arXiv subjects

David J. Wilner

Publications and source records attributed to David J. Wilner.

At least 127 records · Page 7Linked to original sources

arXiv2020

A Dust Trap in the Young Multiple System HD 34700

Millimeter observations of disks around young stars reveal substructures indicative of gas pressure traps that may aid grain growth and planet formation. We present Submillimeter Array observations of HD 34700- two Herbig Ae stars in a close binary system (Aa/Ab, $\sim$0.25 AU), surrounded by a disk presenting a large cavity and spiral arms seen in scattered light, and two distant, lower mass companions. These observations include 1.3 mm continuum emission and the $^{12}$CO 2-1 line at $\sim0.5$" (178 AU) resolution. They resolve a prominent azimuthal asymmetry in the continuum, and Keplerian rotation of a circumbinary disk in the $^{12}$CO line. The asymmetry is located at a radius of $155^{+11}_{-7}$ AU, consistent with the edge of the scattered light cavity, being resolved in both radius ($72 ^{+14}_{-15}$ AU) and azimuth (FWHM = $64 ^{\circ +8}_{-7}$). The strong asymmetry in millimeter continuum emission could be evidence for a dust trap, together with the more symmetric morphology of $^{12}$CO emission and small grains. We hypothesize an unseen circumbinary companion, responsible for the cavity in scattered light and creating a vortex at the cavity edge that manifests in dust trapping. The disk mass has limitations imposed by the detection of $^{12}$CO and non-detection of $^{13}$CO. We discuss its consequences for the potential past gravitational instability of this system, likely accounting for the rapid formation of a circumbinary companion. We also report the discovery of resolved continuum emission associated with HD 34700B (projected separation $\sim1850$AU), which we explain through a circumstellar disk.

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arXiv2020

The Disk Substructures at High Angular Resolution Project (DSHARP): II. Characteristics of Annular Substructures

The Disk Substructures at High Angular Resolution Project used ALMA to map the 1.25 millimeter continuum of protoplanetary disks at a spatial resolution of ~5 au. We present a systematic analysis of annular substructures in the 18 single-disk systems targeted in this survey. No dominant architecture emerges from this sample; instead, remarkably diverse morphologies are observed. Annular substructures can occur at virtually any radius where millimeter continuum emission is detected and range in widths from a few au to tens of au. Intensity ratios between gaps and adjacent rings range from near-unity to just a few percent. In a minority of cases, annular substructures co-exist with other types of substructures, including spiral arms (3/18) and crescent-like azimuthal asymmetries (2/18). No clear trend is observed between the positions of the substructures and stellar host properties. In particular, the absence of an obvious association with stellar host luminosity (and hence the disk thermal structure) suggests that substructures do not occur preferentially near major molecular snowlines. Annular substructures like those observed in DSHARP have long been hypothesized to be due to planet-disk interactions. A few disks exhibit characteristics particularly suggestive of this scenario, including substructures in possible mean-motion resonance and "double gap" features reminiscent of hydrodynamical simulations of multiple gaps opened by a planet in a low-viscosity disk.

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arXiv2020

Large-scale CO spiral arms and complex kinematics associated with the T Tauri star RU Lup

While protoplanetary disks often appear to be compact and well-organized in millimeter continuum emission, CO spectral line observations are increasingly revealing complex behavior at large distances from the host star. We present deep ALMA maps of the $J=2-1$ transition of $^{12}$CO, $^{13}$CO, and C$^{18}$O, as well as the $J=3-2$ transition of DCO$^+$, toward the T Tauri star RU Lup at a resolution of $\sim0.3''$ ($\sim50$ au). The CO isotopologue emission traces four major components of the RU Lup system: a compact Keplerian disk with a radius of $\sim120$ au, a non-Keplerian ``envelope-like'' structure surrounding the disk and extending to $\sim260$ au from the star, at least five blueshifted spiral arms stretching up to 1000 au, and clumps outside the spiral arms located up to 1500 au in projection from RU Lup. We comment on potential explanations for RU Lup's peculiar gas morphology, including gravitational instability, accretion of material onto the disk, or perturbation by another star. RU Lup's extended non-Keplerian CO emission, elevated stellar accretion rate, and unusual photometric variability suggest that it could be a scaled-down Class II analog of the outbursting FU Ori systems.

