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Stefano Facchini

Publications and source records attributed to Stefano Facchini.

At least 37 records · Page 2Linked to original sources
arXiv2026

exoALMA XXI: The Morphology and Dynamics of Vertical Flows

Vertical gas flows, such as winds and meridional circulations, are natural outcomes of protoplanetary disk processes and play a critical role in the earliest stages of planet formation. We analyze vertical gas motions in 14 disks as part of the exoALMA Large Program, focusing on the 12CO J=3-2 and 13CO J=3-2 emission lines. Using discminer to model the Keplerian velocity field, we extract line-of-sight velocity residuals and measure the radial and vertical components of the gas motion. Vertical motions are detected in most disks. Two types of patterns emerge: (1) oscillatory up/down flows, likely linked to instabilities, and (2) transitions from downward to upward motions that we interpret as the base of a disk wind. In most cases, the velocity amplitudes are of a few tens of m/s. Two disks, however, MWC758 and CQ Tau, show two spiral velocity features in their residual maps, red- and blue-shifted, which we interpret as vertical velocities reaching up to 350 m/s (0.7 Cs), consistent with gas motion in eccentric disks. Fast upward motions (up to 500 m/s; 1.8 Cs) is also detected in the outer disk of MWC758. Synthetic observations from (magneto)hydrodynamic simulations validate the reliability of our method. Although strong molecular winds appear to be relatively rare in 12CO and 13CO, our study shows that, when traced by deep high spectral resolution line data, protoplanetary disks exhibit ubiquitous vertical flows. However, their overall velocity structure is highly complex, preventing to identify a coherent, dominant physical mechanism driving the vertical motions across all disks, thus requiring further theoretical investigation.

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arXiv2026

exoALMA XXIII. Estimating Disk and Planet Properties from Dust Morphologies with DBNets2.0

The exoALMA large program provided an unprecedented view of the morphology and kinematics of 15 circumstellar disks, offering a biased but homogenous and well-characterized sample for population-level analysis. Continuum observations revealed numerous dust substructures, known to be potential signatures of embedded planets. We analyze the observed dust morphologies with the simulation-based inference tool DBNets2.0, assuming these are due to embedded planets at fixed locations, to infer the system properties. We estimate the putative planet mass, the disk $α$-viscosity, scale-height, and dust Stokes number that would reproduce 19 substructures in 13 of the 15 exoALMA disks. We compare our results with literature estimates derived with different methods, and find good agreement in most cases. We further explore the implications of the inferred disk properties for accretion, showing that for the Herbig stars in our sample, the implied viscous accretion timescales are too long to account for their observed stellar accretion rates. Regarding planet migration, our results favor inward migration, with only three putative planets expected to migrate outward. Finally, we check for correlations of the inferred disk and planet properties with the disks' gas-to-dust mass ratio, non-axisymmetry index, and masses of the gas, dust, and host stars, finding no remarkable trend.

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arXiv2026

exoALMA XX: Tomographic Detection of Embedded Planets in Protoplanetary Disks

The exoALMA Large Program has revealed a wealth of substructures in the dust and molecular line emission of several protoplanetary discs, suggesting that planet formation may unfold within highly dynamic environments. Using synthetic observations of planet-disc interactions and disc instabilities, we demonstrate how the origin of these substructures can be investigated through a tomographic study of molecular lines, extending the scope of the analysis beyond line-centroid kinematics alone. Our results indicate that with only a few hours of ALMA integration at moderate angular resolution ($0.15''-0.30''$), it is possible to identify the key signatures driven by planets more massive than 0.1% of the stellar mass. These signatures manifest not only as deviations from Keplerian motion but also as localized line broadening, enabling accurate constraints on the orbital radius and azimuthal location of the planets. We further show that a diagnostic based on line skewness in spectrally resolved observations can help distinguish between planetary and instability-driven signatures, owing to the distinct degrees of velocity coherence associated with each mechanism. Finally, we apply this tomographic analysis to exoALMA CO line data for the discs of HD 135344B and MWC 758. In HD 135344B, we identify strongly localized velocity and line-width perturbations, suggesting the possibility of three massive planets embedded in the disc: one at $R=95$ au, exterior to the continuum substructures, and two within dust gaps at $R=41$ au and $R=73$ au. For MWC 758, the dominance of vertical-velocity spirals over localized signatures is consistent with predictions from models of moderate disc eccentricities or warps, potentially induced by a substellar companion in the inner regions of the system.

