arXiv subjects

David J. Wilner

Publications and source records attributed to David J. Wilner.

At least 163 records · Page 9Linked to original sources

arXiv2018

Science with an ngVLA: Resolved Substructures in Protoplanetary Disks

Terrestrial planets and the cores of giant planets are thought to be built by the collisional agglomeration of solids spanning over 20 orders of magnitude in size within a few million years. However, there is tension between this basic picture of planet formation and standard theoretical assumptions associated with the migration of "pebbles" ($\sim$mm/cm-sized particles) in gas-rich disks and the presumably much longer timescales necessary to assemble ($\sim$km-scale) "planetesimals". To confront these potential theoretical discrepancies with observational constraints, the ideal tracer of the solids concentrated in protoplanetary disk substructures is the 30-100 GHz continuum, which strikes the best balance in sensitivity (emission still bright), optical depth (low enough to reliably estimate densities), and angular resolution (high enough to resolve fine-scale features at disk radii as small as 1 au). With its combination of sensitivity, frequency coverage, and angular resolution, the next-generation VLA will be the only facility that has the capabilities to open up this new window into the physics of planetesimal formation.

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arXiv2018

Constraining Gas-Phase Carbon, Oxygen, and Nitrogen in the IM Lup Protoplanetary Disk

We present new constraints on gas-phase C, N, and O abundances in the molecular layer of the IM Lup protoplanetary disk. Building on previous physical and chemical modeling of this disk, we use new ALMA observations of C$_2$H to constrain the C/O ratio in the molecular layer to be $\sim0.8$, i.e., higher than the solar value of $\sim0.54$. We use archival ALMA observations of HCN and H$^{13}$CN to show that no depletion of N is required (assuming an interstellar abundance of $7.5\times10^{-5}$ per H). These results suggest that an appreciable fraction of O is sequestered in water ice in large grains settled to the disk mid-plane. Similarly, a fraction of the available C is locked up in less volatile molecules. By contrast, N remains largely unprocessed, likely as N$_2$. This pattern of depletion suggests the presence of true abundance variations in this disk, and not a simple overall depletion of gas mass. If these results hold more generally, then combined CO, C$_2$H, and HCN observations of disks may provide a promising path for constraining gas-phase C/O and N/O during planet-formation. Together, these tracers offer the opportunity to link the volatile compositions of disks to the atmospheres of planets formed from them.

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arXiv2018

Scaling Relations Associated with Millimeter Continuum Sizes in Protoplanetary Disks

We present a combined, homogenized analysis of archival Submillimeter Array (SMA) and Atacama Large Millimeter/submillimeter Array (ALMA) observations of the spatially resolved 340 GHz (870 $μ$m) continuum emission from 105 nearby protoplanetary disks. Building on the previous SMA survey, we infer surface brightness profiles using a simple model of the observed visibilities to derive the luminosities ($L_{\rm mm}$) and effective sizes ($R_{\rm eff}$) of the continuum emission. With this sample, we confirm the shapes, normalizations, and dispersions for the strong correlations between $L_{\rm mm}$, $M_\ast$ (or $L_\ast$), and $\dot{M}_\ast$ found in previous studies. We also verify the continuum size--luminosity relation determined from the SMA survey alone (extending to an order of magnitude lower $L_{\rm mm}$), demonstrating that the amount of emission scales linearly with the emitting surface area. Moreover, we identify new, although weaker, relationships between $R_{\rm eff}$ and the host and accretion properties, such that disks are larger around more massive hosts with higher accretion rates. We explore these inter-related demographic properties with some highly simplified approximations. These multi-dimensional relationships can be explained if the emission is optically thick with a filling factor of $\sim$0.3, or if the emission is optically thin and disks have roughly the same optical depth profile shapes and normalizations independent of host properties. In both scenarios, we require the dust disk sizes to have a slightly sub-linear relationship with the host mass and a non-negligible dispersion ($\sim$0.2 dex at a given $M_\ast$).

