretion, mutual scattering, gas drag, and migration in the outer disc is not fully understood, particularly regarding the final architecture of giant planet systems and the fate of the primordial planetesimal population.

2. Methodology

The authors conducted high-resolution N-body simulations using the GENGA code (Gravitational Encounters with GPU Acceleration), which utilizes GPU acceleration to handle large particle counts.

• Simulation Domain: The study focuses on the giant-planet formation region between 10 and 50 AU around a solar-mass star.
• Initial Conditions:
  • Planetesimal Mass Distribution: Based on streaming instability simulations, an exponentially tapered power-law Initial Mass Function (IMF) was used. This ranges from ~200 km planetesimals to ~0.1 $M_{\oplus}$ embryos.
  • Spatial Distributions: Two scenarios were tested:
    1. Narrow Rings: Planetesimals placed in four spatially separated rings (mimicking streaming instability filaments).
    2. Wide Ring: A spatially uniform distribution connecting the rings.
  • Mass Budgets: Simulations were run with total planetesimal masses of 1 $M_{\oplus}$ (low-mass) and 10 $M_{\oplus}$ (high-mass) to test formation efficiency.
• Physical Prescriptions:
  • Pebble Accretion: Implemented via a custom CUDA kernel. The model distinguishes between 3D and 2D accretion regimes based on embryo mass and pebble scale height. It accounts for the reduction of pebble flux as outer planets accrete material before it reaches inner planets.
  • Migration & Damping: Type-I migration, eccentricity, and inclination damping were modeled using Cresswell & Nelson (2008) prescriptions. Transition to Type-II migration occurs upon reaching pebble isolation mass.
  • Gas Accretion: Once the pebble isolation mass is reached, planets accrete gas via Kelvin-Helmholtz contraction and runaway gas accretion (Lambrechts et al. 2019a).
  • Disc Model: A viscous disc model with stellar irradiation heating was used. The gas disc lifetime was set to 4.1 Myr, followed by a gas-free phase extending to 100 Myr.
• Computational Scale: The simulations included ~4,000 fully interacting bodies (and ~36,000 test particles for high-mass runs), requiring GPU acceleration to complete 4.1 Myr of nebular evolution in days and 100 Myr of gas-free evolution in weeks.

3. Key Contributions

• Full Population Simulation: This is one of the first studies to simulate the entire growth process from a streaming-instability-inspired planetesimal population to giant planets, rather than starting with pre-formed embryos.
• GPU-Accelerated Peble Accretion: The authors developed a new module for GENGA that handles pebble accretion and the complex logic of pebble flux reduction (filtering) across multiple planets simultaneously.
• Stochastic Analysis: By running multiple realizations with randomized initial conditions, the study provides statistical insights into the variability of giant planet formation outcomes.
• Scattered Disc Origin: The study explicitly traces the dynamical fate of the primordial planetesimal population, linking giant planet formation directly to the creation of a scattered disc.

4. Key Results

• Insensitivity to Initial Distribution: The final planetary architecture is largely independent of whether planetesimals started in narrow rings or a uniform wide ring. Rapid dynamical scattering and diffusion within the first ~1 Myr erase the memory of the initial spatial configuration.
• Formation of Giant Planets:
  • Gas Giants: Typically, 1 to 2 gas giants form per simulation. They migrate inward from their birth locations (10–50 AU) to final semi-major axes between 3 and 15 AU.
  • Ice Giants & Super-Earths: A handful of planets with masses between 2 and 10 $M_{\oplus}$ (ice giants/super-Earths) form and generally remain near their birth locations (10–50 AU).
  • Mass Budget Independence: Increasing the initial planetesimal mass from 1 $M_{\oplus}$ to 10 $M_{\oplus}$ did not significantly increase the number of gas giants formed. This is due to self-regulation: a higher number of embryos leads to stronger filtering of the pebble flux, limiting the growth of individual cores.
• Pebble Flux Reduction: The presence of multiple accreting bodies significantly reduces the pebble flux reaching the inner disc. By 4.1 Myr, the flux at ~10 AU is reduced by ~50%.
• Scattered Disc Formation: After gas disc dissipation, the giant planets dynamically excite the remaining planetesimals. This creates a scattered disc extending from ~20 AU to >200 AU, containing a wide mass distribution of bodies (from km-sized planetesimals to Earth-mass embryos). This is an inherent outcome of giant planet formation.
• Giant Impacts: Giant impacts (collisions between planetary cores with mass ratios >0.1) are rare within the first 100 Myr in the giant-planet formation region. Most collisions involve a large planet and a small planetesimal.
• Orbital Characteristics: The formed gas giants have low eccentricities ($e \lesssim 0.1$), similar to the Solar System, though this may be influenced by the specific eccentricity damping prescription used.

5. Significance

• Validation of Pebble Accretion: The results confirm that pebble accretion is a robust mechanism for forming giant planets in wide orbits, even when starting from a realistic, stochastic distribution of planetesimals.
• Exoplanet Demographics: The findings align with observed exoplanet populations, suggesting that cold giants (3–15 AU) are common and often found in multiples, while super-Jupiters at very wide orbits (>20 AU) are rare.
• Solar System Context: The formation of a scattered disc containing Pluto-mass objects and larger embryos supports theories regarding the origin of the Kuiper Belt and the dynamical sculpting of the outer Solar System.
• Inner Disc Implications: The filtering of pebble flux by outer giant planets may significantly impact the formation of terrestrial planets in the inner disc by reducing the available solid material.
• Methodological Advancement: The successful use of GPU acceleration to simulate thousands of interacting bodies with pebble accretion sets a new standard for future population synthesis studies of planet formation.