Pebble Accretion in Planet Formation

• Pebble accretion is a planet formation mechanism where gas-assisted drag enables the capture of drifting solid particles within a protoplanetary disk.
• It operates in distinct 3D and 2D regimes, with efficiency governed by particle size, disk turbulence, and aerodynamic drag effects.
• The process influences planetary architecture by linking pebble supply, disk evolution, and migration, affecting the growth of both giant and terrestrial planets.

Searching arXiv for recent and foundational papers on pebble accretion to ground the article in current literature. Pebble accretion is a planet-growth mechanism in which a planetary embryo accretes aerodynamically coupled solid particles drifting through a gaseous protoplanetary disk. Its defining feature is gas-assisted gravitational capture: drag dissipates pebble kinetic energy during an encounter, allowing particles to settle toward the planet rather than pass ballistically. In current usage, pebbles are characterized primarily by their Stokes number, $\tau_s \equiv t_{\rm stop}\Omega_K$, and the most favorable regime is typically $\tau_s \sim 10^{-2}$–$10^{0}$; observations also confirm pebble-sized particles in protoplanetary disks and in the early Solar System (Ormel, 2024). The framework is now applied to giant-planet cores, close-in exoplanets, and terrestrial planets, but recent work emphasizes that its outcome is inseparable from disk evolution, pebble supply, turbulence, migration, planetesimal formation, and pebble isolation (Johansen et al., 2024).

1. Definition and dynamical basis

Pebble accretion admits both a broad and a strict definition. In the broad sense, it is growth by accreting solids that drift over significant disk distances. In the standard sense, it is the capture of such particles inside the planet’s Hill sphere, where gas drag removes enough energy for them to become bound and settle to the planet. The relevant gravitational scale is the Hill radius,

$R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$

and the basic settling picture compares the encounter time, $t_{\rm enc}\sim b/\Delta v$, with the drag-mediated settling time. Capture requires that the interaction lasts long enough for drag to matter; pebble accretion is therefore neither pure collision nor pure gravitational focusing, but a dissipative three-body process (Ormel, 2024).

A central conceptual point is that planets accrete from a flux, not from a static local reservoir. In flux-based formulations, the inward pebble supply is written as

$F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$

or, in production-front models,

$$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$

The growth of an embryo therefore depends on how long drifting pebbles continue to be generated and delivered, not simply on the instantaneous surface density at its orbital radius (Johansen et al., 2021, Qiao et al., 2023).

This flux-based character distinguishes pebble accretion from classical planetesimal accretion. Planetesimal accretion is governed mainly by geometric and gravitational focusing under velocity dispersions set by eccentricity and inclination, whereas pebble accretion is governed by aerodynamic size, layer thickness, and the ability of gas drag to dissipate encounter energy. The contrast is physical rather than semantic: the same solids inventory can feed qualitatively different growth laws depending on whether it resides in km-scale planetesimals or in drifting particles with favorable stopping times (Ormel, 2024).

2. Regimes, onset thresholds, and pebble isolation

The accretion geometry is conventionally divided into 3D and 2D regimes, depending on whether the pebble layer thickness exceeds the effective capture cross section, and into headwind-dominated Bondi and shear-dominated Hill limits, depending on whether the approach speed is set primarily by gas headwind or Keplerian shear. In the small-pebble settling limit, the 3D accretion rate scales as $\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$, whereas the 2D rate scales as $$\dot m_{\rm 2D}\sim \sqrt{Gm t_{\rm stop}\Delta v}\,\Sigma$$; in the 2D shear regime the asymptotic form becomes

$$\dot m_{\rm 2D-shear}\sim R_H^2\Omega_K\,\tau_s^{2/3}\Sigma.$$

This Hill/shear regime is the high-efficiency limit in which almost all particles entering the Hill sphere can be accreted for $\tau_s \sim 10^{-2}$0–1 (Ormel, 2024).

Pebble accretion is not active for arbitrarily small seeds. The initiation mass is obtained from the condition that the encounter time exceed the stopping time,

$\tau_s \sim 10^{-2}$1

Below this threshold, growth is ballistic rather than settling-dominated. A practical fit for the corresponding initiation size is

$\tau_s \sim 10^{-2}$2

while explicit trajectory calculations identify a critical stopping-time scale $\tau_s \sim 10^{-2}$3 and an onset radius

$\tau_s \sim 10^{-2}$4

for $\tau_s \sim 10^{-2}$5 (Ormel, 2024, Visser et al., 2015).

At the opposite end of growth lies pebble isolation. Once the planet perturbs the gas strongly enough to create a pressure structure that halts inward drift, pebble accretion stalls. A general scaling is

$\tau_s \sim 10^{-2}$6

and one fitted expression is

$\tau_s \sim 10^{-2}$7

while close-in planet models often use

$\tau_s \sim 10^{-2}$8

Isolation is therefore not a universal number; it depends on disk thickness, turbulence, and, in diffusion-modified treatments, pebble size (Ormel, 2024, Narayan et al., 30 Apr 2025, Andama et al., 2021).