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arXiv2018

The Millimeter Continuum Size-Frequency Relationship in the UZ Tau E Disk

We present high spatial resolution observations of the continuum emission from the young multiple star system UZ Tau at frequencies from 6 to 340 GHz. To quantify the spatial variation of dust emission in the UZ Tau E circumbinary disk, the observed interferometric visibilities are modeled with a simple parametric prescription for the radial surface brightnesses at each frequency. We find evidence that the spectrum steepens with radius in the disk, manifested as a positive correlation between the observing frequency and the radius that encircles a fixed fraction of the emission ($R_{eff} \propto ν^{0.34 \pm 0.08}$). The origins of this size--frequency relation are explored in the context of a theoretical framework for the growth and migration of disk solids. While that framework can reproduce a similar size--frequency relation, it predicts a steeper spectrum than is observed. Moreover, it comes closest to matching the data only on timescales much shorter ($\le 1$ Myr) than the putative UZ Tau age (~2-3 Myr). These discrepancies are the direct consequences of the rapid radial drift rates predicted by models of dust evolution in a smooth gas disk. One way to mitigate that efficiency problem is to invoke small-scale gas pressure modulations that locally concentrate drifting solids. If such particle traps reach high continuum optical depths at 30-340 GHz with a ~30-60% filling fraction in the inner disk ($r \lesssim20$ au), they can also explain the observed spatial gradient in the UZ Tau E disk spectrum.

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arXiv2018

High-resolution SMA imaging of bright submillimetre sources from the SCUBA-2 Cosmology Legacy Survey

We have used the Submillimeter Array at 860$\,μ$m to observe the brightest SCUBA-2 sources in 4$\,$deg$^{2}$ of the Cosmology Legacy Survey. We have targeted 75 of the brightest single-dish SCUBA-2 850$\,μ$m sources down to $S_{850}\,{\approx}\,8\,$mJy, achieving an average synthesized beam of 2.4$^{\prime\prime}$ and an average rms of $σ_{860}\,{=}\,1.5\,$mJy in our primary beam-corrected maps. We searched our maps for $4σ$ peaks, corresponding to $S_{860}\,{\gtrsim}\,6\,$mJy sources, and detected 59 single galaxies and three pairs of galaxies. We include in our study 28 archival observations, bringing our sample size to 103 bright single-dish submillimetre sources with interferometric follow-up. We compute the cumulative and differential number counts of our sample, finding them to overlap with previous single-dish survey number counts within the uncertainties, although our cumulative number count is systematically lower than the parent SCUBA-2 cumulative number count by $24\,{\pm}\,6$ per cent between 11 and 15$\,$mJy. We estimate the probability that a ${\gtrsim}\,10\,$mJy single-dish submillimetre source resolves into two or more galaxies with similar flux densities, causing a significant change in the number counts, to be about 15 per cent. Assuming the remaining 85 per cent of the targets are ultra-luminous starburst galaxies between $z\,{=}\,2$-3, we find a likely volume density of ${\gtrsim}\,400\,$M$_{\odot}\,$yr$^{-1}$ sources to be ${\sim}\,3^{+0.7}_{-0.6}\,{\times}\,10^{-7}\,$Mpc$^{-3}$. We show that the descendants of these galaxies could be ${\gtrsim}\,4\,{\times}\,10^{11}\,$M$_{\odot}$ local quiescent galaxies, and that about 10 per cent of their total stellar mass would have formed during these short bursts of star-formation.

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arXiv2018

MESAS: Measuring the Emission of Stellar Atmospheres at Submm/mm wavelengths

In the early stages of planet formation, small dust grains grow to become mm sized particles in debris disks around stars. These disks can in principle be characterized by their emission at submillimeter and millimeter wavelengths. Determining both the occurrence and abundance of debris in unresolved circumstellar disks of A-type main-sequence stars requires that the stellar photospheric emission be accurately modeled. To better constrain the photospheric emission for such systems, we present observations of Sirius A, an A-type star with no known debris, from the JCMT, SMA, and VLA at 0.45, 0.85, 0.88, 1.3, 6.7, and 9.0 mm. We use these observations to inform a PHOENIX model of Sirius A's atmosphere. We find the model provides a good match to these data and can be used as a template for the submm/mm emission of other early A-type stars where unresolved debris may be present. The observations are part of an ongoing observational campaign entitled Measuring the Emission of Stellar Atmospheres at Submm/mm wavelengths (MESAS)

