How leaky? A large parameter study of leaky dust traps to quantify the transport of pebbles and ice in protoplanetary discs

Abstract: In protoplanetary discs, the presence of dust traps can significantly alter the transport of solids from the outer to the inner regions, and hence they are often invoked as an explanation for the chemical diversity of inner discs observed with JWST (e.g., varying oxygen abundances and C/O ratios). As a detailed treatment of dust transport around dust traps is computationally expensive, earlier works investigating the impact of outer traps on the inner disc composition have often used simplified dust models representing the size distribution with a single effective size and drift speed. In this paper, we revisit the impact of outer traps on dust transport using the state-of-the-art one-dimensional dust evolution code \texttt{DustPy}, which simulates the transport and evolution of dust particles including detailed coagulation and fragmentation. We quantify and map the leakiness of dust traps across a broad parameter space, performing over 300 simulations while varying the disc viscosity, turbulence strength, planet mass and location, and dust fragmentation velocity. We find that dust traps are leakier than previously thought, on a broader parameter space, such that most outer traps (r > 5 au) will result in a long-lived O-rich inner disc with gas-phase C/O < 1. In similar conditions (e.g., carved by the same planet mass), we find inner traps are much leakier than outer traps, though their relative efficiency in reducing the pebble flux is time-dependent. Highly blocking traps altering the inner disc composition dramatically (leading, e.g., to C/O > 1) are possible to set up but necessitate low viscosity and weak turbulence, along with efficient planetesimal formation by the streaming instability. In that case, we find that is the formation of planetesimals, rather than the dust traps themselves, that is capable of significantly altering the inner disc composition.

• The paper quantifies dust-trap leakage with 300+ DustPy simulations, finding that a fiducial trap transmits 75% of its outer solid mass inward within 5 Myr and never fully blocks pebbles.
• Blocking efficiency increases with low viscosity, weak turbulence, massive or distant planets, and streaming-instability planetesimal formation, which can reduce pebble flux by up to two orders of magnitude.
• Full grain-size modeling predicts more leakage than two-population models and suggests cold water vapor is a more reliable observational tracer than C/O ratios for diagnosing trap permeability.

Dust traps—local pressure maxima in protoplanetary discs, often attributed to gap-carving planets—are frequently invoked to explain both the chemical diversity of inner discs observed with JWST and the isotopic dichotomy between carbonaceous and non-carbonaceous meteorites. The implicit assumption is that such traps block a significant fraction of the inward pebble flux. This paper by Houge, Johansen, Banzatti and Grant tests that assumption systematically using DustPy (2604.11925), a one-dimensional dust evolution code with a full grain size distribution including coagulation and fragmentation, across more than 300 simulations spanning disc viscosity $\alpha_\mathrm{visc}$, local turbulence strength $\delta_\mathrm{turb}$, planet mass $M_\mathrm{p}$, planet location $a_\mathrm{p}$, and fragmentation velocity $v_\mathrm{frag}$.

Methods and diagnostic framework

The authors adopt a 0.05 $M_\odot$ tapered disc around a solar-mass star, an MRN initial size distribution from 0.1 to 1 μm monomers, and a fiducial fragile-grain fragmentation velocity of 1 m s$^{-1}$. Crucially, they decouple the global viscosity $\alpha_\mathrm{visc}$ (which sets accretion and gap depth via the Kanagawa et al. prescription) from the local turbulence parameter $\delta_\mathrm{turb}$ (which controls collision velocities, maximum grain size, and diffusion), reflecting growing evidence that MHD winds may drive accretion while local turbulence remains weak. Planetesimal formation via the streaming instability is triggered when the midplane dust-to-gas ratio exceeds unity, converting dust at a rate proportional to each size bin's settling timescale.