Recent analytical work has also shown that monodisperse treatments can misrepresent early growth. For a polydisperse MRN distribution, 2D Hill accretion is reduced by an exact factor $\tau_s \sim 10^{-2}$9 relative to the monodisperse benchmark, but Bondi-regime accretion can be larger by 1–2 orders of magnitude, extending efficient pebble accretion to seeds 1–2 orders of magnitude lower in mass. In that framework, seeds of $10^{0}$0–$10^{0}$1 can grow on Myr timescales, overlapping the high-mass end of the streaming-instability planetesimal mass function and reducing the need for a long collisional prelude (Lyra et al., 2023).

3. Disk physics regulating pebble accretion

The lifetime and radial extent of the pebble source are set by dust growth, drift, and outer-disk evolution. In inside-out growth models, the pebble production front evolves as

$10^{0}$2

with $10^{0}$3 and $10^{0}$4. Pebbles are continuously generated at this front and drift inward; once the shrinking outer disk edge reaches $10^{0}$5, no new pebbles can be produced outside that point and the pebble flux terminates. External photoevaporation therefore modulates pebble accretion primarily by removing the outer dust reservoir before it can grow into pebbles, not by directly entraining mature pebbles (Qiao et al., 2023).

This supply-limited view makes environmental effects strongly nonlinear. In one explicit example, a $10^{0}$6 seed at 25 au remains at about 25 au with a lunar mass under immediate irradiation by a $10^{0}$7 field, but becomes approximately Earth-like in both mass and orbital radius if the disk is shielded for 1 Myr. For embryos at 25 au, the dependence on shielding time remains nonlinear up to about $10^{0}$8 Myr in strong fields ($10^{0}$9–$R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$0), and shielding for $R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$1 Myr essentially nullifies the environmental impact because the pebble reservoir has already been processed before irradiation truncates the disk (Qiao et al., 2023).

Turbulence modifies pebble accretion in two distinct ways: it thickens the pebble layer and it perturbs individual trajectories. Local 3D shearing-box simulations with laminar runs, weakly turbulent ambipolar-diffusion runs ($R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$2), and strongly turbulent ideal-MHD runs show that accretion remains efficient for marginally coupled particles with $R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$3–1 even in strong MRI turbulence. Turbulence broadens the feeding zone but lowers the capture probability of any given particle, and the two effects largely cancel; the dominant impact on the net rate is therefore the dust-layer thickness rather than a dramatic change in the intrinsic Hill-regime capture physics. A clear reduction appears mainly for strongly coupled particles around $R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$4 and low-mass cores, where the intrinsic efficiency can fall by a modest factor of about 2–3 (Xu et al., 2017).

Fragmentation and disk size regulate the pebble reservoir in complementary ways. Detailed coagulation–fragmentation calculations show that fragmentation can be beneficial because it prevents solids from growing beyond the pebble-accretion “sweet spot” and sustains a longer-lived pebble flux. In compact disks ($R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$5 au), the pebble flux can exceed $R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$6 but lasts only $R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$7 yr; in large disks ($R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$8 au), the flux is almost an order of magnitude lower but persists much longer. Low turbulence strongly favors growth, whereas at $R_H = r\left(\frac{m}{3m_\star}\right)^{1/3},$9 no embryo reaches pebble isolation mass in the studied compact-disk models unless the fragmentation threshold is much higher than $t_{\rm enc}\sim b/\Delta v$0 (Drazkowska et al., 2021).

Very young self-gravitating disks impose a different limitation. In steady self-gravitating models, the pebble-to-gas density ratio generally fails to exceed 0.01, the fiducial mm-grain case gives $t_{\rm enc}\sim b/\Delta v$1 and $t_{\rm enc}\sim b/\Delta v$2, and streaming instability is therefore expected to struggle. The literature allows a rare exception if 10 cm grains are available and spiral structure concentrates them in regions of low gravito-turbulence; under those assumptions, lunar-mass cores might assemble on timescales of a few thousand years, but the same work explicitly states that this is likely to be rare and is far from proven (Forgan, 2019).

4. Architectures and planetary populations

Pebble accretion is not only a growth mechanism but an architectural one. Hybrid simulations of whole systems show a two-stage pattern in which small planetesimals first grow by mutual collisions and then, once they reach roughly 1000 km in size, transition into efficient pebble accretors. In a 200 AU disk with moderately high turbulent viscosity, this pathway yields giant-planet cores that can begin runaway gas accretion; in very low-viscosity disks, however, planets reach pebble isolation earlier, open gaps before runaway gas accretion begins, and the resulting systems contain several Neptune-size planets rather than gas giants (Morishima, 2018).

