Pebble Snow in Planet Formation

• Pebble snow is a planet formation process where an inward migrating snow line delivers icy pebbles that provide water and volatiles to growing planets.
• The mechanism involves pebble drift, rapid sublimation at the snow line, and accretion filtering as modeled by the PPOLs framework.
• Population synthesis models show that disk mass and snow line timing critically influence planetary water delivery, leading to diverse system architectures.

“Pebble snow” is a term denoting a planet formation process in which icy pebbles generated in the outer disk are delivered to the inner regions as the water ice line (snow line) migrates inward during the evolution of a protoplanetary disk. This mechanism fundamentally reshapes the compositional structure and planetary architectures by regulating the volatile (notably water) delivery through a combination of pebble drift, sublimation, and accretion filtering. The latest generation of population synthesis models systematically explores “pebble snow” across broad disk and stellar parameters, revealing the diversity of planetary system outcomes.

1. Physical Basis of “Pebble Snow” and Mechanism

“Pebble snow” is predicated on the radial migration of the snow line, the location where disk temperatures fall below the condensation threshold for water ice, typically parameterized by

$$r_\mathrm{SL} = 4.74 \times (\alpha/10^{-2})^{0.61} \times (\Sigma_{0,\mathrm{gas}}/1000\ \mathrm{g\,cm^{-2}})^{0.704} \times (f_\mathrm{DG}/0.01)^{0.37} \ \mathrm{au}$$

(McCloat et al., 17 Sep 2025). As viscous heating and disk surface densities decline over time, the snow line migrates inward, traversing a pre-existing field of icy pebbles.

Icy pebbles forming exterior to the instantaneous snow line (radius $r > r_\mathrm{SL}$) are rich in volatiles and composed of a roughly 50:50 rock–ice mixture. Their typical fragmentation velocity is high due to the presence of ice mantles, promoting continued coagulation to pebble-scale sizes. As inward drift ensues, these pebbles are advected toward the snow line, where a rapid sublimation (“snow”) event occurs: the ice component transitions to vapor, leaving a surviving rocky pebble core. For planetary embryos interior to the migrating snow line, this process constitutes a major water (and volatile) delivery mechanism, supplementing or replacing local in situ volatile synthesis. The effect is especially pronounced during epochs when the ice line sweeps across the region now corresponding to the habitable zone.

2. Modeling Frameworks: The PPOLs Paradigm

The "PPOLs Model" (McCloat et al., 17 Sep 2025)—an integrated, multi-embryo pebble growth/accretion and snow line evolution framework—illustrates the pebble snow process. Distinct technical features include:

• Parallel Growth and Filtering: Multiple protoplanetary embryos are initiated at a range of radial locations; each tracks mass and composition evolution as pebbles drift through its zone. The pebble flux at each subsequent seed is decremented by the accretion efficiency ($\epsilon$) realized by prior, exterior seeds:

$$f_{\mathrm{peb},i, t+1} = f_{\mathrm{peb},i, t+1} \times (1 - \epsilon_{\mathrm{out},t})$$

• Pebble Composition Bifurcation: Exterior to the snow line, pebbles are icy; after snow line crossing (or after the snow line overtakes the seed), pebbles convert to rocky, and the water mass fraction delivered to the seed is correspondingly set.
• Self-consistent Snow Line Migration: The snow line position is updated at each timestep using the underlying disk properties (e.g., surface density, dust-to-gas ratio, turbulence α parameter), allowing physically realistic tracking of icy pebble delivery across disk evolution.
• Pebble Isolation Mass and Starvation: Protoplanets reaching the pebble isolation mass (set by local disk properties) filter or completely halt the inward pebble flux, starving interior planets of further volatile delivery.

3. Emergent System Architectures and Water Delivery Outcomes

Synthesizing results across stellar mass $M_\star \in [0.125, 2.0]\, M_\odot$ and disk mass fraction ($f_\mathrm{disk} \in [0.01, 0.4]$), three robust planetary system classes are identified (McCloat et al., 17 Sep 2025):

Architecture	Disk Mass Fraction	Mass Distribution	Water Delivery Pattern
Low-disk mass	$f_\mathrm{disk} \lesssim 0.03$	Mars/Earth-mass embryos close in	Habitable zone planets span wide water fractions due to persistent pebble snow
Medium-disk mass	$0.04 \lesssim f_\mathrm{disk} \lesssim 0.08$	Bimodal: Earth-mass inner, ~10 $M_\oplus$ outer	Efficient snow delivery to inner system; outer core dominates pebble accretion
High-disk mass	$f_\mathrm{disk} > 0.11$	Massive ($\gtrsim 5-10 M_\oplus$) outer cores	Pebble isolation by outer cores starves interior planets, limiting water delivery

In low-mass disks, the snow line’s inward sweep passes through the inner disk relatively early, bathing Mars- to Earth-mass seeds in a range of icy pebble fluxes. This yields broad water fraction diversity—potentially producing both rocky and water-rich worlds even at short period orbits. In the medium-mass regime, pebble accretion is efficient enough that outer seeds rapidly reach larger masses and isolation, sharply limiting the subsequent interior delivery: a configuration reminiscent of the terrestrial–giant dichotomy of the Solar System. In high-mass disks, the first major core beyond the evolving snow line accretes pebbles so efficiently that inner zone embryos are strongly starved, with outer planets dominating water and solid accretion.