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arXiv2026

Hunting for methanol in the water rich, planet forming disk around HL Tau

Methanol, the simplest complex organic molecule found in space, is considered a key compound necessary for the formation of chemical species of prebiotic interest. Methanol detections in protoplanetary disks remain scarce, even though it is frequently detected in the material surrounding other Young Stellar Objects. We investigate the presence of methanol in the protoplanetary disk around the HL Tau protostar, motivated by the detection of spatially resolved warm water emission. Given the similar volatility of methanol and water, thermally desorbed gas-phase methanol is expected to emit from the same region of the HL Tau disk where water vapour has been observed. Accordingly, we selected and imaged the most promising ALMA archival observations to search for rotational methanol lines. We found no methanol emission in the analysed archival datasets. Assuming optically thin emission and LTE, we derive stringent upper limits on the methanol column density for different excitation temperatures: < 7.2 x 10^(14) cm^(-2) at 100 K and < 1.8 x 10^(15) cm^(-2) at 200 K, assuming a circular emitting region with a radius of 17 au (~ 0.12''). Furthermore, we obtain a stringent upper limit on the methanol-to-water column density ratio (< 0.55 x 10^(-3) at 100 K and < 1.4x 10^(-3) at 200 K), which is, on average, an order of magnitude lower than the values measured for other Young Stellar Objects and Solar System comets. We argue that the most likely explanation for the methanol non-detection in HL Tau is the presence of optically thick dust in the central region of the disk, which obscures part of the methanol emission. The upper limit on the methanol-to-water ratio in the HL Tau disk is at least an order of magnitude smaller than most clouds, YSOs and comets, possibly due to radiative transfer and/or excitation effects, or due to a different chemical evolution compared to the other sources.

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arXiv2026

Astrometric view of companions in the inner dust cavities of protoplanetary disks

Protoplanetary disks with inner dust cavities (often referred to as "transition disks") are potential signposts of planet formation. We use Gaia astrometry to search for planetary and stellar companions in a sample of 98 transition disks, assessing the occurrence rate of such companions and their potential influence on cavity formation. For the 98 Young Stellar Objects (YSOs), we compute Gaia proper motion anomalies which, together with the RUWE, identify companions with mass ratios $q \gtrsim 0.01$ at $\sim$0.1-30 au. We assess the impact of disk gravity, accretion, disk-scattered light, dippers, starspots, jets, and outflows on the measured proper motion anomalies, concluding that astrometric techniques such as the one of this work can be robustly applied to YSOs. Significant proper motion anomalies are found in 31 transition disks (32% of the sample), indicative of companions. We recover 85% of known companions within our sensitivity range. We model the semi-major axis and mass required for a companion to reproduce the observed astrometric signals. Most inferred companions have $M > 30$ M$\rm{_{J}}$, placing many within or near the stellar mass regime. Seven sources host companions compatible with a planetary mass ($M < 13$ M$\rm{_{J}}$, HD 100453, J04343128+1722201, J16102955-3922144, MHO6, MP Mus, PDS 70, and Sz 76). For the non-detections, we provide the companion masses and semi-major axes that can be excluded in future searches. About half (53%) of detected companions cannot be reconciled with having carved the observed dust cavities. We find that transition disks host as many companions within our sensitivity range as do randomly sampled groups of YSOs and main-sequence stars. If dust cavities are shaped by companions, such companions must reside at larger orbital separations than those of the companions detected here, and we predict them to be of planetary mass. [abridged]

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arXiv2026

Towards ALMA2040: An update from the European community and invitation to contribute