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arXiv2018

Turbulence in the TW Hya Disk

Turbulence is a fundamental parameter in models of grain growth during the early stages of planet formation. As such, observational constraints on its magnitude are crucial. Here we self-consistently analyze ALMA CO(2-1), SMA CO(3-2), and SMA CO(6-5) observations of the disk around TW Hya and find an upper limit on the turbulent broadening of $<$0.08c$_s$ ($α<$0.007 for $α$ defined only within 2-3 pressure scale heights above the midplane), lower than the tentative detection previously found from an analysis of the CO(2-1) data. We examine in detail the challenges of image plane fitting vs directly fitting the visibilities, while also considering the role of the vertical temperature gradient, systematic uncertainty in the amplitude calibration, and assumptions about the CO abundance, as potential sources of the discrepancy in the turbulence measurements. These tests result in variations of the turbulence limit between $<$0.04c$_s$ and $<$0.13c$_s$, consistently lower than the 0.2-0.4c$_s$ found previously. Having ruled out numerous factors, we restrict the source of the discrepancy to our assumed coupling between temperature and density through hydrostatic equilibrium in the presence of a vertical temperature gradient and/or the confinement of CO to a thin molecular layer above the midplane, although further work is needed to quantify the influence of these prescriptions. Assumptions about hydrostatic equilibrium and the CO distribution are physically motivated, and may have a small influence on measuring the kinematics of the gas, but they become important when constraining small effects such as the strength of the turbulence within a protoplanetary disk.

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arXiv2018

Detection of a Millimeter Flare From Proxima Centauri

We present new analyses of ALMA 12-m and ACA observations at 233 GHz (1.3 mm) of the Proxima Centauri system with sensitivities of 9.5 and 47 $μ$Jy beam$^{-1}$, respectively, taken from 2017 January 21 through 2017 April 25. These analyses reveal that the star underwent a significant flaring event during one of the ACA observations on 2017 March 24. The complete event lasted for approximately 1 minute and reached a peak flux density of $100\pm4$ mJy, nearly a factor of $1000\times$ brighter than the star's quiescent emission. At the flare peak, the continuum emission is characterized by a steeply falling spectral index with frequency, $F_ν\propto ν^α$ with $α= -1.77\pm0.45$, and a lower limit on the fractional linear polarization of $|Q/I| = 0.19\pm0.02$. Since the ACA observations do not show any quiescent excess emission, we conclude that there is no need to invoke the presence of a dust belt at $1-4$ AU. We also posit that the slight excess flux density of $101\pm9$ $μ$Jy observed in the 12-m observations compared to the photospheric flux density of $74\pm4$ $μ$Jy extrapolated from infrared wavelengths may be due to coronal heating from continual smaller flares, as is seen for AU Mic, another nearby, well-studied, M dwarf flare star. If this is true, then the need for warm dust at $\sim0.4$ AU is also removed.

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arXiv2018

Resolved Millimeter Observations of the HR 8799 Debris Disk

We present 1.3 millimeter observations of the debris disk surrounding the HR 8799 multi-planet system from the Submillimeter Array to complement archival ALMA observations that spatially filtered away the bulk of the emission. The image morphology at $3.8$ arcsecond (150 AU) resolution indicates an optically thin circumstellar belt, which we associate with a population of dust-producing planetesimals within the debris disk. The interferometric visibilities are fit well by an axisymmetric radial power-law model characterized by a broad width, $ΔR/R\gtrsim 1$. The belt inclination and orientation parameters are consistent with the planet orbital parameters within the mutual uncertainties. The models constrain the radial location of the inner edge of the belt to $R_\text{in}= 104_{-12}^{+8}$ AU. In a simple scenario where the chaotic zone of the outermost planet b truncates the planetesimal distribution, this inner edge location translates into a constraint on the planet~b mass of $M_\text{pl} = 5.8_{-3.1}^{+7.9}$ M$_{\rm Jup}$. This mass estimate is consistent with infrared observations of the planet luminosity and standard hot-start evolutionary models, with the uncertainties allowing for a range of initial conditions. We also present new 9 millimeter observations of the debris disk from the Very Large Array and determine a millimeter spectral index of $2.41\pm0.17$. This value is typical of debris disks and indicates a power-law index of the grain size distribution $q=3.27\pm0.10$, close to predictions for a classical collisional cascade.

