arXiv subjects

Geoffroy Lesur

Publications and source records attributed to Geoffroy Lesur.

At least 19 recordsLinked to original sources

arXiv2026

Ionized gas emission in protoplanetary disks with the SKAO

Protoplanetary disks represent a crucial stage in the evolution of Young Stellar Objects towards the formation of fully formed planetary systems. While substantial progress has been made in the last decades in the characterization of the dust and molecular gas in these systems, the ionized component remains poorly understood. Ionized gas traces important processes such as photoevaporation, accretion, disk winds, and jets, and therefore is key to studying disk dynamics, evolution, and ultimately planet formation. In this paper, we investigate the capabilities of the forthcoming SKA telescope to probe this component in protoplanetary disks within nearby star forming regions. We present state-of-the-art simulations of photoevaporative, magneto-thermal, and magnetohydrodynamic winds, and generate theoretical predictions and synthetic SKAO observations to assess its potential in detecting and characterizing free-free emission and Hydrogen recombination lines. Finally, we discuss synergies with complementary facilities and how they will provide a comprehensive, multi-scale view of disk winds and offer critical insights on the mechanisms driving disk evolution and the onset of planet formation.

astro-ph.SR↗

arXiv2026

A nonrelativistic radiative transfer module for Idefix

Radiation magnetohydrodynamic (RMHD) simulations are essential for comparisons with observations, particularly in the regime where fluids and radiation are dynamically coupled. Although computationally expensive, RMHD is becoming increasingly accessible with the advent of exascale computing. However, only a few public RMHD codes are currently able to fully exploit the diversity of modern accelerated architectures. We present a nonrelativistic radiative transfer module for the public magnetohydrodynamic code IDEFIX; it is built on the Kokkos library to ensure performance portability. Our goal is to provide a user-friendly RMHD code capable of running efficiently on current and future exascale supercomputers. The radiative transfer module is based on the M1 approximation and implemented using a split explicit-implicit scheme. A reduced speed of light approximation is employed to alleviate the timestep constraint imposed by radiation. The module supports several radiation Riemann solvers and Cartesian, cylindrical, and spherical geometries in one, two, and three dimensions. The implicit step relies on a simple matrix inversion, ensuring both robustness and high performance. Users can choose between built-in opacity models or supply tabulated opacities and custom user-defined functions. The radiative module of IDEFIX demonstrates excellent performance on accelerated architectures, including the AMD MI250X and MI300 partitions of the AdAstra supercomputer. On MI250X nodes, it achieves up to $7.\times 10^8$ cell updates per second per node, at a computational cost only 1.6 times higher than a pure magnetohydrodynamic simulation. These results establish IDEFIX as a fast, robust, and portable RMHD code suitable for the wider community.

astro-ph.IM↗

arXiv2026

exoALMA XXII: A Two-dimensional Atlas of Deviations from Keplerian Disks

Protoplanetary disks are the birthplaces of planetary systems, and deviations from Keplerian rotation imprinted in disk gas kinematics serve as key tracers of physical processes and the presence of protoplanets within disks. Using the the CO (J=3-2) data from the exoALMA Large Program encompassing 15 disks, we constructed two-dimensional (2D) maps of centroid velocity, line width, and peak intensity, and extracted non-Keplerian deviations by subtracting smooth Keplerian models. This paper provides the first systematic and uniform overview of 2D gas substructures across the entire exoALMA sample. We find that all targets exhibit large-scale deviations from smooth Keplerian disks, displaying a variety of morphologies including spiral-like structures, arc- or ring-like features, and patterns indicative of variations in the emitting surface height. Non-axisymmetric spiral-arm features are detected or suggested in five disks (CQ Tau, MWC 758, HD 135344B, HD 34282, and SY Cha), and are preferentially found in Herbig Ae/Fe systems. In contrast, some other sources (J1852, PDS 66, and V4046 Sgr), despite exhibiting noticeable deviations, appear to be dynamically quieter. This 2D atlas suggests that kinematic substructures are ubiquitous in large ($\gtrsim$ 100 au) protoplanetary disks with ages of a few million years, based on the observations obtained with sufficient sensitivity at moderate-to-high spatial resolution of $\sim$20 au and high velocity resolution of $\sim$0.1 km s$^{-1}$.

