arXiv subjects

Sean M. Andrews

Publications and source records attributed to Sean M. Andrews.

At least 127 records · Page 7Linked to original sources

arXiv2020

An evolutionary study of volatile chemistry in protoplanetary disks

The volatile composition of a planet is determined by the inventory of gas and ice in the parent disk. The volatile chemistry in the disk is expected to evolve over time, though this evolution is poorly constrained observationally. We present ALMA observations of C18O, C2H, and the isotopologues H13CN, HC15N, and DCN towards five Class 0/I disk candidates. Combined with a sample of fourteen Class II disks presented in Bergner et al. (2019b), this data set offers a view of volatile chemical evolution over the disk lifetime. Our estimates of C18O abundances are consistent with a rapid depletion of CO in the first ~0.5-1 Myr of the disk lifetime. We do not see evidence that C2H and HCN formation are enhanced by CO depletion, possibly because the gas is already quite under-abundant in CO. Further CO depletion may actually hinder their production by limiting the gas-phase carbon supply. The embedded sources show several chemical differences compared to the Class II stage, which seem to arise from shielding of radiation by the envelope (impacting C2H formation and HC15N fractionation) and sublimation of ices from infalling material (impacting HCN and C18O abundances). Such chemical differences between Class 0/I and Class II sources may affect the volatile composition of planet-forming material at different stages in the disk lifetime.

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arXiv2020

Dual-Wavelength ALMA Observations of Dust Rings in Protoplanetary Disks

We present new Atacama Large Millimeter/submillimeter Array (ALMA) observations for three protoplanetary disks in Taurus at 2.9\,mm and comparisons with previous 1.3\,mm data both at an angular resolution of $\sim0.''1$ (15\,au for the distance of Taurus). In the single-ring disk DS Tau, double-ring disk GO Tau, and multiple-ring disk DL Tau, the same rings are detected at both wavelengths, with radial locations spanning from 50 to 120\,au. To quantify the dust emission morphology, the observed visibilities are modeled with a parametric prescription for the radial intensity profile. The disk outer radii, taken as 95\% of the total flux encircled in the model intensity profiles, are consistent at both wavelengths for the three disks. Dust evolution models show that dust trapping in local pressure maxima in the outer disk could explain the observed patterns. Dust rings are mostly unresolved. The marginally resolved ring in DS Tau shows a tentatively narrower ring at the longer wavelength, an observational feature expected from efficient dust trapping. The spectral index ($α_{\rm mm}$) increases outward and exhibits local minima that correspond to the peaks of dust rings, indicative of the changes in grain properties across the disks. The low optical depths ($τ\sim$0.1--0.2 at 2.9\,mm and 0.2--0.4 at 1.3\,mm) in the dust rings suggest that grains in the rings may have grown to millimeter sizes. The ubiquitous dust rings in protoplanetary disks modify the overall dynamics and evolution of dust grains, likely paving the way towards the new generation of planet formation.

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arXiv2020

Protoplanetary disk masses in NGC 2024: Evidence for two populations

Protoplanetary disks in dense, massive star-forming regions are strongly affected by their environment. How this environmental impact changes over time is an important constraint on disk evolution and external photoevaporation models. We characterize the dust emission from 179 disks in the core of the young (0.5 Myr) NGC 2024 cluster. By studying how the disk mass varies within the cluster, and comparing these disks to those in other regions, we aim to determine how external photoevaporation influences disk properties over time. Using the Atacama Large Millimeter/submillimeter Array, a 2.9' x 2.9' mosaic centered on NGC 2024 FIR 3 was observed at 225 GHz with a resolution of 0.25'', or ~100 AU. The imaged region contains 179 disks identified at IR wavelengths, seven new disk candidates, and several protostars. The overall detection rate of disks is $32 \pm 4\%$. Few of the disks are resolved, with the exception of a giant (R = 300 AU) transition disk. Serendipitously, we observe a millimeter flare from an X-ray bright young stellar object (YSO), and resolve continuum emission from a Class 0 YSO in the FIR 3 core. Two distinct disk populations are present: a more massive one in the east, along the dense molecular ridge hosting the FIR 1-5 YSOs, with a detection rate of $45 \pm 7\%$. In the western population, towards IRS 1, only $15 \pm 4\%$ of disks are detected. NGC 2024 hosts two distinct disk populations. Disks along the dense molecular ridge are young (0.2 - 0.5 Myr) and partly shielded from the far ultraviolet radiation of IRS 2b; their masses are similar to isolated 1 - 3 Myr old SFRs. The western population is older and at lower extinctions, and may be affected by external photoevaporation from both IRS 1 and IRS 2b. However, it is possible these disks had lower masses to begin with.

