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Francesco Zagaria

Publications and source records attributed to Francesco Zagaria.

At least 19 recordsLinked to original sources

Mapping the WISPIT2 Planet-Hosting Cavity at Sub-Hill-Radius scales

We present new deep, very high angular resolution observations of the sub-mm continuum (19x13 mas) and 12CO (67x52 mas) emission from the disk surrounding the planet host WISPIT2. Our analysis reveals a clear gas gap carved by WISPIT 2b and an empty cavity within the orbit of WISPIT 2c. We also find a gaseous and optically thin dusty ring located between the orbits of the two planets. Channel maps show a pronounced change in the emission surface height of the disk, which transitions from flat within the cavity to strongly flared beyond the orbit of planet b, producing clear breaks in the velocity channels. A pronounced thunderbolt-shaped feature, identified as a kinematic planetary signature (KPS), is detected at the location of WISPIT 2b, in agreement with predictions from planet-disk interaction simulations. This constitutes the first system with a confirmed kinematic signature associated with a directly imaged planet. By mirroring opposite velocity-channel maps about the systemic velocity, we further investigate the KPS and identify spatially resolved excess emission in the vicinity of WISPIT 2b. We find that this emission is resolved across the full Hill sphere of the planet, significantly exceeding the expected extent of a circumplanetary disk. We therefore suggest that the observed emission arises from a combination of processes, including prominent planet-driven spiral wakes, localized heating induced by the planet and a circumplanetary disk. Although higher spectral resolution is required to disentangle these contributions, our observations demonstrate the potential to directly characterize the birth environment of forming massive planets at scales down to sub-Hill radius.

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Dust characterization of the HD 163296 disk with high-resolution multi-wavelength ALMA observations

Context. Planets form through the growth and accumulation of dust grains in protoplanetary disks. Characterizing dust properties such as size, surface density, and temperature is key to understanding planet formation. Aims. We characterize the dust properties of the protoplanetary disk around HD 163296 by performing spectral energy distribution (SED) fitting of multi-wavelength high-resolution observations. Methods. We present new high-resolution ALMA Band 9 (0.45 mm) observations, which are sensitive to the temperature. We performed SED fitting at a common resolution of 0.066 arcsec using these new Band 9 observations along with archival ALMA Band 3, 4, 6, and 7 observations. We compared the fitted results with VLA observations and explored multiple dust models with different optical constants and porosities. Results. The Band 9 image shows the central disk, two rings at 0.67 and 1.00 arcsec, and outer extended emission previously seen at other wavelengths. At higher frequencies, the rings appear wider, the gaps appear shallower, and the extended emission appears brighter, which can be explained by optical-depth effects and/or size segregation. We characterized the dust properties, including temperature, surface density, and dust size, for each dust model. However, the inferred dust properties are dependent on the dust model, and the ALMA data alone do not allow us to determine which dust model is preferred. We identified the DSHARP Zubko (porous) model as the preferred model based on VLA profiles and physical and observational constraints. The outer ring temperature is lower than predicted by a passively irradiated disk model, suggesting shadowing by the inner ring. Although the surface density and dust size depend on the dust model, the preferred model indicates that the central disk, both rings, and the extended disk each contain more than a few Earth masses of dust.

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The 12CO Gas Structures of Protoplanetary Disks in the Upper Scorpius Region

We present measurements of key protoplanetary disk properties inferred from parametric models of ALMA 12CO spectral line visibilities. We derive gas-disk radii, integrated fluxes, optically thick emission layers, and brightness temperature profiles for the disk population of the old (4 - 14 Myr) Upper Scorpius star-forming region. We measure CO emission sizes for 37 disks with bright CO J=3-2 emission (S/N > 10 on the integrated flux; out of the 83 disks with CO detections), finding that the median radius containing 90% of the flux is ~84 au, with radii spanning from 23 up to 243 au. We report a correlation between the 12CO brightness temperatures and stellar luminosities, with a Pearson coefficient of 0.6, and we use it to prove that the 12CO optically thick emission layer primarily emanates from a region below the super-heated dust, which is optically thin to the stellar irradiation. Moreover, we derive 33 CO emission surface height profiles, finding a median aspect ratio ~ 0.16 in a range from ~0.01 up to ~0.45 over the sample. Finally, we comment on the multiple systems in our sample, of which only some were already known. These results re-affirm how it is possible to derive bulk disk properties by modeling moderate angular resolution ALMA visibilities.