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arXiv2018

Observational constraints on the physical nature of submillimetre source multiplicity: chance projections are common

Interferometric observations have demonstrated that a significant fraction of single-dish submillimetre (submm) sources are blends of multiple submm galaxies (SMGs), but the nature of this multiplicity, i.e. whether the galaxies are physically associated or chance projections, has not been determined. We performed spectroscopy of 11 SMGs in six multi-component submm sources, obtaining spectroscopic redshifts for nine of them. For an additional two component SMGs, we detected continuum emission but no obvious features. We supplement our observed sources with four sources from the literature. This sample allows us to statistically constrain the physical nature of single-dish submm source multiplicity for the first time. In three [3/7, or 43 (-33/+39) per cent at 95% confidence] of the single-dish sources for which the nature of the blending is unambiguous, the components for which spectroscopic redshifts are available are physically associated, whereas 4/7 [57 (-39/+33) per cent] have at least one unassociated component. When components whose spectra exhibit continuum but no features and for which the photometric redshift is significantly different from the spectroscopic redshift of the other component are also considered, 6/9 [67 (-37/+26) per cent] of the single-dish sources are comprised of at least one unassociated component. The nature of the multiplicity of one single-dish source is ambiguous. We conclude that physically associated systems and chance projections both contribute to the multi-component single-dish submm source population. This result contradicts the conventional wisdom that bright submm sources are solely a result of merger-induced starbursts, as blending of unassociated galaxies is also important.

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arXiv2018

CO and dust properties in the TW Hya disk from high-resolution ALMA observations

We analyze high angular resolution ALMA observations of the TW Hya disk to place constraints on the CO and dust properties. We present new, sensitive observations of the $^{12}$CO $J = 3-2$ line at a spatial resolution of 8 AU (0\farcs14). The CO emission exhibits a bright inner core, a shoulder at $r\approx70$ AU, and a prominent break in slope at $r\approx90$ AU. Radiative transfer modeling is used to demonstrate that the emission morphology can be reasonably reproduced with a $^{12}$CO column density profile featuring a steep decrease at $r\approx15$ AU and a secondary bump peaking at $r\approx70$ AU. Similar features have been identified in observations of rarer CO isotopologues, which trace heights closer to the midplane. Substructure in the underlying gas distribution or radially varying CO depletion that affects much of the disk's vertical extent may explain the shared emission features of the main CO isotopologues. We also combine archival 1.3 mm and 870 $μ$m continuum observations to produce a spectral index map at a spatial resolution of 2 AU. The spectral index rises sharply at the continuum emission gaps at radii of 25, 41, and 47 AU. This behavior suggests that the grains within the gaps are no larger than a few millimeters. Outside the continuum gaps, the low spectral index values of $α\approx 2$ indicate either that grains up to centimeter size are present, or that the bright continuum rings are marginally optically thick at millimeter wavelengths.

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arXiv2017

The Association of Molecular Gas and Natal Super Star Clusters in Henize 2-10

We present ALMA observations of the dwarf starburst galaxy Henize 2-10 in combination with previous SMA CO observations to probe the molecular environments of natal super star clusters. These observations include the HCO$^+$(1-0), HCN(1-0), HNC(1-0), and CCH(1-0) molecular lines, as well as 88 GHz continuum with a spatial resolution of $1''.7\times 1''.6$. After correcting for the contribution from free-free emission to the 88 GHz continuum flux density ($\sim$ 60% of the 88 GHz emission), we derive a total gas mass for He~2-10 of $M_{gas} = 4-6\times10^8$ M$_{\odot}$, roughly 5-20% of the dynamical mass. Based on a principle component analysis, HCO$^+$ is found to be the best "general" tracer of molecular emission. The line widths and luminosities of the CO emission suggests that the molecular clouds could either be as small as $\sim 8$ pc, or alternately have enhanced line widths. The CO emission and 88 GHz continuum are anti-correlated, suggesting that either the dust and molecular gas are not cospatial, which could reflect the 88 GHz continuum is dominated by free-free emission. The CO and CCH emission are also relatively anti-correlated, which is consistent with the CCH being photo-enhanced, and/or the CO being dissociated in the regions near the natal super star clusters. The molecular line ratios of regions containing the natal star clusters are different from the line ratios observed for regions elsewhere in the galaxy. In particular, the regions with thermal radio emission all have CO(2-1)/HCO$^+(1-0) < 16$, and the HCO$^+$/CO ratio appears to be correlated with the evolutionary stage of the clusters.