Over the last 15 years, the Atacama Large Millimeter/submillimeter Array (ALMA) has revolutionized astrophysics by providing unprecedented resolution and sensitivity in observing the cold universe, including the formation of stars, planets, and galaxies. With groundbreaking discoveries ranging from the first detailed images of protoplanetary disks to the kinematics of galaxies in the Epoch of Reionization, ALMA has showcased the vast discovery potential of the (sub-)mm wavelength regime. However, in another 15 years from now--in the 2040s--the science landscape will have changed dramatically as new major observational facilities will have started their operations or have come towards advanced maturity in their scientific outcome (e.g., JWST, Rubin Observatory, ELT, Euclid, Gaia, Plato, Ariel, Roman Space Telescope, SPHEREx, LiteBIRD, LISA, SKA and others). At the same time, ALMA's current Wideband Sensitivity Upgrade will have been in place for ~10 years, and ALMA itself will have been operational for 30 years. To fully exploit this era, the community needs a next-generation facility operating at (sub-)mm wavelengths with capabilities far beyond those possible within ALMA's current infrastructure. To this end, ALMA2040 is a community-driven initiative to define the key scientific questions of the 2040s and translate them into a technical vision for a next-generation transformational (sub-)millimeter facility. Our goal with this document is to summarize the current status of the effort, synthesize outcomes from the 2025 workshops, outline next steps toward a reference design concept, and invite broad participation from the global mm/sub-mm community to help shape this future facility. In the following we provide details on the process and scope. We invite everyone who wishes to join the effort and/or contribute to the dedicated White Papers planned for 2026.

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arXiv2026

A Protoplanet Candidate in the PDS 66 Disk Indicated by Silicon Sulfide Isotopologues

Despite observational progress in planet formation, the stage in which planetesimals grow into planets remains poorly understood. During this phase, protoplanets may develop gaseous envelopes that are warmer than the surrounding disk gas, potentially providing observable signatures through molecules otherwise depleted in cold regions. In this Letter, we report the detection of the silicon sulfide isotopologues ${\rm ^{28}SiS}\ J{=}16{-}15$ and ${\rm ^{30}SiS}\ J{=}18{-}17$ in the protoplanetary disk around PDS 66 (MP Mus) at a significance of ${\sim}5{-}6σ$, using the Atacama Large Millimeter/submillimeter Array. These constitute the second and first detections of $\rm ^{28}SiS$ and $\rm ^{30}SiS$ in a protoplanetary disk, respectively. The emission appears as a compact source at $r \simeq 60$ au in the southwestern region of the disk, unresolved with a ${\sim}0.\!\!^{\prime\prime}5$ beam, and shows a velocity consistent with Keplerian rotation, suggesting a protoplanetary origin. By modeling the line fluxes, we constrain the emitting radius to ${\sim}0.5{-}4$ au and estimate an SiS mass of $10^{22}{-}10^{23}$ g, corresponding to at least ${\sim}10\%$ of the silicon contained in local dust grains. Because complete sublimation of a substantial fraction of dust grains by local processes is difficult to achieve, this result instead implies an accumulation of silicon from a larger region. We propose that a circumplanetary envelope surrounding a low-mass protoplanet, where pebble accretion and subsequent sublimation of grains may enhance gaseus silicon abundance with respect to observable dust grains around it, can account for the observed characteristics.

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arXiv2026

exoALMA XIX: Confirmation of Non-thermal Line Broadening in the DM Tau Protoplanetary Disk

Turbulence is expected to transport angular momentum and drive mass accretion in protoplanetary disks. One way to directly measure turbulent motion in disks is through molecular line broadening. DM Tau is one of only a few disks with claimed detection of nonthermal line broadening of 0.25cs-0.33cs, where cs is the sound speed. Using the radiative transfer code mcfost within a Bayesian inference framework that evaluates over five million disk models to efficiently sample the parameter space, we fit high-resolution (0.15", 28 m s-1) 12CO J = 3-2 observations of DM Tau from the exoALMA Large Program. This approach enables us to simultaneously constrain the disk structure and kinematics, revealing a significant nonthermal contribution to the line width of ~0.4cs, inconsistent with purely thermal motions. Using the CO-based disk structure as a starting point, we reproduce the CS J = 7-6 emission well, demonstrating that the CS (which is more sensitive to nonthermal motions than CO) agrees with the turbulence inferred from the CO fit. Establishing a well-constrained background disk model further allows us to identify residual structures in the moment maps that deviate from the expected emission, revealing localized perturbations that may trace forming planets. This framework provides a powerful general approach for extracting disk structure and nonthermal broadening directly from molecular line data and can be applied to other disks with high-quality observations.