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arXiv2020

An unbiased ALMA spectral survey of the LkCa 15 and MWC 480 protoplanetary disks

The volatile contents of protoplanetary disks both set the potential for planetary chemistry and provide valuable probes of defining disk system characteristics such as stellar mass, gas mass, ionization, and temperature structure. Current disk molecular inventories are fragmented, however, giving an incomplete picture: unbiased spectral line surveys are needed to assess the volatile content. We present here an overview of such a survey of the protoplanetary disks around the Herbig Ae star MWC 480 and the T Tauri star LkCa 15 in ALMA Band 7, spanning $\sim$36 GHz from 275--317 GHz and representing an order of magnitude increase in sensitivity over previous single-dish surveys. We detect 14 molecular species (including isotopologues), with 5 species (C$^{34}$S, $^{13}$CS, H$_{2}$CS, DNC, and C$_2$D) detected for the first time in protoplanetary disks. Significant differences are observed in the molecular inventories of MWC~480 and LkCa~15, and we discuss how these results may be interpreted in light of the different physical conditions of these two disk systems.

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arXiv2020

Multiband GPI Imaging of the HR 4796A Debris Disk

We have obtained Gemini Planet Imager (GPI) J-, H-, K1-, and K2-Spec observations of the iconic debris ring around the young, main-sequence star HR 4796A. We applied several point-spread function (PSF) subtraction techniques to the observations (Mask-and-Interpolate, RDI-NMF, RDI-KLIP, and ADI-KLIP) to measure the geometric parameters and the scattering phase function for the disk. To understand the systematic errors associated with PSF subtraction, we also forward-modeled the observations using a Markov Chain Monte Carlo framework and a simple model for the disk. We found that measurements of the disk geometric parameters were robust, with all of our analyses yielding consistent results; however, measurements of the scattering phase function were challenging to reconstruct from PSF-subtracted images, despite extensive testing. As a result, we estimated the scattering phase function using disk modeling. We searched for a dependence of the scattering phase function with respect to the GPI filters but found none. We compared the H-band scattering phase function with that measured by Hubble Space Telescope STIS at visual wavelengths and discovered a blue color at small scattering angles and a red color at large scattering angles, consistent with predictions and laboratory measurements of large grains. Finally, we successfully modeled the SPHERE H2 HR 4796A scattered phase function using a distribution of hollow spheres composed of silicates, carbon, and metallic iron.

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arXiv2020

Dust Populations in the Iconic Vega Planetary System Resolved by ALMA

The Vega planetary system hosts the archetype of extrasolar Kuiper belts, and is rich in dust from the sub-au region out to 100's of au, suggesting intense dynamical activity. We present ALMA mm observations that detect and resolve the outer dust belt from the star for the first time. The interferometric visibilities show that the belt can be fit by a Gaussian model or by power-law models with a steep inner edge (at 60-80 au). The belt is very broad, extending out to at least 150-200 au. We strongly detect the star and set a stringent upper limit to warm dust emission previously detected in the infrared. We discuss three scenarios that could explain the architecture of Vega's planetary system, including the new {ALMA} constraints: no outer planets, a chain of low-mass planets, and a single giant planet. The planet-less scenario is only feasible if the outer belt was born with the observed sharp inner edge. If instead the inner edge is currently being truncated by a planet, then the planet must be $\gtrsim$6 M$_{\oplus}$ and at $\lesssim71$ au to have cleared its chaotic zone within the system age. In the planet chain scenario, outward planet migration and inward scattering of planetesimals could produce the hot and warm dust observed in the inner regions of the system. In the single giant planet scenario, an asteroid belt could be responsible for the warm dust, and mean motion resonances with the planet could put asteroids on star-grazing orbits, producing the hot dust.