The central diagnostic is the trap blocking efficiency $\mathcal{B}(t)$, defined as unity minus the ratio of cumulative solid mass crossing the gap location in a gapped simulation to that in an identical smooth-disc control run. This normalization isolates the effect of the gap itself from global changes in drift speed caused by varying turbulence or viscosity. The complementary quantity $\delta_\mathrm{turb}$0 measures leakiness. Simulations are initialized with the inner disc emptied of dust so that any material inside the gap demonstrably leaked through; an appendix demonstrates this does not bias the blocking efficiency.

The mechanism of leakage

The fiducial model (a 100 $\delta_\mathrm{turb}$1 planet at 10 au, $\delta_\mathrm{turb}$2, $\delta_\mathrm{turb}$3) illustrates the physics. Pebbles grow to mm sizes ($\delta_\mathrm{turb}$4) and are blocked at the pressure maximum, where the critical Stokes number for trapping is $\delta_\mathrm{turb}$5 (~10 μm grains). Although small grains constitute only ~20% of the solid mass in fragmentation-limited equilibrium, continuous fragmentation of trapped pebbles replenishes them, allowing mass to bleed through. By 5 Myr, 75% of the total solid mass initially outside the gap has crossed into the inner disc, and the blocking efficiency has decayed to only $\delta_\mathrm{turb}$6. Notably, the slowed pebble flux is longer-lived: after 5 Myr the planet-hosting disc delivers more solid material to the inner disc than the smooth-disc counterpart. A further subtlety is that the Stokes number rises by roughly an order of magnitude inside the low-density gap, restricting which grain sizes can cross—but leaky grains fragment and re-coagulate dynamically throughout their transit rather than drifting at fixed size.

Parameter space results

The full grid reveals four regimes:

Regime	Blocking efficiency	Conditions
Highly/fully permeable	$\delta_\mathrm{turb}$7–0.2	High $\delta_\mathrm{turb}$8, strong $\delta_\mathrm{turb}$9, low $M_\mathrm{p}$0, or small $M_\mathrm{p}$1
Super-leaky	$M_\mathrm{p}$2	Deep wide gaps (Jupiter-mass planets, $M_\mathrm{p}$3 au) accelerate inward gas flow
Moderately leaky	$M_\mathrm{p}$4–0.9	Intermediate parameters; flux reduced by factors of a few
Highly blocking	$M_\mathrm{p}$5	Low $M_\mathrm{p}$6, weak $M_\mathrm{p}$7, $M_\mathrm{p}$8, often aided by planetesimal formation

Several results stand out quantitatively. The most blocking case found—a Jupiter-mass planet at 40 au with $M_\mathrm{p}$9 and $a_\mathrm{p}$0—reaches $a_\mathrm{p}$1. Conversely, the most super-leaky case ($a_\mathrm{p}$2 at 5 au, strong turbulence) yields $a_\mathrm{p}$3, meaning solids reach the inner disc faster than in a smooth disc. Complete blocking ($a_\mathrm{p}$4) is never achieved anywhere in the grid. Inner traps ($a_\mathrm{p}$5 au) are systematically leakier than outer traps because lower gas density at large radii raises particle Stokes numbers, making grains easier to trap—an effect that dominates over the fact that planets carve deeper gaps closer to the star. However, the relative importance of inner versus outer traps is time-dependent: inner traps regulate water delivery most effectively before ~1 Myr, whereas outer traps dominate thereafter, a behavior not captured by models assuming position-independent blocking efficiency.

The decisive role of planetesimal formation

A key finding is that highly blocking traps are almost always also sites of efficient streaming-instability-driven planetesimal formation. Most traps never reach the critical midplane dust-to-gas ratio, either because they leak or because vertical diffusion keeps solids stirred; those that do form planetesimals convert 10–100 $a_\mathrm{p}$6 of dust. Control simulations with planetesimal formation disabled show that the same traps would otherwise be far leakier—the pebble flux drops by up to two orders of magnitude only when planetesimals form. This role was not identified in earlier work based on simpler dust models. The implication is direct: it is planetesimal formation, not the dust trap per se, that can dramatically alter inner disc composition. If streaming instability is suppressed near zero pressure gradient, or if planet-induced turbulence stirs the trap, even the strongest traps would fall back to the moderately leaky regime. The paper notes this conclusion depends on the assumed formation efficiency $a_\mathrm{p}$7 and neglects ablation of planetesimals back into dust, which would raise the leaking flux.