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arXiv2026

A 2 au resolution view by ALMA of the planet-hosting WISPIT 2 disk

We present deep, high spatial resolution interferometric observations of 0.88 mm continuum emission from the TYC 5709-354-1 system, hereafter WISPIT 2, obtained with the goal of detecting circumplanetary emission in the vicinity of the newly discovered WISPIT 2b planet. Observations with the most extended baseline configuration offered by ALMA, achieving an angular resolution of $25 \times 17$ mas ($3.3 \times 2.2$ au), revealed a single, narrow ring with a deprojected radius of 144.4 au and width of 7.2 au, and no evidence of circumplanetary emission within the cavity. Injection and recovery tests demonstrate that these observations can rule out point-like emission at the location of WISPIT 2b brighter than $\approx 45$ $μ$Jy at the $3σ$ level. While these data can rule out PDS 70c like circumplanetary emission, the upper limit is consistent with empirical mass-flux relationships extrapolated from the stellar regime. Visibility modeling of the continuum ring confirms that WISPIT 2b lies significantly interior to the mm dust ring, raising doubts about the ability of WISPIT 2b to be the only driver of the dust structure. Possible solutions include either another lower mass companion, residing between WISPIT 2b and the cavity edge, likely in the gap seen by SPHERE at $\sim130$ au, or that WISPIT 2b is either substantially more massive than IR-photometry based estimates ($\sim15$ $M_{\rm Jup}$) or on a moderately eccentric orbit. The combination of observations sensitive to the gas and dust distributions on larger spatial scales and dedicated hydrodynamical modeling will help differentiate between scenarios.

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arXiv2026

Circumplanetary Disk Candidate in the Disk of HD 163296 Traced by Localized Emission from Simple Organics

Atacama Large Millimeter/submillimeter Array observations suggest that the disc of HD 163296 is being actively shaped by embedded, yet unseen protoplanets, as indicated by numerous gas and dust substructures consistent with planet-disc interaction models. We report the first detection of simple organic molecules, HCN and C2H, tracing a candidate circumplanetary disc (CPD) in the HD 163296 system, located at an orbital radius of $R=88\pm7$ au and azimuth $ϕ=46\pm3^\circ$ (or $R=0.75''$, $\rm{PA}=350^\circ$ in projected sky coordinates), and originating near the midplane of the circumstellar disc. The signature is localised but spectrally resolved, and it overlaps with a previously reported planet candidate, P94, identified through kinematic perturbations traced by CO lines. We propose a scenario in which the observed chemical anomalies arise from increased heating driven by the forming planet and ongoing accretion through its CPD, facilitating the thermal desorption of species that would otherwise remain frozen out in the disc midplane, and potentially triggering the activation barriers of chemical reactions that lead to enhanced molecular production. Based on a first-order dynamical analysis of the HCN spectrum from the CPD--isolated with a 7$σ$ significance--we infer an upper limit on the planet mass of 1.8 $M_{\rm Jup}$, consistent with predictions from CO kinematics and constraints from direct imaging studies. By comparing the CPD sizes derived from our models with theoretical expectations where the CPD radius corresponds to roughly one-third of the planet's Hill radius, we favor CPD gas temperatures $T > 150$ K, planet masses $M_{\rm p} < 1.0$ $M_{\rm Jup}$, and CPD radii $R_{\rm CPD} < 2$ au.

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arXiv2026

Water vapor emission at the warm cavity wall of the HD 100546 disk as revealed by ALMA

We present spatially resolved ALMA observations of the water line at 183 GHz in the disk around the Herbig star HD 100546. The water vapor emission peaks at the inner edge of the warm dust cavity, located ~15 au from the central star. We attribute this to thermal desorption at the water snowline, shifted outward at the dust cavity wall directly heated by the intense radiation. This represents the first spatially resolved image of the water snowline using ALMA observations of the main water isotopologue in a protoplanetary disk. The water emission morphology peaking inside the first dust ring is consistent with previous ALMA detections of oxygen-bearing complex organic molecules in the disk, including thermally desorbed methanol. These findings signal that warm cavities of transition disks provide ideal targets to directly reconstruct the spatial distribution of water vapor and the snowline location with ALMA, and directly connect water vapor emission to ice desorption of complex organic species.