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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

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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arXiv2019

From scattered-light to millimeter emission: A comprehensive view of the Gyr-old system of HD 202628 and its eccentric debris ring

We present here new observations of the eccentric debris ring surrounding the Gyr-old solar-type star HD 202628: at millimeter wavelengths with ALMA, at far-infrared wavelengths with \textit{Herschel}, and in scattered light with \textit{HST}. The ring inner edge is found to be consistent between ALMA and \textit{HST} data. As radiation pressure affects small grains seen in scattered-light, the ring appears broader at optical than at millimeter wavelengths. The best fit to the ring seen with ALMA has inner and outer edges at $143.1 \pm 1.7$ AU and $165.5 \pm 1.4$, respectively, and an inclination of $57.4^\circ \pm 0.4$ from face-on. The offset of the ring centre of symmetry from the star allows us to quantify its eccentricity to be $e=0.09_{-0.01}^{+0.02}$. This eccentric feature is also detected in low resolution \textit{Herschel}/PACS observations, under the form of a pericenter-glow. Combining the infrared and millimeter photometry, we retrieve a disk grain size distribution index of $\sim -3.4$, and therefore exclude in-situ formation of the inferred belt-shaping perturber, for which we provide new dynamical constraints. Finally, ALMA images show four point-like sources that exceed 100$\,μ$Jy, one of them being just interior to the ring. Although the presence of a background object cannot be excluded, we cannot exclude either that this source is circumplanetary material surrounding the belt-shaper, in which case degeneracies between its mass and orbital parameters could be lifted, allowing us to fully characterize such a distant planet in this mass and age regime for the very first time.

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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 REASONS Survey: Resolved Millimeter Observations of a Large Debris Disk Around the Nearby F Star HD 170773

Debris disks are extrasolar analogs to our own Kuiper Belt and they are detected around at least 17% of nearby Sun-like stars. The morphology and dynamics of a disk encode information about its history, as well as that of any exoplanets within the system. We used ALMA to obtain 1.3 mm observations of the debris disk around the nearby F5V star HD 170773. We image the face-on ring and determine its fundamental parameters by forward-modeling the interferometric visibilities through a Markov Chain Monte Carlo approach. Using a symmetric Gaussian surface density profile, we find a 71 $\pm$ 4 au wide belt with a radius of 193$^{+2}_{-3}$ au, a relatively large radius compared to most other millimeter-resolved belts around late A / early F type stars. This makes HD 170773 part of a group of four disks around A and F stars with radii larger than expected from the recently reported planetesimal belt radius - stellar luminosity relation. Two of these systems are known to host directly imaged giant planets, which may point to a connection between large belts and the presence of long-period giant planets. We also set upper limits on the presence of CO and CN gas in the system, which imply that the exocomets that constitute this belt have CO and HCN ice mass fractions of <77% and <3%, respectively, consistent with Solar System comets and other exocometary belts.

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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

Resolved Molecular Gas and Star Formation Properties of the Strongly Lensed z=2.26 Galaxy SDSS J0901+1814

We present ~1" resolution (~2 kpc in the source plane) observations of the CO(1-0), CO(3-2), Halpha, and [N II] lines in the strongly-lensed z=2.26 star-forming galaxy SDSS J0901+1814. We use these observations to constrain the lensing potential of a foreground group of galaxies, and our source-plane reconstructions indicate that SDSS J0901+1814 is a nearly face-on (i~30 degrees) massive disk with r_{1/2}>~4 kpc for its molecular gas. Using our new magnification factors (mu_tot~30), we find that SDSS J0901+1814 has a star formation rate (SFR) of 268^{+63}_{-61} M_sun/yr, M_gas=(1.6^{+0.3}_{-0.2})x10^11x(alpha_CO/4.6) M_sun, and M_star=(9.5^{+3.8}_{-2.8})x10^10 M_sun, which places it on the star-forming galaxy "main sequence." We use our matched high-angular resolution gas and SFR tracers (CO and Halpha, respectively) to perform a spatially resolved (pixel-by-pixel) analysis of SDSS J0901+1814 in terms of the Schmidt-Kennicutt relation. After correcting for the large fraction of obscured star formation (SFR_Halpha/SFR_TIR=0.054^{+0.015}_{-0.014}), we find SDSS J0901+1814 is offset from "normal" star-forming galaxies to higher star formation efficiencies independent of assumptions for the CO-to-H_2 conversion factor. Our mean best-fit index for the Schmidt-Kennicutt relation for SDSS J0901+1814, evaluated with different CO lines and smoothing levels, is n=1.54+/-0.13; however, the index may be affected by gravitational lensing, and we find n=1.24+/-0.02 when analyzing the source-plane reconstructions. While the Schmidt-Kennicutt index largely appears unaffected by which of the two CO transitions we use to trace the molecular gas, the source-plane reconstructions and dynamical modeling suggest that the CO(1-0) emission is more spatially extended than the CO(3-2) emission.

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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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