astro-ph.EP↗

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.

astro-ph.EP↗

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.

astro-ph.EP↗

arXiv2026

A Comparative Study of the Streaming Instability: Unstratified Models with Marginally Coupled Grains

The streaming instability is a leading mechanism for concentrating solids and initiating planetesimal formation in protoplanetary disks. Although numerous studies have explored its linear growth, nonlinear evolution, and implications for planet formation, the diversity of numerical methods and dust treatments used across the literature has made it difficult to assess which features of the instability are physically robust and which arise from code-dependent choices. We present the first systematic comparison of seven hydrodynamic codes--spanning finite-volume and finite-difference schemes and modeling dust either as Lagrangian particles or as a pressureless fluid--applied to the unstratified streaming instability with a dimensionless stopping time of unity. All codes reproduce the characteristic sequence of exponential growth, filament formation, and turbulent saturation, demonstrating broad agreement in the qualitative behavior of the instability. Quantitatively, however, the dust model remains the dominant source of variation at moderate resolution: particle-based simulations reach higher peak densities and exhibit broader high-density tails than fluid-based models at $512^2$ resolution, although increasing the number of particles brings their initial maximum density evolution into close agreement with that of dust-fluid models. At $1024^2$, these differences diminish substantially, indicating better agreement of the saturated-state statistics across dust treatments. In terms of computational performance, most particle implementations suffer from imbalanced parallelized loads, while execution on a GPU is at least two to three times more energy efficient and scales better at higher resolutions than on CPUs. Given the intrinsic stochasticity of this nonlinear system, only statistical diagnostics remain meaningful across codes.

astro-ph.EP↗

arXiv2026

Global magnetohydrodynamic simulations of the inner regions of protoplanetary discs. II. Vertical-net-flux regime

The inner regions of protoplanetary discs, which encompass the putative habitable zone, are dynamically complex, featuring a relatively well-ionised, turbulent active zone located interior to a poorly ionised 'dead' zone. In this second paper, we investigate a model of the magnetohydrodynamic processes around the interface between these two regions, using five three-dimensional global magnetohydrodynamic simulations of discs threaded by a large-scale poloidal-net-flux magnetic field. We employ physically motivated profiles for Ohmic resistivity and ambipolar diffusion, alongside a simplified thermodynamic model comprising a cool disc and hot corona. Our results show that, first, the interface acts as a one-way barrier to inward transport of large-scale magnetic flux from the dead zone. This leads to magnetic flux depletion throughout most of the active zone, whereby it either advects inwards to the inner numerical boundary or accumulates just inside the interface. Second, two sources of strong variability emerge from the interface due to the difficulty of maintaining a constant, vertically integrated electrical current across distinct and evolving magnetic-field states. Third, despite the weak magnetothermal wind in the dead zone, a pressure maximum forms at the interface, leading to Rossby-wave-induced vortices. Fourth, unlike the model of Iwasaki et al. (2024), there is no 'transition zone' devoid of magnetic flux and magnetic winds. Instead, multiple outflow zones span all disc radii reflecting the radially varying launch conditions, with an inner turbulent wind impinging upon an outer, more laminar one. Fifth, a heated corona prevents the 'puffing up' of poloidal-net-flux, active disc regions.

astro-ph.EP↗

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.

astro-ph.EP↗

arXiv2026

Magnetic winds in resistive compact binary discs

Dwarf Novae and low-mass X-ray binaries are eruptive binary systems comprised of a Roche-lobe overflowing solar-type star and an accreting compact object. Their recurrence time can be explained by a low-accreting phase, the quiescence, during which the angular momentum transport parameter is inferred to be $\alpha \approx 0.01$ by the Disc Instability Model. Non-magnetics mechanisms, such as spiral wave transport, only achieve angular momentum transport an order of magnitude too low, at best, because these discs are so thin in quiescence. During this phase, the Magneto-rotational Instability is known to be suppressed by the increased resistivity of the weakly ionised plasma. Studying these thin magnetised discs is a numerical challenge because of the wide range of scales to be resolved. Thanks to the new GPU-accelerated code Idefix, we produce global 3D MHD simulations of a very thin disc $(H/R = 0.01)$ for the first time. We explore the possibility that an MHD wind arises and increases accretion in low magnetic Reynolds number $(\mathrm{Rm}\approx100)$ and realistic plasma parameter ($\beta \approx 1000$) regimes. We observe that the MRI is only quenched in the resistive disc bulk but survives in the disc atmosphere. This drives strong accretion and wind launching. We quantify the efficiency of the resulting wind and measure its global effect on the disc. We explore the effect of the initial disc magnetisation and compare the accretion/ejection regime with and without resistivity.

