The ALMA Survey of Gas Evolution of PROtoplanetary Disks (AGE-PRO): Constraints on disk turbulence, fragmentation velocity, and inner pebble fluxes

Abstract: How substructures and disk properties affect dust evolution and the delivery of solids and volatiles into planet-forming regions remains an open question. We present results from tailored dust evolution modeling of the AGE-PRO ALMA large program, a sample of 30 protoplanetary disks spanning different evolutionary stages. Visibility fitting of the AGE-PRO ALMA data (at 1.3\,mm) reveals that approximately half of the disks exhibit radial substructures. Combined with stellar properties, disk inclinations, and gas mass estimates from CO isotopologues and N$<em>2$H$<sup>+$, this well-characterized set of disks provides an ideal testbed to constrain dust evolution models across different ages and disk morphologies. Using the dust evolution code \texttt{DustPy}, we simulate dust evolution in each disk under four model configurations, varying two key free parameters: the turbulent viscosity ($α= 10^{-4}, 10<sup>{-3}$) and fragmentation velocity ($$v</em>{\rm{frag}} = 1 \mathrm{m\,s^{-1}}, 10 \mathrm{m\,s<sup>{-1}}$$). Pressure traps are incorporated by perturbing the gas surface density based on the continuum intensity profiles, and synthetic observations generated with \texttt{RADMC-3D} are compared to these profiles. While no single model fits all disks, nearly half are best reproduced by the configuration with low turbulence and low fragmentation velocity ($$α= 10^{-4}, v_{\rm{frag}} = 1\,\mathrm{m\,s<sup>{-1}}$$). Models of smooth disks underpredict dust mass, possibly indicating unresolved substructures. Pebble fluxes into inner disk regions correlate more strongly with disk age than with the presence of substructures, highlighting time-dependent dust transport as a key factor in shaping inner disk composition. Our results also provide a comparative baseline for interpreting multiwavelength and JWST water vapor observations.

• The paper models 30 AGE-PRO disks with DustPy and RADMC-3D across four combinations of turbulence and fragmentation velocity, finding that about half favor low turbulence ($\alpha=10^{-4}$) and low fragmentation velocity ($v_{\rm frag}=1\,\mathrm{m\,s^{-1}$).
• The paper finds that no single dust-evolution prescription matches radial profiles, dust masses, sizes, and spectral indices simultaneously, while pressure traps help retain dust and explain substantially higher median dust masses in structured disks, particularly in Lupus and Upper Scorpius.
• The paper shows that pebble fluxes decline with age but remain up to 2–3 orders of magnitude higher in older structured disks, and predicts a testable correlation between cold-water mass and the location of the innermost dust trap for future JWST observations.

This paper presents tailored dust evolution modeling of the 30 protoplanetary disks in the AGE-PRO ALMA large program, using the DustPy code to constrain two key free parameters of dust evolution — the turbulent viscosity parameter $\alpha$ and the fragmentation velocity $v_{\rm frag}$ — and to predict inner-disk pebble fluxes relevant to JWST water observations. The sample spans three star-forming regions (Ophiuchus, Lupus, Upper Scorpius) with representative ages of 0.5, 1.5, and 5 Myr, a narrow stellar mass range ($\sim$0.3–0.8 $M_\odot$), and uniformly characterized gas masses from CO isotopologues and N$_2$H$^+$ (Trapman et al., 12 Jun 2025).

Modeling framework

Each disk is evolved with DustPy under four configurations spanning $\alpha = \{10^{-4}, 10^{-3}\}$ and $v_{\rm frag} = \{1, 10\}\,\mathrm{m\,s^{-1}}$. The gas surface density is held fixed at a viscous profile whose normalization matches the AGE-PRO gas mass; this choice isolates dust physics but explicitly neglects gas evolution, disk winds, and photoevaporation. For the roughly half of the sample identified as substructured through FRANK visibility fitting (Vioque et al., 12 Jun 2025), Gaussian pressure bumps are inserted into the gas surface density at the observed ring/gap locations, with amplitudes scaled from the relative contrast of features exceeding 10% of the peak brightness. Synthetic ALMA images are produced with RADMC-3D at Bands 3, 5, 6, and 7 using Ricci et al. opacities (chosen for their superior performance against population-level fluxes and spectral indices), convolved to match either the FRANK effective resolution or the observational beam, and compared via reduced $\chi^2$ on normalized radial profiles, plus dust masses, $R_{90\%}$ sizes, and spectral indices.

A deliberate restriction of the parameter space is worth noting: although dust-settling analyses suggest $v_{\rm frag}$0 as low as $v_{\rm frag}$1 (Villenave et al., 7 Mar 2025), such values are excluded because grains would grow beyond cm sizes in traps and become invisible at sub-mm wavelengths, inconsistent with the observed structures.

Representative disks

Three case studies illustrate the model behavior. In Upp Sco 1, only configurations that retain mm-sized grains in the outer ring reproduce the ALMA morphology: low-$v_{\rm frag}$2/low-$v_{\rm frag}$3 or high-$v_{\rm frag}$4/high-$v_{\rm frag}$5. The low-$v_{\rm frag}$6, high-$v_{\rm frag}$7 case grows grains so efficiently into cm sizes that 1.3 mm emission is suppressed. All models overpredict the inner disk brightness, which the authors attribute to overly leaky traps; the best match uses $v_{\rm frag}$8, $v_{\rm frag}$9. For Oph 2 and Lup 2, all four configurations yield similar morphologies at the survey resolution, and synthetic emission is generally more compact than observed because efficient drift concentrates large grains at a single trap while depleting the outer disk. Multiwavelength comparisons broadly reproduce the observed trend of more compact emission at longer wavelengths for weakly trapped disks, whereas strongly trapped disks show nearly wavelength-independent $\sim$0 (e.g., $\sim$183–85 AU across Bands 3–6 for Upp Sco 1).