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arXiv2020

Measuring turbulent motion in planet-forming disks with ALMA: A detection around DM Tau and non-detections around MWC 480 and V4046 Sgr

Turbulence is a crucial factor in many models of planet formation, but it has only been directly constrained among a small number of planet forming disks. Building on the upper limits on turbulence placed in disks around HD 163296 and TW Hya, we present ALMA CO J=2-1 line observations at $\sim0.3"$ (20-50 au) resolution and 80 ms$^{-1}$ channel spacing of the disks around DM Tau, MWC 480, and V4046 Sgr. Using parametric models of disk structure, we robustly detect non-thermal gas motions around DM Tau of between 0.25 c$_s$ and 0.33 c$_s$, with the range dominated by systematic effects, making this one of the only systems with directly measured non-zero turbulence. Using the same methodology, we place stringent upper limits on the non-thermal gas motion around MWC 480 ($<$0.08c$_s$) and V4046 Sgr ($<$0.12 c$_s$). The preponderance of upper limits in this small sample, and the modest turbulence levels consistent with dust studies, suggest that weak turbulence ($α\lesssim10^{-3}$) may be a common, albeit not universal, feature of planet-forming disks. We explore the particular physical conditions around DM Tau that could lead this system to be more turbulent than the others.

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arXiv2020

ALMA 0.88 mm Survey of Disks around Planetary-mass Companions

Characterizing the physical properties and compositions of circumplanetary disks can provide important insights into the formation of giant planets and satellites. We report ALMA 0.88 mm (Band 7) continuum observations of six planetary-mass (10-20 $M_{\rm Jup}$) companions: CT Cha b, 1RXS 1609 b, ROXs 12 b, ROXs 42B b, DH Tau b, and FU Tau b. No continuum sources are detected at the locations of the companions down to 3$σ$ limits of 120-210 $μ$Jy. Given these non-detections, it is not clear whether disks around planetary-mass companions indeed follow the disk flux-host mass trend in the stellar regime. The faint radio brightness of these companion disks may result from a combination of fast radial drift and a lack of dust traps. Alternatively, as disks in binary systems are known to have significantly lower millimeter fluxes due to tidal interactions, these companion disks may instead follow the relationship of moderate-separation binary stars. This scenario can be tested with sensitive continuum imaging at rms levels of $\lesssim$10 $μ$Jy.

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arXiv2020

An ALMA Survey of H$_2$CO in Protoplanetary Disks

H$_2$CO is one of the most abundant organic molecules in protoplanetary disks and can serve as a precursor to more complex organic chemistry. We present an ALMA survey of H$_2$CO towards 15 disks covering a range of stellar spectral types, stellar ages, and dust continuum morphologies. H$_2$CO is detected towards 13 disks and tentatively detected towards a 14th. We find both centrally-peaked and centrally-depressed emission morphologies, and half of the disks show ring-like structures at or beyond expected CO snowline locations. Together these morphologies suggest that H$_2$CO in disks is commonly produced through both gas-phase and CO-ice-regulated grain-surface chemistry. We extract disk-averaged and azimuthally-averaged H$_2$CO excitation temperatures and column densities for four disks with multiple H$_2$CO line detections. The temperatures are between 20-50K, with the exception of colder temperatures in the DM Tau disk. These temperatures suggest that H$_2$CO emission in disks is generally emerging from the warm molecular layer, with some contributions from the colder midplane. Applying the same H$_2$CO excitation temperatures to all disks in the survey, we find that H$_2$CO column densities span almost three orders of magnitude ($\sim 5 \times 10^{11} - 5 \times 10^{14} \mathrm{cm}^{-2}$). The column densities appear uncorrelated with disk size and stellar age, but Herbig Ae disks may have less H$_2$CO compared to T Tauri disks, possibly because of less CO freeze-out. More H$_2$CO observations towards Herbig Ae disks are needed to confirm this tentative trend, and to better constrain under which disk conditions H$_2$CO and other oxygen-bearing organics efficiently form during planet formation.