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Compact CO emission and no evidence of radial drift. ALMA observations of the faintest planet-forming disks in Lupus

A large fraction of planet-forming disks observed with ALMA show faint CO emission, often interpreted as strong CO depletion. However, faint emission may also arise from spatially unresolved disks, whose sizes are overestimated, making them appear intrinsically faint. The limited sensitivity of previous observations has prevented testing this scenario, hindering our understanding of disk evolution and planet formation. We present new ALMA Band 7 observations of 12CO (J=3-2) and 13CO (J=3-2) in 17 of the faintest disks in Lupus, aiming to assess whether compact disk structure can explain their weak CO emission. The data reach an angular resolution of 0.25arcsec (about 20 au at 160 pc) and are an order of magnitude deeper than archival observations. We apply line stacking to enhance sensitivity and compare the derived CO luminosities with physical-chemical models of compact and extended disks, also estimating gas and dust sizes. We detect both isotopologues in 10 disks, only 12CO in 4, and neither in 3. Several disks are consistent with being intrinsically compact and optically thick in both lines, providing an alternative to the CO depletion scenario. The inferred gas radii (Rco less than 40 au) support this interpretation and suggest that a significant fraction of disks may be born compact, in line with recent Class 0/I results. Gas-to-dust size ratios show no clear evidence for dust evolution, indicating these disks are not drift-dominated.

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Large Dust Grains and a Possible Dust Trap in the Polar Circumbinary Disc of HD 98800B

HD 98800 is a nearby hierarchical quadruple system comprising two binaries orbiting each other. Surprisingly, despite its $\sim$ 10 Myr age and dynamic environment, the Ba-Bb component is surrounded by a compact gas-rich disc in a polar configuration. Previous millimetre continuum observations of this disc found a low millimetre spectral index ($α\sim$ 2.1 up to 9 mm), potentially arising from large dust grains, optically thick emission, or both. Furthermore, the interpretation was complicated by emission mechanisms other than dust thermal continuum at longer wavelengths. We present new observations of this system with the Very Large Array (VLA) at 6.8 mm and 3 cm, providing crucial additional sampling of the emission at millimetre/centimetre wavelengths. By combining these with ancillary data, we derive a dust spectral index $α_{\rm dust} <$ 3 for wavelengths $\le$ 1 cm. Our modeling suggests that the emission is optically thick at short millimetre wavelengths ($λ\le$ 3 mm) and it becomes at least partially optically thin for the VLA observations. The shallow spectral index thus indicates the existence of large grains in the disc. We also identify gyro-synchrotron emission from the A and B components at $λ\gtrsim $ 3 cm. The VLA images also reveal an azimuthal asymmetry at 6.8 mm and 8.8 mm, which is not present in high-resolution ALMA 1.3 mm data. After ruling out geometric and illumination effects, we interpret this asymmetry as a local dust overdensity, possibly induced by a vortex or a relic of the previous passage of the A component.

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The Circumbinary Disc of HD 34700A II. Analysis of a strong dust asymmetry

ALMA observations have shown that substructures are ubiquitous in protoplanetary discs. A sub-group, the transition discs, shows large cavities and rings in dust continuum. Among these, some present very high contrast asymmetries possibly due to the presence of vortices. HD 34700A is a binary system featuring a cavity, a ring, and multiple spiral arms detected in scattered light, a prominent crescent in the ALMA continuum and a complex gas morphology possibly connected with ongoing infall. We present new ALMA band 6 (1.3 mm) continuum images of the circumbinary disc around HD 34700A and compare them with two other systems showcasing high ($\gtrsim30$, measured as the peak-to-azimuthal-average ratio) contrast continuum asymmetries, IRS 48 and HD 142527. We aim to characterise the crescent morphology and discuss their possible origin. We perform visibility modelling of the new high resolution (0.''11x0.''09) ALMA band 6 continuum data of HD 34700A, together with improved visibility modelling of the other two targets. Our visibility model is in remarkable agreement with the HD 34700A data, featuring only localised residuals in the region of the disc corresponding to the tail of the asymmetry. We reproduce the double-peaked emission in HD 142527, and recover the crescent shape in IRS 48. We then run a hydrodynamic model of a vortex with different dust fluids, reproducing the general asymmetric crescent morphology observed in the HD 34700A and IRS 48 systems. With a combination of visibility, dust evolution and hydrodynamical models, we have constrained the morphology of the dust continuum emission of HD 34700A for the first time, and improved existing models for IRS 48 and HD 142527. The high azimuthal contrast of the asymmetries rules out the orbit clustering of eccentric cavities scenario, while the dust evolution models we consider suggest that the vortex scenario is a plausible option.

