Testing the Icy Pebble Accretion Hypothesis with Primordial Main Belt Asteroids

Large main-belt asteroids (diameter $D \gtrsim 120\ \mathrm{km}$) exhibit a surface composition gradient as a function of heliocentric distance, ranging from anhydrous bodies to those rich in hydrated and, possibly, ammoniated materials. Their primordial nature holds key clues to the evolution of the Solar System. It has been suggested that the volatile-rich bodies formed in the outer Solar System and were implanted into the main belt. Alternatively, volatiles may have been delivered via inward-drifting icy pebbles in the protosolar disk. Here, we examine whether in-situ formed rocky embryos can acquire volatiles through pebble accretion as the snowline migrated inward. With the turbulence strength of the disk, radial pebble flux, and the dimensionless stopping time of pebbles (St) as parameters, we calculate the growth of large asteroids. The results are then compared with mass and compositional constraints based on asteroid observations. We find that a moderate pebble flux ($\lesssim18~M_\oplus / \text{Myr}$) is required to enable volatile delivery while preventing the largest asteroids from becoming more massive than Ceres. Water accretion is feasible with $\mathrm{St} \sim 10^{-3}$ ($\sim 1$ mm). However, only the largest asteroids (D > 200 km) can accumulate sufficient ammonia under such conditions. For most asteroids with D between 100 and 200 km, ammonia ice accretion requires $\mathrm{St} \sim 10^{-4}$ ($\sim 100,μ$m). Such small particle sizes may pose both theoretical and observational challenges. Thus, we propose that the intermediate-sized, potentially ammonia-bearing asteroids serve as a record of the Solar System’s dynamic evolution.

💡 Research Summary

This paper investigates whether the volatile‑rich composition of the largest main‑belt asteroids (diameters ≳120 km) can be explained by in‑situ icy pebble accretion as the water, ammonia, and carbon‑dioxide snowlines migrated inward during the early Solar‑System epoch. The authors adopt a simplified, static protoplanetary‑disk model based on the Minimum‑Mass Solar Nebula (Σ_g = 1700 (r/1 au)⁻³ᐟ² g cm⁻²) and a time‑dependent temperature law that reproduces the observed inward drift of the water snowline from ~3.6 au to ~2.0 au within the first half‑million years, followed by a slower, irradiation‑dominated cooling. Snowlines for NH₃ and CO₂ start beyond Jupiter and later reach ~2.5 au and ~3.2 au, respectively.

Pebble accretion is parameterized by three free quantities: (1) the turbulent viscosity parameter α, (2) the radial pebble mass flux Ṁ_d, and (3) the dimensionless stopping time St (the Stokes number). The authors explore α = 10⁻⁴–10⁻³, Ṁ_d = 5–30 M⊕ Myr⁻¹, and St = 10⁻⁴–10⁻³, which correspond roughly to pebble sizes from ~100 µm to ~1 mm. Using the analytic accretion efficiency ε ∝ (St/α)¹ᐟ²·(R_p/H_g)³ᐟ², they calculate growth tracks for planetesimal embryos of various initial radii placed at 2–3 au.

The key findings are:

1. Water delivery – With St ≈ 10⁻³ (∼1 mm pebbles) and a moderate pebble flux ≤ 18 M⊕ Myr⁻¹, embryos that grow to 120–200 km can acquire 5–10 wt % water, consistent with the hydrated signatures seen in C‑complex asteroids and with Ceres’ inferred ∼30 wt % water‑ice fraction.

2. Ammonia delivery – Under the same St, the accretion efficiency for NH₃‑bearing pebbles is roughly five times lower than for water because of the higher sublimation temperature and lower sticking probability. Consequently, only the largest bodies (diameter > 200 km) can accumulate enough ammonia (∼1–2 wt %) to explain the 3 µm band features observed on Ceres and a few other large asteroids.

3. Requirement for smaller pebbles – To endow the more common 100–200 km asteroids with comparable ammonia, the pebble Stokes number must drop to ≈10⁻⁴ (∼100 µm). Such small pebbles are difficult to maintain in a turbulent disk: they are prone to fragmentation, rapid radial drift, and sublimation/re‑condensation cycles near the snowlines. Current dust‑growth models and ALMA observations typically find dominant pebble sizes in the mm–cm regime, making the required St somewhat at odds with theory and observations.

4. Mass constraint – A pebble flux higher than ~18 M⊕ Myr⁻¹ would cause embryos to overgrow, exceeding Ceres’ mass and contradicting the observed size distribution of the primordial asteroid population.

The authors acknowledge several simplifications: the gas disk is static (no viscous spreading or photo‑evaporation), planetary migration is ignored, and the pebble flux is assumed constant in time. Real disks would exhibit evolving α, time‑varying Ṁ_d, and possible feedback between growing embryos and the gas flow, all of which could modify the accretion histories.

Observationally, the paper ties its results to the well‑documented S–C taxonomic dichotomy and the 3 µm spectral band diversity. The “Sharp‑type” spectra (inner belt, hydrated minerals) and “Not‑Sharp‑type” spectra (outer belt, showing NH₃‑related absorptions) can be interpreted as a gradient in pebble‑accreted volatiles, with the intermediate‑size asteroids preserving a mixed signature.

In summary, the study supports the notion that inward‑drifting icy pebbles can plausibly deliver water to main‑belt embryos, but ammonia delivery is efficient only for the largest bodies unless unrealistically small pebbles dominate the flux. Consequently, the intermediate‑sized (100–200 km) ammonia‑bearing asteroids likely record the dynamical history of snowline migration and pebble flux variations in the early Solar System. The authors recommend future work that couples full disk evolution, planetesimal dynamics, and high‑resolution observations (e.g., ALMA, JWST) to refine pebble size distributions and test the icy pebble accretion hypothesis more rigorously.