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The CO snow line favours strong clumping by the streaming instability in protoplanetary discs with porous grains

This study demonstrates that incorporating porous grains and the CO snow line into protoplanetary disc models creates favorable conditions for the streaming instability to trigger strong dust clumping and planetesimal formation within the first 100,000 years, whereas neglecting the snow line significantly delays this process.

Original authors: Jean-François Gonzalez, Stéphane Michoulier

Published 2026-01-29

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CC BY 4.0

Original authors: Jean-François Gonzalez, Stéphane Michoulier

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a cosmic construction site: a swirling, dusty disc around a newborn star. This is where planets are born. But building a planet is surprisingly difficult. The tiny dust grains that start the process face three major "traffic jams" that usually stop them from growing into the massive rocks needed to become planets.

The Bouncing Barrier: If grains hit each other too gently, they just bounce off like rubber balls.
The Shattering Barrier: If they hit too hard, they smash into dust again.
The Drift Barrier: The gas in the disc acts like a strong wind, pushing the growing pebbles inward toward the star before they can get big enough to survive.

To solve this, scientists look for a "magic trick" called the Streaming Instability (SI). Think of this like a sudden, massive traffic jam on a highway. If enough cars (dust) pile up in one spot, they stop moving with the flow of traffic (the gas) and start clumping together under their own gravity. If this clump gets heavy enough, it collapses instantly into a planetesimal (a baby planet).

The Problem:
Usually, it's very hard to get enough dust to pile up in one place. The dust is too spread out, or it drifts away too fast.

The New Discovery:
This paper asks: What if the dust grains aren't solid rocks, but fluffy, porous aggregates (like cosmic cotton candy)? And what if there is a specific "freezing line" for Carbon Monoxide (CO) gas in the disc?

The authors ran computer simulations to see how these fluffy grains behave over time. Here is what they found, using simple analogies:

1. The Fluffy Advantage

Imagine trying to catch a solid marble versus a giant, fluffy snowball. The snowball has a much larger surface area. In the disc, these "fluffy" grains act like giant snowballs. Because they are fluffy, they grow faster and interact with the gas differently. This helps them reach the "sweet spot" where they can start to clump together.

2. The CO Snow Line: The Cosmic Dam

This is the most important part of the discovery. Imagine the disc is a river flowing toward a waterfall (the star).

Without the CO Snow Line: The fluffy grains grow too fast and get swept away by the "wind" of the gas, piling up only very close to the star or not at all. It's like a dam that breaks too early, letting the water rush through without filling the reservoir.
With the CO Snow Line: The CO snow line is a specific distance from the star where it gets cold enough for Carbon Monoxide gas to freeze into ice. The authors found that beyond this line, the grains get a "coat of ice" that makes them more fragile.

The Analogy: Think of the CO snow line as a speed bump or a gatekeeper.

Outside this line, the icy coating makes the grains break apart easily if they hit too hard. This stops them from growing too big too fast.
Because they don't grow too big, they don't get swept away by the gas wind as quickly.
Instead, they drift slowly and pile up in a wide area, creating a massive "traffic jam" of dust.

The Result

The paper concludes that porous grains alone aren't enough to create the perfect conditions for planet formation everywhere. However, when you combine fluffy grains with the CO snow line, the conditions for the "Streaming Instability" (the traffic jam) are met very quickly and over a huge area of the disc.

Without the CO snow line: The "traffic jam" only happens in a tiny, narrow strip near the star, or it takes hundreds of thousands of years to form.
With the CO snow line: The "traffic jam" forms early (within 150,000 years) and stretches out for tens of millions of miles (dozens of astronomical units).

In short: The paper argues that the "freezing line" of Carbon Monoxide acts like a crucial traffic controller. By slowing down the growth of fluffy dust grains just enough, it allows them to pile up in massive, dense clumps. These clumps are the perfect breeding ground for the Streaming Instability to kick in and turn dust into the building blocks of new planets. Without this specific "freezing line," the process is much slower and less likely to happen over large areas.