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arXiv2017

Optical and Radio Observations of the T Tauri Binary KH 15D (V582 Mon): Stellar Properties, Disk Mass Limit and Discovery of a CO Outflow

We present VRIJHK photometry of the KH 15D T Tauri binary system for the 2015/16 and 2016/17 observing seasons. For the first time in the modern (CCD) era we are seeing Star B fully emerge from behind the trailing edge of the precessing circumbinary ring during each apastron passage. We are, therefore, able to measure its luminosity and color. Decades of photometry on the system now allow us to infer the effective temperature, radius, mass and age of each binary component. We find our values to be in good agreement with previous studies, including archival photographic photometry from the era when both stars were fully visible, and they set the stage for a full model of the system that can be constructed once radial velocity measurements are available. We also present the first high sensitivity radio observations of the system, taken with ALMA and the SMA. The respective 2.0 and 0.88 mm observations provide an upper limit on the circumbinary (gas and dust) disk mass of 1.7 Jupiter masses and reveal an extended CO outflow which overlaps with the position, systemic velocity and orientation of the KH 15D system and is certainly associated with it. The low velocity, tight collimation, and extended nature of the emission suggest that the outflow is inclined nearly orthogonal to the line of sight, implying it is also orthogonal to the circumbinary ring. The position angle of the radio outflow also agrees precisely with the direction of polarization of the optical emission during the faint phase. A small offset between the optical image of the binary and the central line of the CO outflow remains as a puzzle and possible clue to the jet launching mechanism.

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arXiv2017

The Architecture of the GW Ori Young Triple Star System and Its Disk: Dynamical Masses, Mutual Inclinations, and Recurrent Eclipses

We present spatially and spectrally resolved Atacama Large Millimeter/submillimeter Array (ALMA) observations of gas and dust orbiting the pre-main sequence hierarchical triple star system GW Ori. A forward-modeling of the ${}^{13}$CO and C${}^{18}$O $J$=2-1 transitions permits a measurement of the total stellar mass in this system, $5.29 \pm 0.09\,M_\odot$, and the circum-triple disk inclination, $137.6 \pm 2.0^\circ$. Optical spectra spanning a 35 year period were used to derive new radial velocities and, coupled with a spectroscopic disentangling technique, revealed that the A and B components of GW Ori form a double-lined spectroscopic binary with a $241.50\pm0.05$ day period; a tertiary companion orbits that inner pair with a $4218\pm50$ day period. Combining the results from the ALMA data and the optical spectra with three epochs of astrometry in the literature, we constrain the individual stellar masses in the system ($M_\mathrm{A} \approx 2.7\,M_\odot$, $M_\mathrm{B} \approx 1.7\,M_\odot$, $M_\mathrm{C} \approx 0.9\,M_\odot$) and find strong evidence that at least one (and likely both) stellar orbital planes are misaligned with the disk plane by as much as $45^\circ$. A $V$-band light curve spanning 30 years reveals several new $\sim$30 day eclipse events 0.1-0.7~mag in depth and a 0.2 mag sinusoidal oscillation that is clearly phased with the AB-C orbital period. Taken together, these features suggest that the A-B pair may be partially obscured by material in the inner disk as the pair approaches apoastron in the hierarchical orbit. Lastly, we conclude that stellar evolutionary models are consistent with our measurements of the masses and basic photospheric properties if the GW Ori system is $\sim$1 Myr old.

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arXiv2017

An SMA Continuum Survey of Circumstellar Disks in the Serpens Star-Forming Region

We present observations with the Submillimeter Array of the continuum emission at $λ= 1.3$ mm from 62 young stars surrounded by a protoplanetary disk in the Serpens star-forming region. The typical angular resolution for the survey in terms of beam size is $3.5^{\prime \prime}\times2.5^{\prime \prime}$ with a median rms noise level of 1.6 mJy beam$^{-1}$. These data are used to infer the dust content in disks around low-mass stars $(0.1$-$2.5\,M_{\odot})$ at a median stellar age of $1$-$3$ Myr. Thirteen sources were detected in the 1.3 mm dust continuum with inferred dust masses of ${\approx} 10$-$260\,M_{\oplus}$ and an upper limit to the median dust mass of $5.1_{-4.3}^{+6.1}\,M_{\oplus}$, derived using survival analysis. Comparing the protoplanetary disk population in Serpens to those of other nearby star-forming regions, we find that the populations of dust disks in Serpens and Taurus, which have a similar age, are statistically indistinguishable. This is potentially surprising since Serpens has a stellar surface density two orders of magnitude in excess of Taurus. Hence, we find no evidence that dust disks in Serpens have been dispersed as a result of more frequent and/or stronger tidal interactions due its elevated stellar density. We also report that the fraction of Serpens disks with $M_{\rm{dust}} \geq 10\,M_{\oplus}$ is less than 20%, which supports the notion that the formation of giant planets is likely inherently rare or has substantially progressed by a few Myrs.