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arXiv2020

A multi-frequency ALMA characterization of substructures in the GM Aur protoplanetary disk

The protoplanetary disk around the T Tauri star GM Aur was one of the first hypothesized to be in the midst of being cleared out by a forming planet. As a result, GM Aur has had an outsized influence on our understanding of disk structure and evolution. We present 1.1 and 2.1 mm ALMA continuum observations of the GM Aur disk at a resolution of ~50 mas (~8 au), as well as HCO$^+$ $J=3-2$ observations at a resolution of ~100 mas. The dust continuum shows at least three rings atop faint, extended emission. Unresolved emission is detected at the center of the disk cavity at both wavelengths, likely due to a combination of dust and free-free emission. Compared to the 1.1 mm image, the 2.1 mm image shows a more pronounced "shoulder" near R~40 au, highlighting the utility of longer-wavelength observations for characterizing disk substructures. The spectral index $α$ features strong radial variations, with minima near the emission peaks and maxima near the gaps. While low spectral indices have often been ascribed to grain growth and dust trapping, the optical depth of GM Aur's inner two emission rings renders their dust properties ambiguous. The gaps and outer disk ($R>100$ au) are optically thin at both wavelengths. Meanwhile, the HCO$^+$ emission indicates that the gas cavity is more compact than the dust cavity traced by the millimeter continuum, similar to other disks traditionally classified as "transitional."

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arXiv2020

Observations of Protoplanetary Disk Structures

The disks that orbit young stars are the essential conduits and reservoirs of material for star and planet formation. Their structures, meaning the spatial variations of the disk physical conditions, reflect the underlying mechanisms that drive those formation processes. Observations of the solids and gas in these disks, particularly at high resolution, provide fundamental insights on their mass distributions, dynamical states, and evolutionary behaviors. Over the past decade, rapid developments in these areas have largely been driven by observations with the Atacama Large Millimeter/submillimeter Array (ALMA). This review highlights the state of observational research on disk structures, emphasizing three key conclusions that reflect the main branches of the field: (1) Relationships among disk structure properties are also linked to the masses, environments, and evolutionary states of their stellar hosts; (2) There is clear, qualitative evidence for the growth and migration of disk solids, although the implied evolutionary timescales suggest the classical assumption of a smooth gas disk is inappropriate; and (3) Small-scale substructures with a variety of morphologies, locations, scales, and amplitudes -- presumably tracing local gas pressure maxima -- broadly influence the physical and observational properties of disks. The last point especially is reshaping the field, with the recognition that these disk substructures likely trace active sites of planetesimal growth or are the hallmarks of planetary systems at their formation epoch.

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arXiv2019

The DSHARP Rings: Evidence of Ongoing Planetesimal Formation?

Recent high-resolution interferometric observations of protoplanetary disks at (sub-)millimeter wavelengths reveal omnipresent substructures, such as rings, spirals, and asymmetries. A detailed investigation of eight rings detected in five disks by the DSHARP survey came to the conclusion that all rings are just marginally optically thick with optical depths between 0.2 and 0.5 at a wavelength of 1.25 mm. This surprising result could either be coincidental or indicate that the optical depth in all of the rings is regulated by the same process. We investigated if ongoing planetesimal formation could explain the "fine-tuned" optical depths in the DSHARP rings by removing dust and transforming it into "invisible" planetesimals. We performed a one-dimensional simulation of dust evolution in the second dust ring of the protoplanetary disk around HD 163296, including radial transport of gas and dust, dust growth and fragmentation, and planetesimal formation via gravitational collapse of sufficiently dense pebble concentrations. We show that planetesimal formation can naturally explain the observed optical depths if streaming instability regulates the midplane dust-to-gas ratio to unity. Furthermore, our simple monodisperse analytical model supports the hypothesis that planetesimal formation in dust rings should universally limit their optical depth to the observed range.