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Benchmarking pre-main sequence stellar evolutionary tracks using disk-based dynamical stellar masses

Stellar masses are a fundamental property to understand models of pre-main sequence evolution, but their values derived from Hertzsprung-Russell (HR) diagrams are strongly model dependent. We benchmark pre-main sequence stellar evolutionary tracks using stellar masses dynamically estimated by fitting a parametric model to ALMA observations of the $^{12}$CO $(J=3-2)$ line transition emitted by the disks orbiting 20 sources in the old ($4-14$ Myr) Upper Scorpius star forming region. We derive stellar masses from HR diagram fitting for ten different stellar evolutionary models, which we then compare with their stellar dynamical masses for comparison in the stellar mass range $0.1-1.3 \> M_\odot$. Models with a moderate-to-low fraction of cold stellar spots ($f=17\%$) most accurately reproduce the dynamical stellar masses ($100\%$ of the targets agree within $\pm1σ$). While a higher spot coverage ($f=34\%$) provides similar stellar mass predictions similar to magnetic equipartition models, larger fractions ($f\geq51\%$) significantly disagree with dynamical masses. Magnetic equipartition models overestimate stellar masses up to a factor $\sim20\%$, whereas non-magnetic models underestimate them up to $\sim12\%$. For some models, there is evidence that the stellar mass discrepancies are anticorrelated with dynamical stellar masses. When stellar dynamical mass priors are considered in HR diagram fitting, the median age of a single source can change up to $\sim25\%$, while the median ages inferred across different tracks become consistent, with the age scatter decreasing by $\gtrsim77\%$. These results provide strong empirical constraints for testing and developing evolutionary models of pre-main sequence stars.

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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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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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A young gas giant and hidden substructures in a protoplanetary disk

The detection of planets in protoplanetary disks has proven to be extremely challenging. In contrast, rings and gaps, usually attributed to planet-disk interactions, have been found in virtually every large protoplanetary (Class II) disk observed at 0.9-1.3 mm with sufficient spatial resolution (5 au). The nearby disk around MP Mus (PDS 66) stands as an exception to this rule, and its advanced age (7-10 Myr) is particularly difficult to reconcile with its apparent lack of substructures. Despite the disk's smooth appearance, Gaia data of MP Mus show a significant proper motion anomaly, signalling the presence of a companion. Here we present ALMA 3 mm observations of the system with comparable high spatial resolution to previous 1.3 mm data. The new observations pierce deeper into the disk midplane and reveal an inner cavity (<3 au) and a ring at 10 au. The disk structure inferred from ALMA observations narrows down the properties of the companion to a gas giant orbiting at 1-3 au, and hydrodynamic simulations further confirm that such a planet can produce the observed cavity. These independent pieces of evidence constitute an indirect but compelling detection of an exoplanet within a protoplanetary disk using Gaia astrometry. MP Mus is the first system in which undetected substructures are revealed thanks to the lower optical depths at longer wavelengths, suggesting that rings and gaps are even more abundant than what is currently believed.

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SO emission in the dynamically perturbed protoplanetary disks around CQ Tau and MWC 758

We report the serendipitous detection of the SO $J_N=6_5-5_4$ (219.949 GHz) rotational transition in archival Atacama Large Millimeter/submillimeter Array (ALMA) observations of the spiral hosting protoplanetary disks around CQ Tau (with $\approx4.9σ$ significance) and MWC 758 (with $\approx3.4σ$ significance). In the former, the SO emission comes in the shape of a ring, arises from the edge of the continuum cavity, and is qualitatively consistent, at the currently available spectral resolution, with being in Keplerian rotation. In the latter, instead, while arising primarily from inside the continuum cavity, the SO emission also extends to the continuum ring(s), and its morphology and kinematics are less clear. We put these sources in the context of the other protoplanetary disks where SO detections have been previously reported in the literature and discuss the possible origins of SO in terms of (thermal) desorption or formation in the gas phase. We argue that these processes might be fostered by dynamical perturbations caused by unseen embedded massive companions, shadows, or late-time infall, thus suggesting a possible link between perturbed dynamics and SO emission in (these) protoplanetary disks. If confirmed, our interpretation would imply that chemical evolution timescales could be significantly shorter in these systems than is commonly assumed, indicating that dynamical perturbations might influence the composition of newborn (proto-)planets by altering the volatile makeup of their formation environment.