astro-ph.HE↗

arXiv2025

High-resolution models of the vertical shear instability

(abridged) Context: The vertical shear instability (VSI) is a promising mechanism to generate turbulence and transport angular momentum in protoplanetary discs. While most recent work has focused on adding more complex physics, the saturation properties of the instability in radially extended discs and its convergence as a function of resolution are still largely unknown. We tackle the question of VSI saturation and associated turbulence using radially extended fully 3D global disc models at very high resolution so as to capture both the largest VSI scales and the small-scale turbulent cascade. We use the GPU-accelerated code Idefix to achieve resolutions of up to 200 points per scale height in the 3 spatial directions, with a full 2pi azimuthal extent and disc aspect ratio H/R=0.1. Results: We demonstrate that large-scale transport properties are converged with 100 points per scale height, leading to a Shakura-Sunyaev alpha=1.3e-3. Inner boundary condition artifacts propagate deep inside the computational domain, leading to reduced alpha in these regions. The large-scale corrugation wave zones identified in 2D models survive in 3D, albeit with less coherence. Our models show no sign of long-lived zonal flows, pressure bumps or vortices, in contrast to lower-resolution simulations. Finally, we show that the turbulent cascade resulting from VSI saturation can be interpreted in the framework of critically balanced rotating turbulence. Conclusion: The VSI leads to vigorous turbulence in protoplanetary discs, associated with outward angular momentum transport but without any significant long-lived features that could enhance planet formation. The innermost regions of VSI simulations are always polluted by boundary-condition artifacts affecting the first VSI wave train, so radially extended domains should be used in a more systematic manner.

astro-ph.EP↗

arXiv2025

Global magnetohydrodynamic simulations of the inner regions of protoplanetary discs. I. Zero-net flux regime

The inner regions of protoplanetary discs, which encompass the putative habitable zone, are dynamically complex, featuring a well-ionised, turbulent active inner region and a poorly ionised `dead' outer region. In this first paper, we investigate a base-level model of the magnetohydrodynamic processes around the interface between these two regions, using five three-dimensional global magnetohydrodynamic simulations in the zero-net flux regime. We employ physically motivated profiles for Ohmic resistivity and ambipolar diffusion, alongside a simplified thermodynamic model comprising a cool disc and hot corona. Our results show that, first, large-scale coherent poloidal magnetic field loops form in the magnetorotational instability active region. These loops lead to the accumulation of tightly wound magnetic flux at the disc-corona temperature transition, driving strong, localised accretion flows in the surface layers of the active region. Second, an axisymmetric pressure maximum, extending across multiple disc scale heights, develops as a result of outward mass transport from the active region. This, in turn, triggers the Rossby wave instability and leads to the development of anticyclonic vortices. Third, the dead zone develops magnetic field with a distinct morphology, likely resulting from the outward diffusion of the large-scale poloidal loops in the active zone. This self-consistently generated field exhibits a vertical structure that can drive accretion in the inner dead zone via a weak magnetic-pressure wind. In the second paper in the series, we extend this work to the vertical-net flux regime, where global magnetic flux transport and magnetically driven outflows become dynamically significant.

astro-ph.EP↗

arXiv2025

exoALMA XIV. Gas Surface Densities in the RX J1604.3-2130 A Disk from Pressure-broadened CO Line Wings