Technical Summary: The CO Snow Line Favouring Strong Clumping by the Streaming Instability in Protoplanetary Discs with Porous Grains

Problem Statement
The formation of planetesimals from dust grains in protoplanetary discs faces significant barriers, specifically the fragmentation, bouncing, and radial-drift limits. While the streaming instability (SI) is currently regarded as the leading mechanism for direct planetesimal formation, its efficacy relies on specific conditions: a local dust-to-gas volume ratio ( $\epsilon$ ) exceeding a critical threshold ( $\epsilon_{crit}$ ) and marginal dust-gas coupling (Stokes number $St \lesssim 1$ ). Previous studies have established that $\epsilon_{crit}$ is sensitive to external turbulence and particle size distributions, yet it remains unverified whether these conditions are naturally met in evolving protoplanetary discs containing porous grains. Specifically, the interplay between grain porosity, which accelerates growth and alters drag regimes, and the presence of snow lines (particularly CO) has not been fully assessed regarding their ability to trigger strong clumping.

Methodology
The authors utilized a subset of 3D Smoothed Particle Hydrodynamics (SPH) simulations previously presented in Michoulier et al. (2024b, "Paper I"), which model the evolution of porous silicate grains subject to growth, fragmentation, compaction, and bouncing. The simulations covered a $0.01 M_\odot$ disc orbiting a $1 M_\odot$ star, extending from 10 to 400 au, with a turbulent viscosity parameter $\alpha = 5 \times 10^{-3}$ .

Two specific cases were analyzed:

Without CO snow line: Grains have a uniform fragmentation threshold ( $v_{frag} = 20$ m s $^{-1}$ ).
With CO snow line: Beyond the CO snow line ( $T = 20$ K, $r \gtrsim 100$ au), the fragmentation threshold is reduced to $v_{frag} = 5$ m s $^{-1}$ due to CO ice coating.

Rather than using vertically integrated surface densities (metallicity $Z$ ), the study focused on the local dust-to-gas volume ratio $\epsilon$ to account for vertical settling. The authors compared the simulated $\epsilon$ and $St$ values against the critical threshold derived by Lim et al. (2024), which accounts for external turbulence:
$\log \epsilon_{crit} = 0.42 (\log St)^2 + 0.72 \log St + 0.37$
Strong clumping was identified in regions where the simulated $\epsilon > \epsilon_{crit}$ .

Key Results
The analysis of the simulations at $t = 150$ kyr reveals distinct differences based on the inclusion of the CO snow line:

Without CO Snow Line: Conditions for strong clumping are met only in a limited region at the inner disc edge (interior to $\sim 15$ au). This region forms early ( $\sim 20$ kyr) but shrinks and disappears by 300 kyr. A second region of strong clumping eventually emerges at intermediate distances ( $\sim 25-90$ au) but only after $\sim 200$ kyr.
With CO Snow Line: The presence of the CO snow line significantly expands the viable region for planetesimal formation. Strong clumping occurs early ( $\sim 70$ kyr) and extends from the inner edge out to $\sim 80$ au. This region includes two zones of high dust enrichment ( $\epsilon$ peaks $\sim 5$ ) centered around 15 au and 40 au. The outer region extends a few au above the midplane.

The mechanism driving this difference involves the CO snow line acting as a barrier. It prevents grains from growing too rapidly and limits their Stokes numbers to $St \lesssim 0.1$ . Consequently, grains drift more slowly and accumulate farther out in the disc, creating extended regions of enhanced $\epsilon$ much earlier in the disc's evolution compared to the non-snow-line case.

Significance and Claims
The paper claims that the evolution of porous grains, when combined with the CO snow line, creates favorable conditions for strong clumping by the streaming instability much earlier and over larger areas than previously considered in models neglecting these factors.

The authors assert that while porous grains alone can lead to clumping, the inclusion of the CO snow line is "key" to promoting planetesimal formation in discs with porous grains. This is because the snow line facilitates the retention of larger grains in the outer disc, allowing them to drift slowly and accumulate in regions where the SI can effectively operate. The authors note that this mechanism, while physically distinct from the water snow line effect, shares a similar importance in triggering planet formation.

Limitations and Caveats
The authors explicitly acknowledge that the critical threshold $\epsilon_{crit}$ used was derived for monodisperse particle distributions (mSI), whereas their simulations involve a polydisperse distribution (PSI). While they cite literature suggesting that non-linear saturation states and linear growth for distributions peaking at large grains may resemble the mSI, they concede that polydisperse dampening could lower growth rates. Furthermore, they note that the role of magnetic fields in stabilizing or destabilizing the SI in polydisperse systems remains an open question requiring further investigation. The study does not perform direct SI simulations within the evolving disc but rather assesses the viability of the instability based on the derived dust properties.

1. The Fluffy Advantage

2. The CO Snow Line: The Cosmic Dam

The Result

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