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arXiv2019

Probing CO and N$_2$ Snow Surfaces in Protoplanetary Disks with N$_2$H$^+$ Emission

Snowlines of major volatiles regulate the gas and solid C/N/O ratios in the planet-forming midplanes of protoplanetary disks. Snow surfaces are the 2D extensions of snowlines in the outer disk regions, where radiative heating results in a decreasing temperature with disk height. CO and N$_2$ are two of the most abundant carriers of C, N and O. N$_2$H$^+$ can be used to probe the snow surfaces of both molecules, because it is destroyed by CO and formed from N$_2$. Here we present Atacama Large Millimeter/submillimeter Array (ALMA) observations of N$_2$H$^+$ at 0.2$''$-0.4$''$ resolution in the disks around LkCa 15, GM Aur, DM Tau, V4046 Sgr, AS 209, and IM Lup. We find two distinctive emission morphologies: N$_2$H$^+$ is either present in a bright, narrow ring surrounded by extended tenuous emission, or in a broad ring. These emission patterns can be explained by two different kinds of vertical temperature structures. Bright, narrow N$_2$H$^+$ rings are expected in disks with a thick Vertically Isothermal Region above the Midplane (VIRaM) layer (LkCa 15, GM Aur, DM Tau) where the N$_2$H$^+$ emission peaks between the CO and N$_2$ snowlines. Broad N$_2$H$^+$ rings come from disks with a thin VIRaM layer (V4046 Sgr, AS 209, IM Lup). We use a simple model to extract the first sets of CO and N$_2$ snowline pairs and corresponding freeze-out temperatures towards the disks with a thick VIRaM layer. The results reveal a range of N$_2$ and CO snowline radii towards stars of similar spectral type, demonstrating the need for empirically determined snowlines in disks.

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arXiv2019

The Degree of Alignment Between Circumbinary Disks and Their Binary Hosts

All four circumbinary (CB) protoplanetary disks orbiting short-period ($P < 20$ day) double-lined spectroscopic binaries (SB2s)---a group that includes UZ Tau E, for which we present new ALMA data---exhibit sky-plane inclinations $i_{\rm disk}$ which match, to within a few degrees, the sky-plane inclinations $i_\star$ of their stellar hosts. Although for these systems the true mutual inclinations $θ$ between disk and binary cannot be directly measured because relative nodal angles are unknown, the near-coincidence of $i_{\rm disk}$ and $i_\star$ suggests that $θ$ is small for these most compact of systems. We confirm this hypothesis using a hierarchical Bayesian analysis, showing that 68% of CB disks around short-period SB2s have $θ< 3.0^\circ$. Near co-planarity of CB disks implies near co-planarity of CB planets discovered by Kepler, which in turn implies that the occurrence rate of close-in CB planets is similar to that around single stars. By contrast, at longer periods ranging from $30-10^5$ days (where the nodal degeneracy can be broken via, e.g., binary astrometry), CB disks exhibit a wide range of mutual inclinations, from co-planar to polar. Many of these long-period binaries are eccentric, as their component stars are too far separated to be tidally circularized. We discuss how theories of binary formation and disk-binary gravitational interactions can accommodate all these observations.

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arXiv2019

One Solution to the Mass Budget Problem for Planet Formation: Optically Thick Disks with Dust Scattering

ALMA surveys have suggested that the dust in Class II disks may not be enough to explain the averaged solid mass in exoplanets, under the assumption that the mm disk continuum emission is optically thin. This optically thin assumption seems to be supported by recent DSHARP observations where the measured optical depths of spatially resolved disks are mostly less than one. However, we point out that dust scattering can considerably reduce the emission from an optically thick region. If that scattering is ignored, the optical depth will be considerably underestimated. An optically thick disk with scattering can be misidentified as an optically thin disk. Dust scattering in more inclined disks can reduce the intensity even further, making the disk look even fainter. The measured optical depth of $\sim$0.6 in several DSHARP disks can be naturally explained by optically thick dust with an albedo of $\sim$0.9 at 1.25 mm. Using the DSHARP opacity, this albedo corresponds to a dust population with the maximum grain size ($s_{max}$) of 0.1-1 mm. For optically thick scattering disks, the measured spectral index $α$ can be either larger or smaller than 2 depending on if the dust albedo increases or decreases with wavelength. Using the DSHARP opacity, $α<2$ corresponds to $s_{max}$ of 0.03-0.3 mm. We describe how this optically thick scattering scenario could explain the observed scaling between submm continuum sizes and luminosities, and might help ease the tension between the dust size constraints from polarization and dust continuum measurements. We suggest that a significant amount of disk mass can be hidden from ALMA observations at short millimeter wavelengths. For compact disks smaller than 30 au, we can easily underestimate the dust mass by more than a factor of 10. Longer wavelength observations (e.g. VLA or SKA) are desired to probe the dust mass in disks.