The gas surface density is one of the most relevant physical quantities in protoplanetary disks. However, its precise measurement remains highly challenging due to the lack of a direct tracer. In this study, we report the spatially-resolved detection of pressure-broadened line wings in the CO $J=3-2$ line in the RX J1604.3-2130 A transition disk as part of the exoALMA large program. Since pressure-broadened line wings are sensitive to the total gas volume density, we robustly constrain the radial dependence of the gas surface density and midplane pressure in the region located $50-110$ au from the central star, which encompasses the dust ring of the system. The peak radius of the midplane pressure profile matches the dust ring radial location, directly proving radial dust trapping at a gas pressure maximum. The peak gas surface density is $18-44\ {\rm g\ cm^{-2}}$} and decreases at radii interior to and exterior of the dust ring. A comparison of the gas and dust surface densities suggests that the disk turbulence is as low as $\alpha_{\rm turb} \sim 2\times10^{-4}$. Despite dust trapping, the gas-to-dust surface density ratio at the ring peak is { $70-400$}, which implies already-formed protoplanets and/or less efficient dust trapping. The gas surface density drop at radii interior to the ring is consistent with a gas gap induced by a Jupiter-mass planet. The total gas mass within $50 < r < 110$ au is estimated to be $\sim 0.05-0.1\ M_\odot$ ($50-100\ {M_{\rm Jup}}$), suggesting that planetary system formation is possible.

astro-ph.EP↗

arXiv2025

exoALMA. XVI. Predicting Signatures of Large-scale Turbulence in Protoplanetary Disks

Turbulent gas motions drive planet formation and protoplanetary disk evolution. However, empirical constraints on turbulence are scarce, halting our understanding of its nature. Resolving signatures of the large-scale perturbations driven by disk instabilities may reveal clues on the origin of turbulence in the outer regions of planet-forming disks. We aim to predict the observational signatures of such large-scale flows, as they would appear in high-resolution Atacama Large Millimeter/submillimeter Array observations of CO rotational lines, such as those conducted by the exoALMA Large Program. Post-processing 3D numerical simulations, we explored the observational signatures produced by three candidate (magneto-)hydrodynamical instabilities to operate in the outer regions of protoplanetary disks: the vertical shear instability (VSI), the magneto-rotational instability (MRI), and the gravitational instability (GI). We found that exoALMA-quality observations should capture signatures of the large-scale motions induced by these instabilities. Mainly, flows with ring, arc, and spiral morphologies are apparent in the residuals of synthetic velocity centroid maps. A qualitative comparison between our predictions and the perturbations recovered from exoALMA data suggests the presence of two laminar disks and a scarcity of ring- and arc-like VSI signatures within the sample. Spiral features produced by the MRI or the GI are still plausible in explaining observed disk perturbations. Supporting these scenarios requires further methodically comparing the predicted perturbations and the observed disks' complex dynamic structure.

astro-ph.EP↗

arXiv2025

exoALMA XI: ALMA Observations and Hydrodynamic Models of LkCa 15: Implications for Planetary Mass Companions in the Dust Continuum Cavity

In the past decade, the Atacama Large Millimeter/submillimeter Array (ALMA) has revealed a plethora of substructures in the disks surrounding young stars. These substructures have several proposed formation mechanisms, with one leading theory being the interaction between the disk and newly formed planets. In this Letter, we present high angular resolution ALMA observations of LkCa~15's disk that reveal a striking difference in dust and CO emission morphology. The dust continuum emission shows a ring-like structure characterized by a dust-depleted inner region of $\sim$40 au in radius. Conversely, the CO emission is radially smoother and shows no sign of gas depletion within the dust cavity. We compare the observations with models for the disk-planet interaction, including radiative transfer calculation in the dust and CO emission. This source is particularly interesting as the presence of massive planets within the dust cavity has been suggested based on previous NIR observations. We find that the level of CO emission observed within the dust cavity is inconsistent with the presence of planets more massive than Jupiter orbiting between 10-40 au. Instead, we argue that the LkCa~15 innermost dust cavity might be created either by a chain of low-mass planets, or by other processes that do not require the presence of planets.

astro-ph.EP↗

arXiv2025

exoALMA II: Data Calibration and Imaging Pipeline

The exoALMA Large Program was designed to search for subtle kinematic deviations from Keplerian motion, indicative of embedded planets, in high angular and spectral resolution Band 7 observations of $^{12}$CO, $^{13}$CO and CS emission from protoplanetary disks. This paper summarizes the calibration and imaging pipelines used by the exoALMA collaboration. With sources ranging in diameter from 2.4" to 13.8" when probed by $^{12}$CO, multiple antennae configurations were required to maximally recover all spatial information (including the ACA for 7 sources). Combining these datasets warranted particular care in their alignment during calibration and prior to imaging, so as not to introduce spurious features that might resemble the kinematic deviations being investigated. Phase decoherence was found in several datasets, which was corrected by an iterative self-calibration procedure, and we explored the effects of the order of operations of spatial alignment, flux scaling, and self-calibration. A number of different imaging sets were produced for the continuum and line emission, employing an iterative masking procedure that minimizes bias due to non-Keplerian motions in the disk.