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arXiv2025

Spirals and Vertical Motions in the Planet-Forming Disk around HD 100546. A multi-line study of its gas kinematics

HD100546 represents a particularly interesting target to study dynamical planet-disk interactions as various features have been observed in both the dust and gas that provide direct and indirect evidence for ongoing planet formation. In this work, we aim to characterize the gas kinematics of five molecular CO emission lines observed with ALMA in HD 100546, to reveal deviations from Keplerian rotation as well as substructures in the peak intensity and line width. We fit the molecular intensity channels with the Discminer package to model the line profiles. Aside from fitting the full cube, we also conduct runs where the blue- and redshifted sides are modeled separately to search for possible asymmetries. Our analysis reveals prominent kinematical spiral features in all five lines on large scales of the disk and we reproduce their morphology with both a linear and logarithmic spiral. In 12CO 2-1, spirals are also seen in the peak intensity residuals, the line width residuals exhibit a prominent ring of enhanced line widths around 125-330 au. The models further show, that the emission from the redshifted side may originate from higher disk layers than that from the blueshifted side. The pitch angles of the spirals are consistent with those driven by an embedded companion inside of 50 au and they suggest a dynamical mechanism rather than gravitational instabilities. We further find indications of a companion around 90-150 au, where tentative dips are present in the radial profiles of the integrated intensity of 13CO and C18O and pressure minima are observed in the azimuthal velocities. For the first time, we also detect downward vertical flows in this region, which coincide with the observed dust gap. The asymmetry in the emission heights may be a result of infall from the disk's environment. Another explanation is provided by a warped inner disk, casting a shadow onto one side of the disk.

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arXiv2025

True spin-orbit obliquities distribution: data-driven confirmation of no clustering of misaligned planets

Context. True spin-orbit obliquities Ψ offer valuable insights into the evolutionary history of exoplanetary systems. Previous studies have suggested that exoplanets tend to occupy either aligned or perpendicular orbits. However, recent research has indicated potential biases caused by the low sample, questioning whether this dichotomy would persist with a larger dataset. Simultaneously, a similar dichotomous behavior has been suggested for Neptune-sized planets. Aims. We aim to investigate the distribution of true spin-orbit obliquities Ψ with an enlarged sample, looking for confirmation of the disputed dichotomy previously found, with a focus also on the obliquities of Neptunes. Methods. Starting from a sample of 264 projected obliquities λ, we homogeneously compute true obliquities Ψ for 116 planets using the rotation period method. We combine them with 4 further values gathered from literature and we then study their distribution, also as a function of various star-planet system parameters. Results. Our data-driven work based on 120 true obliquities Ψ - the largest sample to date - strongly confirms the presence of a single cluster of aligned planets, followed by an isotropic distribution of misaligned planets with no preferred misalignment. This result is based on a uniform distribution of stellar inclinations {i_\star} , for which non-uniformity could have biased previous interpretations of the arrangement of true obliquities. We confirm that Neptunians show a tentative dichotomous distribution with data available today, but its veracity needs confirmation with an enlarged sample, also because an anisotropic distribution of stellar inclination may be one of the factors hindering the real distribution.

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arXiv2025

Brightness variability in polar circumbinary disks

In binary systems with a strongly misaligned disk, the central binary stars can travel a significant vertical distance above and below the disk's orbital plane. This can cause large changes in illumination of the disk over the course of the binary orbital period. We use both analytic and radiative transfer models to examine the effect of changes in stellar illumination on the appearance of the disk, particularly in the case of the polar disk HD 98800B. We find that the observed flux from the disk can vary significantly over the binary orbital period, producing a periodically varying lightcurve which peaks twice each binary orbit. The amount of flux variation is strongly influenced by the disk geometry. We suggest that these flux variations produce several observable signatures, and that these observables may provide constraints on different properties of the disk such as its vertical structure, geometry, and cooling rate.

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arXiv2025

Pristine ices in a planet-forming disk revealed by heavy water

Water is essential to our understanding of the planet-formation process and habitability on Earth. Although trace amounts of water are seen across all phases of star and planet formation, the bulk of the water reservoir often goes undetected, hiding crucial parts of its journey from giant molecular clouds to planets. This raises the question of whether water molecules in comets and (exo-)planets is largely inherited from the interstellar medium or if the water molecules are destroyed and then reformed in the disk. Water isotopologue ratios involving doubly deuterated water (D$_2$O) are a sensitive tracer to answer this question. We present strong evidence of inheritance through an enhancement of D$_2$O in the outbursting V883 Ori disk. The high D$_2$O/H$_2$O ratio of $(3.2 \pm 1.2) \times 10^{-5}$ is consistent with values seen in protostellar envelopes and a comet and is two orders of magnitude higher than expected if water is reprocessed. The high deuteration of the heaviest isotopologues D$_2$O/HDO = $(2.3 \pm 1.0) \times $HDO/H$_2$O further establishes the inheritance of water. We conclude that water ice in disks originates from the earliest phases of star formation, providing the missing link between cold dark clouds and (exo-)comets.