A similar bifurcation appears in models that emphasize pebble properties. When pebble accretion begins while pebbles are still abundant, multiple gas giants can form beyond the ice line while the inner system remains populated by small planets; if the onset threshold is crossed too late, no giants form and bodies remain Earth-mass or smaller. In these simulations the decisive controls are pebble size, disk radius, turbulence, and the size of the largest planetesimals, because those parameters determine whether embryos enter the pebble-accretion regime before the outer pebble reservoir is depleted (Chambers, 2016).

Global mass-budget analyses temper the impression of uniformly high efficiency. In flux-limited giant-planet calculations, the pebble accretion probability $t_{\rm enc}\sim b/\Delta v$3 is often only about 1%–3%, and for every $t_{\rm enc}\sim b/\Delta v$4 accreted by a core, at least $t_{\rm enc}\sim b/\Delta v$5 and sometimes much more are lost to radial drift. The same calculations find binary outcomes over 0.1–30 AU: either sub-Earth cores remain sub-Earth, or they grow into Jupiters that subsequently migrate inward. The price of forming Jupiter-breeding cores from mm–cm pebbles is that the corresponding solids reservoir drains from the disk in $t_{\rm enc}\sim b/\Delta v$6 yr or less, which that work argues is difficult to reconcile with long-lived mm-bright disks (Lin et al., 2018).

Inside 1 au, pebble accretion remains viable but is extremely parameter-sensitive. A large sample study of 862 close-in planets models growth as a two-stage sequence in which classical planetesimal accretion first reaches the classical isolation mass and pebble accretion then attempts to lift the core to pebble isolation within a 3 Myr disk lifetime. Turbulence is the strongest control parameter: the best-performing model, $t_{\rm enc}\sim b/\Delta v$7 and $t_{\rm enc}\sim b/\Delta v$8, allows about $t_{\rm enc}\sim b/\Delta v$9 of the planets to reach pebble isolation mass, whereas at $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$0 pebble accretion is largely ineffective. The same study finds that if the embryo reaches the classical isolation mass later than roughly $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$1, pebble accretion usually loses the race against pebble drift and disk evolution (Narayan et al., 30 Apr 2025).

The earliest embedded phases may permit even faster growth. In class 0/I disks with high gas and dust inflow, a fiducial model yields a required initial mass of $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$2 at 10 au to reach a $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$3 core within the typical 0.5 Myr lifetime, while an optimistic case with $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$4 lowers the requirement to $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$5. These results suggest that pebble accretion can operate before the class II stage, although the same work stresses non-monotonic dependence on gas accretion rate because larger inflow also increases the headwind-related reduction factor (Tanaka et al., 2019).

5. Terrestrial planets and Earth

Pebble accretion has become a major alternative, and increasingly a complement, to classical terrestrial-planet growth by embryo collisions. In one explicit Solar System model, mm-sized pebbles drift inward through the gaseous nebula while protoplanets form near the primordial water ice line around Mars’s orbit, grow by Hill-regime pebble accretion, and migrate inward by type I migration. With initial protoplanet mass $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$6, a narrow planetesimal birth belt centered at $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$7 AU, fixed 1 mm pebbles, and pebble-flux ratio $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$8 to $F_{\rm p} = 2\pi r\, v_r\, \Sigma_{\rm p},$9, the framework reproduces the masses and orbits of Venus, Mars, proto-Earth, and Theia in a common growth track. It also uses two pebble generations, transitioning at $$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$0–4.0 Myr, to explain Earth–Mars isotopic differences, and it places most water delivery before the embryo exceeds about $$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$1 (Johansen et al., 2021).

Recent debate has centered on whether the terrestrial planets formed “by pebble accretion” or “by giant impacts.” A 2024 comment argues that this framing is misleading: evidence for late giant impacts does not exclude major early pebble accretion. Its central synthesis is that proto-Earth may have reached as much as 70% of its final mass by pebble accretion during the gas-disk phase, followed by an extended period of planetesimal and embryo collisions culminating in the Moon-forming impact. In that view, the Hf-W chronometer does not discriminate directly between pebble and non-pebble models; what matters is the timing of core formation, the amount of late accretion, and metal-silicate equilibration efficiency. The same comment emphasizes an Olson & Sharp scenario in which Earth grows to 70% of its final mass during the disk phase, accretes another 20% from small remnant planetesimals between 10 Myr and 40 Myr, and then undergoes a Mars-mass giant impact with only 10% equilibration, while still reproducing Earth’s Hf-W signature (Johansen et al., 2024).