astro-ph.EP↗

arXiv2025

exoALMA. VI. Rotating under Pressure: Rotation curves, azimuthal velocity substructures, and pressure variations

The bulk motion of the gas in protoplanetary disks around newborn stars is nearly Keplerian. By leveraging the high angular and spectral resolution of ALMA, we can detect small-scale velocity perturbations in molecular line observations caused by local gas pressure variations in the disk, possibly induced by embedded protoplanets. This paper presents the azimuthally averaged rotational velocity and its deviations from Keplerian rotation ($\delta\upsilon_{\phi}$) for the exoALMA sample, as measured in the $^{12}$CO and $^{13}$CO emission lines. The rotation signatures show evidence for vertically stratified disks, in which $^{13}$CO rotates faster than $^{12}$CO due to a distinct thermal gas pressure gradient at their emitting heights. We find $\delta\upsilon_{\phi}$-substructures in the sample on both small ($\sim$10 au) and large ($\sim$100 au) radial scales, reaching deviations up to 15% from background Keplerian velocity in the most extreme cases. More than 75% of the rings and 80% of the gaps in the dust continuum emission resolved in $\delta\upsilon_{\phi}$ are co-located with gas pressure maxima and minima, respectively. Additionally, gas pressure substructures are observed far beyond the dust continuum emission. For the first time, we determined the gas pressure derivative at the midplane from observations and found it to align well with the dust substructures within the given uncertainties. Based on our findings, we conclude that gas pressure variations are likely the dominant mechanism for ring and gap formation in the dust continuum.

astro-ph.EP↗

arXiv2025

exoALMA. XVII. Characterizing the Gas Dynamics around Dust Asymmetries

The key planet-formation processes in protoplanetary disks remain an active matter of research. One promising mechanism to radially and azimuthally trap millimeter-emitting dust grains, enabling them to concentrate and grow into planetesimals, is anticyclonic vortices. While dust observations have revealed crescent structures in several disks, observations of their kinematic signatures are still lacking. Studying the gas dynamics is, however, essential to confirm the presence of a vortex and understand its dust trapping properties. In this work, we make use of the high-resolution and sensitivity observations conducted by the exoALMA large program to search for such signatures in the $^{12}$CO and $^{13}$CO molecular line emission of four disks with azimuthal dust asymmetries: HD 135344B, HD 143006, HD 34282, and MWC 758. To assess the vortex features, we constructed an analytical vortex model and performed hydrodynamical simulations. For the latter, we assumed two scenarios: a vortex triggered at the edge of a dead zone and of a gap created by a massive embedded planet. These models reveal a complex kinematical morphology of the vortex. When compared to the data, we find that none of the sources show a distinctive vortex signature around the dust crescents in the kinematics.

astro-ph.EP↗

arXiv2025

exoALMA XV: Interpreting the height of CO emission layer

The availability of exquisite data and the development of new analysis techniques have enabled the study of emitting heights in proto-planetary disks. In this paper we introduce a simple model linking the emitting height of CO to the disk surface density and temperature structure. We then apply the model to measurements of the emitting height and disk temperature conducted as part of exoALMA, integrated with additional legacy measurements from the MAPS Large Programme, to derive CO column densities and surface density profiles (assuming a CO abundance) for a total of 14 disks. A unique feature of the method we introduce to measure surface densities is that it can be applied to optically thick observations, rather than optically thin as conventionally done. While we use our method on a sample of well studied disks where temperature structures have been derived using two emission lines, we show that reasonably accurate estimates can be obtained also when only one molecular transition is available. With our method we obtain independent constraints from $^{12}$CO and $^{13}$CO and we find they are in general good agreement using the standard $^{12}$C/$^{13}$C isotopic ratio. The masses derived from our method are systematically lower compared with the values derived dynamically from the rotation curve if using an ISM CO abundance, implying that CO is depleted by a median factor $\sim$20 with respect to the ISM value, in line with other works that find that CO is depleted in proto-planetary disks.

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