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arXiv2019

Constraints on a Putative Planet Sculpting the V4046 Sagittarii Circumbinary Disk

We analyze the highest-resolution millimeter continuum and near-infrared (NIR) scattered-light images presented to date of the circumbinary disk orbiting V4046 Sgr, a ~20 Myr old actively accreting, close binary T Tauri star system located a mere 72.4 pc from Earth. We observed the disk with the Atacama Large Millimeter/submillimeter Array (ALMA) at 870-micron during Cycle 4, and we analyze these data in conjunction with archival NIR (H band) polarimetric images obtained with SPHERE/IRDIS on the ESO Very Large Telescope. At 0.3'' (20 au) resolution, the 870-micron image reveals a marginally resolved ring that peaks at ~32 au and has an extension of ~ 90 au. We infer a lower limit on dust mass of ~ 60.0 M_earth within the 870-micron ring, and confirm that the ring is well aligned with the larger-scale gaseous disk. A second, inner dust ring is also tentatively detected in the ALMA observations; its position appears coincident with the inner (~14 au radius) ring detected in scattered light. Using synthetic 870 micron and H-band images obtained from disk-planet interaction simulations, we attempt to constrain the mass of the putative planet orbiting at 20 au. Our trials suggest that a circumbinary Jovian-mass planet may be responsible for generating the dust ring and gap structures detected within the disk. We discuss the longevity of the gas-rich disk orbiting V4046 Sgr in the context of the binary nature of the system.

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arXiv2019

The Disk Substructures at High Angular Resolution Project (DSHARP): III. Spiral Structures in the Millimeter Continuum of the Elias 27, IM Lup, and WaOph 6 Disks

We present an analysis of ALMA 1.25 millimeter continuum observations of spiral structures in three protoplanetary disks from the Disk Substructures at High Angular Resolution Project. The disks around Elias 27, IM Lup, and WaOph 6 were observed at a resolution of $\sim40-60$ mas ($\sim6-7$ au). All three disks feature $m=2$ spiral patterns in conjunction with annular substructures. Gas kinematics established by $^{12}$CO $J=2-1$ observations indicate that the continuum spiral arms are trailing. The arm-interarm intensity contrasts are modest, typically less than 3. The Elias 27 spiral pattern extends throughout much of the disk, and the arms intersect the gap at $R\sim69$ au. The spiral pattern in the IM Lup disk is particularly complex-it extends about halfway radially through the disk, exhibiting pitch angle variations with radius and interarm features that may be part of ring substructures or spiral arm branches. Spiral arms also extend most of the way through the WaOph 6 disk, but the source overall is much more compact than the other two disks. We discuss possible origins for the spiral structures, including gravitational instability and density waves induced by a stellar or planetary companion. Unlike the millimeter continuum counterparts of many of the disks with spiral arms detected in scattered light, these three sources do not feature high-contrast crescent-like asymmetries or large ($R>20$ au) emission cavities. This difference may point to multiple spiral formation mechanisms operating in disks.

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arXiv2018

The Disk Substructures at High Angular Resolution Project (DSHARP): IV. Characterizing substructures and interactions in disks around multiple star systems

To characterize the substructures induced in protoplanetary disks by the interaction between stars in multiple systems, we study the $1.25\,$mm continuum and the $^{12}$CO$(J=2-1)$ spectral line emission of the triple systems HT Lup and AS 205, at scales of $\approx 5\,$au, as part of the 'Disk Substructures at High Angular Resolution Project' (DSHARP). In the continuum emission, we find two symmetric spiral arms in the disk around AS 205 N, with pitch angle of $14^\circ$, while the southern component AS 205 S, itself a spectroscopic binary, is surrounded by a compact inner disk and a bright ring at a radius of $34\,$au. The $^{12}$CO line exhibits clear signatures of tidal interactions, with spiral arms, extended arc-like emission, and high velocity gas, possible evidence of a recent close encounter between the disks in the AS 205 system, as these features are predicted by hydrodynamic simulations of fly-by encounters. In the HT Lup system, we detect continuum emission from all three components. The primary disk, HT Lup A, also shows two-armed symmetric spiral structure with a pitch angle of $4^\circ$, while HT Lup B and C, located at $25$ and $434\,$au in projected separation from HT Lup A, are barely resolved with $\sim5$ and $\sim10\,$au in diameter, respectively. The gas kinematics for the closest pair indicates a different sense of rotation for each disk, which could be explained by either a counter rotation of the two disks in different, close to parallel, planes, or by a projection effect of these disks with a close to $90^\circ$ misalignment between them.