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Inner disc and circumplanetary material in the PDS 70 system

The two giant protoplanets directly imaged in the dust-depleted cavity of PDS 70 offer a unique opportunity to study ongoing planet formation. Both planets have been detected in infrared thermal emission and in H$α$, indicating active accretion. We calibrate and analyse archival ALMA Band 6 and 7 observations of PDS 70 from 2019, 2021, and 2023 to search for circumplanetary material and assess its motion. Using 2D visibility modelling of the high-resolution (~0.11"x0.08" in Band 6; ~0.05"x0.05" in Band 7) dust continuum from the outer disc, we subtract the model and image the cavity at multiple epochs. We re-detect compact dust emission around PDS 70 c in all datasets with >$3.8σ$ significance, and tentatively detect emission near PDS 70 b at ~$3σ$ in Band 6, with peak fluxes of $59\pm17μ$Jy/beam and $46\pm14μ$Jy/beam. The relative astrometry of the compact emission around PDS 70 c is consistent with the expected position of the planet between 2019-2023. We find a peak flux difference up to $64\pm34μ$Jy/beam at 1$σ$, but Bayesian analysis indicates no significant variability. We detect no flux variability in the inner disc. The inferred dust mass near PDS 70 c and in the inner disc ranges from $0.008$-$0.063 M_\oplus$ and $0.04$-$0.31 M_\oplus$, respectively, consistent with prior estimates. Finally, we measure Band 6-7 spectral indices of $2.5\pm1.2$ (PDS 70 c) and $3.2\pm0.5$ (inner disc), suggesting that the inner disc emission is dominated by optically thin dust.

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Dust characterization of protoplanetary disks: a guide to multi-wavelength analyses and accurate dust mass measurements

Multi-wavelength dust continuum observations of protoplanetary disks are essential for accurately measuring two key ingredients of planets formation theories: the dust mass and grain size. Unfortunately, they are also extremely time-expensive. We aim to investigate the most economic way of performing this analysis. We benchmark the dust characterization analysis on multi-wavelength observations of two disk models. We test three different combinations of bands (in the 0.45 mm $\to$ 7.46 mm range) to see how optically thick and thin observations aid the reconstruction of the dust properties for different morphologies and in three different dust mass regimes. We also test different spatial resolutions. Dust properties are robustly measured in a multi-band analysis if optically thin observations are included. For typical disks, this requires wavelengths longer than 3 mm. High-resolution (< 0.03"-0.05") is fundamental to resolve the changes in dust content of substructures. However, lower-resolution results still provide an accurate measurement of the total dust mass and of the level of grain growth of rings. Additionally, we propose a new approach that successfully combines lower and higher resolution observations in the multi-wavelength analysis without losing spatial information. We also test individually enhancing the resolution of each radial intensity profile with Frank but we note the presence of artifacts. Finally, we discuss on the total dust mass that we derive from the SED analyses and compare it with the traditional method of deriving dust masses from millimeter fluxes. Accurate dust mass measurements from the SED analysis can be derived by including optically thin tracers. On the other hand, single-wavelength flux-based masses are always underestimated by even more than one order of magnitude.

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The centimeter emission from planet-forming disks in Taurus

The last decade has witnessed remarkable advances in the characterization of the (sub-)millimeter emission from planet-forming disks. Instead, the study of the (sub-)centimeter emission has made more limited progress, to the point that only a few exceptional disk-bearing objects have been characterized in the centimeter regime. This work takes a broad view of the centimeter emission from a large sample with VLA observations that is selected from previous ALMA surveys of more representative disks in brightness and extent. We report on the detection and characterization of flux at centimeter wavelengths from 21 sources in the Taurus star-forming region. Complemented by literature and archival data, the entire photometry from 0.85 mm to 6 cm is fitted by a two-component model that determines the ubiquitous presence of free-free emission entangled with the dust emission. The flux density of the free-free emission is found to scale with the accretion rate but is independent of the outer disk morphology depicted by ALMA. The dust emission at 2 cm is still appreciable, and offers the possibility to extract an unprecedented large set of dust spectral indices in the centimeter regime. A pronounced change between the median millimeter indices (2.3) and centimeter indices (2.8) suggests that a large portion of the disk emission is optically thick up to 3 mm. The comparison of both indices and fluxes with the ALMA disk extent indicates that this portion can be as large as 40 au, and suggests that the grain population within this disk region that emits the observed centimeter emission is similar in disks with different size and morphology. All these results await confirmation and dedicated dust modeling once facilities like ngVLA or SKA-mid are able to resolve the centimeter emission from planet-forming disks and disentangle the various components.