4. Filtering, Snow Line Self-Regulation, and Compositional Bifurcation

Filtering of the pebble flux by massive, exterior embryos is a crucial nonlinear feedback in sculpting system architecture. The pebble isolation mass—the threshold at which a planet strongly perturbs the local gas pressure gradient and halts further pebble inward drift—sharply divides the disk into compositionally distinct regions. Interior seeds can be effectively starved of icy pebbles after isolation mass is reached by an exterior core. Consequently, the radial position and timing of protoplanet growth relative to the snow line’s migration exert strong control over each planet’s final volatile inventory.

The snow line is not static; its rapid migration during the disk’s evolution means otherwise “dry” inner embryos can transition to icy growth phases as the snow line crosses their orbits. Furthermore, the model incorporates different fragmentation velocities for icy versus rocky pebbles (1000 cm/s for ice-rich vs. 100 cm/s for rocky), which allows larger pebbles to survive and migrate more readily as the snow line progresses inward.

5. Solar System Implications and Diversity Across Stellar Hosts

The bimodal mass architecture identified in mid-mass disks aligns with the observed structure of the Solar System: Earth-mass inner planets accompanied by orders-of-magnitude larger gas giant cores near the primordial snow line location. The paper shows that such architectures emerge only for a restricted set of disk parameters—specifically, intermediate disk masses around F and G stars (McCloat et al., 17 Sep 2025). Lower-mass stars (K/M) more commonly show non-solar-like outcomes, with increased pebble filtering and less efficient generation of large outer cores.

The classic problem of Earth’s “just right” water content (neither bone dry nor ocean world) is naturally addressed in pebble snow models by tuning the timing of snow line migration, pebble isolation mass, and disk dispersal. The interplay between pebble snow and isolation helps explain the observed diversity—some systems end up with inner volatile-rich super-Earths, others with dry Mars-mass embryos—while Solar System analogs are a minority outcome of the available parameter space.

6. Broader Implications for Habitability and Water Worlds

The pebble snow mechanism is fundamental for setting the volatile budgets and, hence, the potential habitability of planets in the habitable zone. In low-mass disks, pebble snow delivers water-rich material efficiently, maximizing the prospects for planets with abundant surface or subsurface water (“water worlds”). In higher-mass disks, or when exterior pebble isolation occurs early, the habitable zone is preferentially populated by dry, rocky planets. The process can thus generate a large spread in water fractions (from dry to nearly 50%) among otherwise similar-mass inner planets. Stellar mass influences the snow line’s trajectory through the disk, further modulating which planets accrue water and where (McCloat et al., 17 Sep 2025).

7. Technical Implementation and Key Formulae

At the core of the PPOLs and similar pebble snow models are the following principles and equations (McCloat et al., 17 Sep 2025):

• Pebble Accretion Efficiency:

$$\frac{dM}{dt} = f_\mathrm{peb}(t) \cdot \epsilon(t)$$

where $f_\mathrm{peb}(t)$ is the pebble flux at the protoplanet’s location/time and $\epsilon(t)$ is the planetary accretion efficiency.

• Snow Line Evolution:

$$r_\mathrm{SL}(t) = 4.74 \, (\alpha/10^{-2})^{0.61} \left( \frac{\Sigma_{0,\mathrm{gas}}}{1000\, \mathrm{g}\,\mathrm{cm}^{-2}} \right)^{0.704} \left( \frac{f_\mathrm{DG}}{0.01} \right)^{0.37} \ \mathrm{au}$$

• Pebble Flux Filtering:

At each seed:

$$f_{\mathrm{peb},i, t+1} = f_{\mathrm{peb},i, t+1} \times (1 - \epsilon_{\mathrm{out}, t})$$

Water mass fractions, core envelope fractions, and mass growth histories are all tracked explicitly as a function of pebble accretion parameters and disk evolution.

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In summary, “pebble snow” is a central mechanism in planet formation theory, coupling the migration of the snow line, pebble drift, and interior accretion filtering to produce a wide variety of planetary masses and volatile contents across stellar types. The latest population models show that the pebble snow process robustly explains both the observed diversity and select similarities (such as the Solar System mass hierarchy) in exoplanet architectures, with direct empirical implications for planet habitability and the distribution of water-rich worlds (McCloat et al., 17 Sep 2025).