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arXiv2018

Disk Substructures at High Angular Resolution Program (DSHARP): VIII. The Rich Ringed Substructures in the AS 209 Disk

We present a detailed analysis of the high-angular resolution (0.''037, corresponding to 5 au) observations of the 1.25 mm continuum and $^{12}$CO $2-1$ emission from the disk around the T Tauri star AS 209. AS 209 hosts one of the most unusual disks from the DSHARP sample, the first high angular resolution ALMA survey of disks (Andrews et al. 2018), as nearly all of the emission can be explained with concentric Gaussian rings. In particular, the dust emission consists of a series of narrow and closely spaced rings in the inner $\sim$60 au, two well-separated bright rings in the outer disk, centered at 74 and 120 au, and at least two fainter emission features at 90 and 130 au. We model the visibilities with a parametric representation of the radial surface brightness profile, consisting of a central core and 7 concentric Gaussian rings. Recent hydro-dynamical simulations of low viscosity disks show that super-Earth planets can produce the multiple gaps seen in AS 209 millimeter continuum emission. The $^{12}$CO line emission is centrally peaked and extends out to $\sim$300 au, much farther than the millimeter dust emission. We find axisymmetric, localized deficits of CO emission around four distinct radii, near 45, 75, 120 and 210 au. The outermost gap is located well beyond the edge of the millimeter dust emission, and therefore cannot be due to dust opacity and must be caused by a genuine CO surface density reduction, due either to chemical effects or depletion of the overall gas content.

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arXiv2018

The Disk Substructures at High Angular Resolution Project (DSHARP): I. Motivation, Sample, Calibration, and Overview

We introduce the Disk Substructures at High Angular Resolution Project (DSHARP), one of the initial Large Programs conducted with the Atacama Large Millimeter/submillimeter Array (ALMA). The primary goal of DSHARP is to find and characterize substructures in the spatial distributions of solid particles for a sample of 20 nearby protoplanetary disks, using very high resolution (0.035 arcsec, or 5 au FWHM) observations of their 240 GHz (1.25 mm) continuum emission. These data provide a first homogeneous look at the small-scale features in disks that are directly relevant to the planet formation process, quantifying their prevalence, morphologies, spatial scales, spacings, symmetry, and amplitudes, for targets with a variety of disk and stellar host properties. We find that these substructures are ubiquitous in this sample of large, bright disks. They are most frequently manifested as concentric, narrow emission rings and depleted gaps, although large-scale spiral patterns and small arc-shaped azimuthal asymmetries are also present in some cases. These substructures are found at a wide range of disk radii (from a few au to more than 100 au), are usually compact ($<$10 au), and show a wide range of amplitudes (brightness contrasts). Here we discuss the motivation for the project, describe the survey design and the sample properties, detail the observations and data calibration, highlight some basic results, and provide a general overview of the key conclusions that are presented in more detail in a series of accompanying articles. The DSHARP data -- including visibilities, images, calibration scripts, and more -- are released for community use at https://almascience.org/alma-data/lp/DSHARP.

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arXiv2018

The Disk Substructures at High Angular Resolution Project (DSHARP) VI: Dust trapping in thin-ringed protoplanetary disks

A large fraction of the protoplanetary disks observed with ALMA display multiple well-defined and nearly perfectly circular rings in the continuum, in many cases with substantial peak-to-valley contrast. The DSHARP campaign shows that several of these rings are very narrow in radial extent. In this paper we test the hypothesis that these dust rings are caused by dust trapping in radial pressure bumps, and if confirmed, put constraints on the physics of the dust trapping mechanism. We model this process analytically in 1D, assuming axisymmetry. By comparing this model to the data, we find that all rings are consistent with dust trapping. Based on a plausible model of the dust temperature we find that several rings are narrower than the pressure scale height, providing strong evidence for dust trapping. The rings have peak absorption optical depth in the range between 0.2 and 0.5. The dust masses stored in each of these rings is of the order of tens of Earth masses, though much ambiguity remains due to the uncertainty of the dust opacities. The dust rings are dense enough to potentially trigger the streaming instability, but our analysis cannot give proof of this mechanism actually operating. Our results show, however, that the combination of very low alpha_turb << 5e-4 and very large grains a_grain >> 0.1 cm can be excluded by the data for all the rings studied in this paper.

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