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arXiv2025

Multi-frequency analysis of the ALMA and VLA high resolution continuum observations of the substructured disc around CI Tau. Preference for sub-mm-sized low-porosity amorphous carbon grains

(Abridged) We present high angular resolution and sensitivity ALMA 3.1 mm and VLA 9.1 mm observations of the disc around CI Tau. These new data were combined with similar-resolution archival ALMA 0.9 and 1.3 mm observations and new and archival VLA 7.1 mm, 2.0, 3.0, and 6.0 cm photometry to study the properties of dust in this system. At wavelengths <3.1 mm, CI Tau's continuum emission is very extended and highly substructured (with three gaps, four rings, and two additional gap-ring pairs identified by non-parametric visibility modelling). Instead, the VLA 9.1 mm data are dominated by a bright central component, only partially (< 50%) due to dust emission, surrounded by a marginally detected, faint, and smooth halo. We fitted the ALMA and VLA 9.1 mm data together, adopting a physical model that accounts for the effects of dust absorption and scattering. For our fiducial dust composition ("Ricci" opacities), we retrieved a flat maximum grain size distribution across the disc radius of $(7.1\pm0.8)\times10^{-2}$ cm, that we tentatively attributed to fragmentation of fragile dust or bouncing. We tested, for the first time, the dependence of our results on the adopted dust composition model to assess which mixture can best reproduce the observations. We found that the "Ricci" opacities work better than the traditionally adopted "DSHARP" ones, while graphite-rich mixtures perform significantly worse. We also show that, for our fiducial composition, the data prefer low-porosity (< 70%) grains, in contrast with claims of highly porous aggregates in younger sources, which we tentatively justified by time-dependent compaction. Our results are in line with constraints from disc population synthesis models and naturally arise from CI Tau's peculiar spectral behaviour, making this disc an ideal target for deeper cm-wavelength and dust polarisation follow-ups.

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arXiv2025

exoALMA. XVIII. Interpreting large scale kinematic structures as moderate warping

The exoALMA program gave an unprecedented view of the complex kinematics of protoplanetary disks, revealing diverse structures that remain poorly understood. We show that moderate disk warps ($\sim 0.5-2^\circ$) can naturally explain many of the observed large-scale velocity features with azimuthal wavenumber $m = 1$. Using a simple model, we interpret line-of-sight velocity variations as changes in the projected Keplerian rotation caused by warping of the disk. While not a unique explanation, this interpretation aligns with growing observational evidence that warps are common. We demonstrate that such warps can also produce spiral structures in scattered light and CO brightness temperature, with $\sim 10$ K variations in MWC 758. Within the exoALMA sample, warp properties correlate with stellar accretion rates, suggesting a link between the inner disc and outer disc kinematics. If warps cause large-scale kinematic structure, this has far reaching implications for turbulence, angular momentum transport, and planet formation.

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arXiv2025

Leaky dust trap in the PDS 70 disk revealed by ALMA Band 9 observations

We present new observations of the PDS 70 disc obtained with the Atacama Large Millimeter/sub-millimeter Array (ALMA) in Band 9 (671 GHz) at 0.242$^{\prime\prime}$ resolution, which provide valuable insights into the spatial distribution of sub-millimetre grains in the disc. The data reveal a ring-like morphology, with a radial peak located between those previously observed at infrared wavelengths and longer millimetre observations. Additionally, we detect a tentative outer shoulder in Band 9 that is not observed at longer wavelengths. These findings suggest that small grains ($\sim 100 μ$m) traced by Band 9 may be escaping from the pressure bump both radially inwards and outwards, or may be tracing different disc layers than those probed at longer wavelengths. A multi-wavelength analysis of the disc at millimetre wavelengths and the best fit to the spectral energy distribution shows the presence of centimetre grains around the ring location, where the dust surface density also peaks, compatible with dust trap models. The grain size in the disc cavity is not well constrained but is consistent with grains as small as 10 $μ$m, supporting the hypothesis that small dust grain filters through the cavity. We use dust evolution models to demonstrate that a turbulent viscosity of $α\gtrsim 10^{-3}$ allows small grains to filter through the disc gap, while $α\lesssim 5 \times 10^{-3}$ is required to retain large grains in the pressure bump. The Band 9 observations of PDS 70 validate theoretical models and confirm the presence of pebble flux through the disc gap.

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