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arXiv2017

ALMA 1.3 Millimeter Map of the HD 95086 System

Planets and minor bodies such as asteroids, Kuiper-belt objects and comets are integral components of a planetary system. Interactions among them leave clues about the formation process of a planetary system. The signature of such interactions is most prominent through observations of its debris disk at millimeter wavelengths where emission is dominated by the population of large grains that stay close to their parent bodies. Here we present ALMA 1.3 mm observations of HD 95086, a young early-type star that hosts a directly imaged giant planet b and a massive debris disk with both asteroid- and Kuiper-belt analogs. The location of the Kuiper-belt analog is resolved for the first time. The system can be depicted as a broad ($ΔR/R \sim$0.84), inclined (30\arcdeg$\pm$3\arcdeg) ring with millimeter emission peaked at 200$\pm$6 au from the star. The 1.3 mm disk emission is consistent with a broad disk with sharp boundaries from 106$\pm$6 to 320$\pm$20 au with a surface density distribution described by a power law with an index of --0.5$\pm$0.2. Our deep ALMA map also reveals a bright source located near the edge of the ring, whose brightness at 1.3 mm and potential spectral energy distribution are consistent with it being a luminous star-forming galaxy at high redshift. We set constraints on the orbital properties of planet b assuming co-planarity with the observed disk.

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arXiv2017

A Millimeter Continuum Size-Luminosity Relationship for Protoplanetary Disks

We present a sub-arcsecond resolution survey of the 340 GHz dust continuum emission from 50 nearby protoplanetary disks, based on new and archival observations with the Submillimeter Array. The observed visibility data were modeled with a simple prescription for the radial surface brightness profile. The results were used to extract intuitive, empirical estimates of the emission "size" for each disk, $R_{\rm eff}$, defined as the radius that encircles a fixed fraction of the total continuum luminosity, $L_{\rm mm}$. We find a significant correlation between the sizes and luminosities, such that $R_{\rm eff} \propto L_{\rm mm}^{0.5}$, providing a confirmation and quantitative characterization of a putative trend that was noted previously. This correlation suggests that these disks have roughly the same average surface brightness interior to their given effective radius, ~0.2 Jy arcsec$^{-2}$ (or 8 K in brightness temperature). The same trend remains, but the 0.2dex of dispersion perpendicular to this relation essentially disappears, when we account for the irradiation environment of each disk with a crude approximation of the dust temperatures based on the stellar host luminosities. We consider two (not mutually exclusive) explanations for the origin of this size-luminosity relationship. Simple models of the growth and migration of disk solids can account for the observed trend for a reasonable range of initial conditions, but only on timescales that are much shorter than the nominal ages present in the sample. An alternative scenario invokes optically thick emission concentrated on unresolved scales, with filling factors of a few tens of percent, that are perhaps manifestations of localized particle traps.

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arXiv2017

A Three-Dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk using DCO$^+$

Gas kinematics are an important part of the planet formation process. Turbulence influences planetesimal growth and migration from the scale of sub-micron dust grains through gas-giant planets. Radio observations of resolved molecular line emission can directly measure this non-thermal motion and, taking advantage of the layered chemical structure of disks, different molecular lines can be combined to map the turbulence throughout the vertical extent of a protoplanetary disk. Here we present ALMA observations of three molecules (DCO$^+$(3-2), C$^{18}$O(2-1) and CO(2-1)) from the disk around HD 163296. We are able to place stringent upper limits ($v_{\rm turb}<$0.06c$_s$, $<$0.05c$_s$ and $<$0.04c$_s$ for CO(2-1), C$^{18}$O(2-1) and DCO$^+$(3-2) respectively), corresponding to $α\lesssim$3$\times$10$^{-3}$, similar to our prior limit derived from CO(3-2). This indicates that there is little turbulence throughout the vertical extent of the disk, contrary to theoretical predictions based on the magneto-rotational instability and gravito-turbulence. In modeling the DCO$^+$ emission we also find that it is confined to three concentric rings at 65.7$\pm$0.9 au, 149.9$^{+0.5}_{-0.7}$ au and 259$\pm$1 au, indicative of a complex chemical environment.

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