Compositional arguments have also shifted from bulk meteorites to accretable components. A 2025 model shows that mixtures of metal grains, chondrules, CAIs, and AOAs match Earth’s major element composition (Fe, Ni, Si, Mg, Ca, Al, O) within uncertainties, whereas no combination of chondrites and iron meteorites does. Its best-fitting mixture is predominantly carbonaceous, includes about 15 wt% refractory inclusions $$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$2, and reproduces Earth’s $$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$3Cr and $$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$4Ti values. Under fixed 1 au conditions with headwind velocity 30 m/s, gas column density $$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$5, and typical pebble column density $$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$6, Hill-regime accretion of these components yields $$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$7–$$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$8 in 2 My; lower column density produces moon-mass outcomes, whereas higher column density leads toward super-Earths (Garai et al., 21 Jul 2025).

The terrestrial-zone literature remains divided. One coupled solid-evolution and N-body study finds that pebble accretion in the inner terrestrial region yields fewer but substantially more massive embryos, strongly enhances super-Earth formation, and can make the embryo mass fraction exceed the planetesimal-disk mass because additional mass is imported from the pebble reservoir; yet it does not substantially expand the embryo-formation zone outward, and embryos beyond about 2 au still fail to form within the pebble-flux lifetime (Voelkel et al., 2020). By contrast, another N-body study concludes that if pebble accretion efficiently augments the inner Solar System, it should import too much outer-Solar-System material and violate the observed nucleosynthetic isotopic dichotomy; in that interpretation, pebble accretion played little or no role in terrestrial planet formation because no parameter set simultaneously preserves isotopic separation and supplies enough mass (Mah et al., 2021). The disagreement is therefore not about whether pebble accretion is dynamically possible, but about how it couples to isotopic transport, volatile processing, and the timing of Jupiter’s barrier.

6. Composition, atmospheres, and unresolved issues

Pebble accretion changes planetary interiors because pebbles are small enough to be thermally processed in envelopes before reaching the core. In direct-core-growth calculations, rocky pebble accretion proceeds through three phases: an early stage of negligible ablation, an intermediate stage of increasing ablation in which some high-$$\dot{M}_{\rm flux} = 2\pi r_g \frac{dr_g}{dt} Z_{\rm peb}(r_g)\Sigma_{\rm gas}(r_g).$$9 vapor rains out to the core, and a final stage in which the vapor-rich inner region expands and absorbs most incoming pebble mass. In that model, rainout ends before the core reaches about $\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$0 for rocky SiO$\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$1 pebbles, and before about $\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$2 for icy H$\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$3O pebbles. Pebble accretion is therefore self-limiting as a mechanism of direct core growth, even though heavy elements can remain stored in the envelope for later indirect growth (Brouwers et al., 2017).

When atmospheric structure is computed with a non-ideal H/He–silicate EOS, pebble sublimation naturally builds a metal-rich lower atmosphere and an outwardly decreasing metallicity profile, $\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$4. Silicate pebbles sublimate once the local temperature approaches $\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$5, and the resulting vapor enrichment increases the mean molecular weight, compresses the lower atmosphere, and produces a dilute-core structure rather than a sharp core–envelope boundary. In those calculations the crossover condition $\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$6 marks the onset of runaway gas accretion, typical diluted-core metallicities are around $\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$7, and small pebbles can dominate opacity strongly enough to help mini-Neptunes survive while pebble supply continues; once pebble accretion subsides, however, the atmosphere clears rapidly and gas accretion accelerates, making atmospheric recycling a more plausible long-term stalling mechanism (Ormel et al., 2020).

Several recurrent misconceptions follow from these results. Pebble accretion is not automatically efficient, because the physically relevant measure is the accretion probability $\dot m_{\rm 3D} \sim Gm\, t_{\rm stop}\,\rho$8, which need not be high (Ormel, 2024). It is not equivalent to “small-particle accretion” in general, because only a restricted aerodynamic range satisfies the settling criterion. It is not negated by later collisions, because hybrid histories with strong early pebble growth and late giant impacts remain compatible with chronometric constraints (Johansen et al., 2024). Nor is it a single-size process: polydisperse and multi-species models show that size distributions, fragmentation thresholds, and species-dependent isolation masses can change both the onset and the termination of growth (Lyra et al., 2023, Andama et al., 2021).

The modern research picture is therefore cumulative rather than exclusive. Pebble accretion links dust growth, radial drift, planetesimal formation, migration, envelope thermodynamics, and disk dispersal. It can form giant-planet cores, alter the architecture of close-in systems, contribute substantially to terrestrial-planet growth, and build composition gradients in planetary interiors. At the same time, the literature continues to debate how efficiently it operated in the inner Solar System, how strongly turbulence and environment regulate it, and how pebble transport maps into isotopic and volatile constraints. Dense rings observed by ALMA are especially favorable sites because reduced drift and concentrated solids raise pebble-accretion efficiency, but in smooth disks the same mechanism may remain supply-limited and lossy (Ormel, 2024).