Comparison with two-population models

Comparing against chemcomp's implementation of the two-population algorithm (two-pop-py), used in prior studies linking traps to inner disc chemistry, reveals systematic discrepancies. For $a_\mathrm{p}$8 the two approaches agree, but at weaker turbulence two-pop-py underestimates leaking by up to three orders of magnitude. The cause is structural: two-pop-py moves the entire dust population at a common mass-weighted velocity dictated by the largest pebbles, so once pebbles halt, leakage proceeds only by diffusion, producing sharp discontinuities in the predicted pebble flux. Because previous composition models built on two-pop-py concluded that most outer traps deplete the inner disc of oxygen and drive C/O > 1, this discrepancy directly challenges those predictions.

Implications for JWST observations

Converting simulated pebble fluxes through the water iceline (1.1 au) into observable cold water vapour masses shows that fully permeable traps reproduce smooth-disc values ($a_\mathrm{p}$9–10 μ$v_\mathrm{frag}$0), while moderately leaky traps yield 0.1–1 μ$v_\mathrm{frag}$1, consistent with JWST measurements. Taking CI Tau as a detection floor, 67% of the simulated traps produce a detectable cold water signal (for $v_\mathrm{frag}$2), rising to 82% for $v_\mathrm{frag}$3 but falling to 25% for $v_\mathrm{frag}$4—so conclusions here hinge on the poorly constrained observable column correction. The prevalence of detectable cold water matches JWST findings that discs hosting ALMA-resolved traps commonly show cold water excesses.

On the C/O question, comparing the oxygen flux carried by icy pebbles against the carbon flux in gas-phase CH$v_\mathrm{frag}$5 (assuming ≤10% of carbon resides in highly volatile carriers) shows oxygen dominates by orders of magnitude in nearly all cases. Only 4 of 250 traps—those with $v_\mathrm{frag}$6 and active planetesimal formation—allow C/O > 1 (only 1 if the ice fraction is raised to 0.5). The authors therefore argue that outer dust traps most likely sustain a long-lived oxygen-rich inner disc with C/O < 1, and that the observed C/O > 1 discs around very low-mass stars likely require additional carbon sources such as refractory carbon processing, CO-to-CH$v_\mathrm{frag}$7 chemistry, or inner cavities. They propose cold water emission as a more reliable tracer of trap leakiness than the C/O ratio.

Limitations and open questions

The one-dimensional DustPy framework cannot model the detailed gas flow around the planet, where 3D simulations show small grains crossing on horseshoe orbits and potentially being accreted by planets beyond the pebble isolation mass; whether re-coagulation in the gap increases that accreted fraction remains open. Gap profiles are imposed from empirical fits rather than evolved self-consistently, though testing an alternative prescription changed little. Porosity evolution is absent, planetesimal ablation is neglected, and the streaming instability threshold and efficiency carry significant uncertainty. Whether perfectly blocking traps exist depends on unconstrained monomer properties; the authors suggest deep transition discs lacking dusty inner discs as candidate systems. Finally, combining full coagulation physics with multidimensional hydrodynamics—e.g., via TriPoD-style subgrid models—remains untested at scale.

Conclusion

This parameter study establishes that dust traps are substantially leakier than inferred from simplified dust models, with most outer traps delivering most of their solid reservoir—and hence water—to the inner disc over 5 Myr. Highly blocking traps exist but require low viscosity, weak turbulence, massive planets, and, decisively, efficient planetesimal formation; it is the latter, not the trap itself, that can push inner discs toward oxygen-poor, carbon-rich compositions. The results favor cold water vapour lines over C/O ratios as observational diagnostics of trap leakiness, and they call into question quantitative predictions of inner disc chemistry derived from two-population-type dust evolution schemes.