Population-level results

Several findings emerge across the full sample:

• Disk sizes: $\sim$2 shows no strong systematic evolution with region age, consistent with the interpretation that pressure bumps maintain approximately constant dust disk sizes. Models reproduce this trend fairly well, but it does not discriminate between $\sim$3–$\sim$4 combinations.
• Spectral indices: Model spectral indices exceed the observed values, and some observed disks have $\sim$5, which no model reproduces. The authors attribute this partly to missing non-thermal (free-free) emission and partly to optical depth effects: the companion multiwavelength analysis suggests many disks remain partially optically thick even at Band 3, whereas the models are predominantly optically thin. Notably, the models predict lower spectral indices for substructured than smooth disks, opposite to the observational finding — an unresolved discrepancy.
• Dust masses: Smooth-disk models systematically underpredict dust masses, particularly in Lupus and Upper Sco. Observed median dust masses separate sharply by morphology:

Region	Smooth median [$\sim$6]	Substructured median [$\sim$7]
Ophiuchus	7.5	16.5
Lupus	3.0	50.0
Upper Sco	0.7	8.4

The order-of-magnitude differences in Lupus and Upper Sco support long-term dust retention by pressure traps at later evolutionary stages. The underprediction also reflects the initial condition assumption: initializing with a 1% dust-to-gas ratio based on current gas masses understates the primordial dust reservoir if gas was lost over time.

• Best-fit parameters: Reduced-$\sim$8 comparison of radial profiles shows that roughly half the disks favor $\sim$9, $M_\odot$0, with no correlation between preferred parameters and morphology or age. However, the population-level trends in $M_\odot$1, $M_\odot$2, and $M_\odot$3 do not consistently favor any single combination — the configuration best matching dust masses ($M_\odot$4, $M_\odot$5) is among the least favored by radial profiles. This tension implies that no universal prescription of $M_\odot$6 and $M_\odot$7 applies across diagnostics, and that these parameters likely vary spatially and temporally within individual disks.

Pebble fluxes and cold water delivery

Pebble fluxes evaluated at the snowline decline strongly with disk age across all configurations, with absolute values varying by up to two orders of magnitude between parameter sets. At fixed parameters, substructured disks sustain higher pebble fluxes than smooth disks at late times, by up to $M_\odot$82–3 orders of magnitude in Lupus and Upper Sco; after normalizing to each disk's initial flux, the separation persists at older ages, indicating that leaky traps themselves prolong inward transport by continuously replenishing small grains through fragmentation. This is consistent with independent modeling showing trap-free disks undergoing steady flux decline while trapped disks converge to sustained fluxes.

The absolute fluxes ($M_\odot$9–$_2$0) are mostly below the $_2$1 required to build 2–5 $_2$2 cores within disk lifetimes. Integrated pebble masses span a wide range (median $_2$32 $_2$4, mean $_2$550 $_2$6, maximum $_2$71000 $_2$8), so many modeled disks fall short of supplying enough solids for sub-Neptune formation unless accretion is highly efficient — though this conclusion inherits the uncertainty in the assumed initial gas masses.

Regarding water delivery, the models do not recover the anti-correlation between cold water luminosity and dust disk size reported by Banzatti et al.; instead, they predict a positive correlation between cold water mass and the radial location of the innermost trap, strongest for $_2$9 (highest Pearson correlation coefficient). Measuring the slope of this relation observationally could discriminate between turbulence regimes, although the favored low-$^+$0 values conflict with accretion-rate constraints, pointing toward layered accretion or magnetized winds as complementary transport mechanisms.

Limitations and open questions

The principal limitations are acknowledged directly by the authors. Gas surface densities are fixed rather than co-evolved, despite evidence that viscous evolution alone cannot explain the observed $^+$1–$^+$2 spread and that winds may dominate gas dispersal; simultaneous gas–dust evolution including MHD winds and external photoevaporation is needed to tighten constraints on $^+$3 and $^+$4. Initial conditions rely on current gas masses with a fixed 1% dust-to-gas ratio, biasing pebble fluxes and dust masses low, especially for older systems. The FRANK resolution of 10–50 AU means substructures interior to these scales — which would affect both trapping efficiency and inferred pebble fluxes — may be missed, and unresolved structures in "smooth" disks could explain the dust-mass underpredictions. Finally, the single-$^+$5 treatment conflates vertical settling and radial transport, and the simplified settling prescription omits MHD-driven vertical mixing.

Conclusion

By applying uniform DustPy/RADMC-3D modeling to the well-characterized AGE-PRO sample, this work establishes that (i) no single $^+$6 combination reproduces all observed disk properties simultaneously, though radial profiles individually favor low turbulence in about half the disks; (ii) time evolution, not substructure presence, dominates the decline of inner pebble fluxes, with leaky traps sustaining fluxes only at later ages; and (iii) a measurable correlation between cold water abundance and innermost-trap location offers a concrete observational test, best expressed at $^+$7, for future JWST comparisons. Resolving the spectral-index discrepancy and the role of hidden inner substructures remains open, requiring higher-resolution observations and self-consistent gas–dust evolution models.