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Inner walls or vortices? Crescent-shaped asymmetries in ALMA observations of protoplanetary discs

Crescent-shaped asymmetries are common in millimetre observations of protoplanetary discs and are usually attributed to vortices or dust overdensities. However, they often appear on a single side of the major axis and roughly symmetric about the minor axis, suggesting a geometric origin. In this work, we interpret such asymmetries as emission from the exposed inner cavity walls of inclined discs and use them to characterise their vertical extent. Here we focus on the discs around CIDA 9 and RY Tau, first modelling their observations in visibility space with a simple geometric prescription for the walls, and then exploring more detailed radiative transfer models. Accounting for the wall emission yields significantly better residuals than purely axisymmetric models, and we estimate the dust scale height of these systems to be 0.4 au at 37 au for CIDA 9 and 0.2 au at 12 au for RY Tau. Finally, we identify crescent-shaped asymmetries in twelve discs, nine of which have constraints on their orientation - in all cases, the asymmetry appears on the far-side of the disc, lending support to the hypothesis that they are due to their inner rims. Modelling this effect in larger samples of discs will help to build a statistical view of their vertical structure.

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Observing planetesimal formation under streaming instability in the rings of HD 163296

We introduce a new technique to determine the gas turbulence and surface density in bright disc rings, under the assumption that dust growth is limited by turbulent fragmentation at the ring centre. We benchmark this prescription in HD 163296, showing that our measurements are consistent with available turbulence upper limits and agree with independent estimates of the gas surface density within a factor of two. We combine our results with literature measurements of the dust surface density and grain size to determine the dust-to-gas ratio and Stokes number in the 67 au and 100 au rings. Our estimates suggest that particle clumping is taking place under the effect of streaming instability (SI) in the 100 au ring. Even though in the presence of external isotropic turbulence this process might be hindered, we provide evidence that turbulence is non-isotropic in both rings and likely originating from mechanisms (such as ambipolar diffusion) that could ease particle clumping under SI. Finally, we determine the mass accretion rate under the assumption that the disc is in steady state and turbulence regulates angular momentum transport. Our results are in tension with spectroscopic measurements and suggest that other mechanisms might be responsible for accretion, in qualitative agreement with the detection of a magneto-centrifugal wind in this system. Applying our method to larger samples can be used to statistically assess if SI is a viable mechanism to form planetesimals in bright rings.

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Testing protoplanetary disc evolution with CO fluxes. A proof of concept in Lupus and Upper Sco

The Atacama Large Millimeter/submillimeter Array (ALMA) revolutionised our understanding of protoplanetary discs. However, the available data have not given conclusive answers yet on the underlying disc evolution mechanisms (viscosity or MHD winds). Improving upon the current results, mostly based on the analysis of disc sizes, is difficult because larger, deeper and higher angular resolution surveys would be required, which could be prohibitive even for ALMA. In this Letter, we introduce an alternative method to study disc evolution based on $^{12}$CO fluxes. In fact, fluxes can be readily collected using less time-consuming, lower resolution observations, while tracing the same disc physico-chemical processes as sizes: assuming that $^{12}$CO is optically thick, fluxes scale with the disc surface area. We developed a semi-analytical model to compute $^{12}$CO fluxes and benchmarked it against the results of DALI thermochemical models, recovering an agreement within a factor of three. As a proof of concept we compared our models with Lupus and Upper Sco data, taking advantage of the increased samples, by a factor 1.3 (Lupus) and 3.6 (Upper Sco), when studying fluxes instead of sizes. Models and data agree well only if CO depletion is considered. However, the uncertainties on the initial conditions limited our interpretation of the observations. Our new method can be used to design future ad hoc observational strategies to collect better data and give conclusive answers on disc evolution.

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Dust dynamics in planet-forming discs in binary systems

In multiple stellar systems interactions among the companion stars and their discs affect planet formation. In the circumstellar case tidal truncation makes protoplanetary discs smaller, fainter and less long-lived than those evolving in isolation, thereby reducing the amount of material (gas and dust) available to assemble planetary embryos. On the contrary, in the circumbinary case the reduced accretion can increase the disc lifetime, with beneficial effects on planet formation. In this chapter we review the main observational results on discs in multiple stellar systems and discuss their possible explanations, focusing on recent numerical simulations, mainly dealing with dust dynamics and disc evolution. Finally, some open issues and future research directions are examined.

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