On the Commonality of 10-30AU Sized Axisymmetric Dust Structures in Protoplanetary Disks

1.4 MB·

by  Ke Zhang

Draftversion January22,2016
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
ON THE COMMONALITY OF 10-30AU SIZED AXISYMMETRIC DUST STRUCTURES
IN PROTOPLANETARY DISKS
Ke Zhang1, Edwin A. Bergin1, Geoffrey A. Blake2, L. Ilsedore Cleeves3, Michiel Hogerheijde4, Vachail
Salinas4, Kamber R. Schwarz1
Draft version January 22, 2016
ABSTRACT
6
An unsolved problem in step-wise core-accretion planet formation is that rapid radial drift in gas-
1
rich protoplanetary disks should drive mm-/meter-sized particles inward to the central star before
0
large bodies can form. One promising solution is to confine solids within small scale structures. Here
2
we investigate dust structures in the (sub)mm continuum emission of four disks (TW Hya, HL Tau,

n HD163296andDMTau),asampleofdiskswiththehighestspatialresolutionALMAobservationsto
a date. We retrieve the surface brightness distributions using synthesized images and fitting visibilities
J
withanalyticalfunctions. Wefindthatthecontinuumemissionofthefourdisksis axi-symmetricbut

1 richin10-30AU-sizedradialstructures,possiblyduetophysicalgaps,surfacedens∼ityenhancementsor
2 localizeddustopacityvariationswithinthedisks. Theseresultssuggestthatsmallscaleaxi-symmetric
duststructuresarelikelytobecommon,asaresultofubiquitousprocessesindiskevolutionandplanet
]
formation. ComparedwithrecentspatiallyresolvedobservationsofCOsnowlinesinthesesamedisks,
P
all four systems show enhanced continuum emission from regions just beyond the CO condensation
E
fronts, potentially suggesting a causal relationship between dust growth/trapping and snowlines.
.
h Subject headings: stars: premain-sequence – protoplanetary disks – techniques: interferometric
p
-
o
1. INTRODUCTION (ALMA) recently imaged the HL Tau protoplanetary
r
t In the core-accretion planet formation scenario, diskwithasuperbspatialresolutionof 5AU,revealing
s ∼
a remarkable series of dark and bright concentric rings
a planet formation starts with micron-sized interstellar
[ medium grains grow into kilometer-sized planetesimals in the continuum emission (ALMA Partnershipet al.
2015). The origin of these rings have been suggested
(Goldreich & Ward 1973) – a size interval that poses
2 to be gap opening(s) induced by embedded planets
great challenges since aggregates in this size range ex-
v (Dipierro et al.2015;Pinte et al.2016;Dong et al.2015)
perience significant drag from the surrounding gas and
2 or changes in the dust properties near condensation
thus drift toward the central star on extremely short
8 frontsofdominanticesandclathrates(Zhang et al.2015;
timescales (Whipple 1972; Weidenschilling 1997). One
1
Okuzumi et al. 2015). Searching for similar small scale
5 promising solution is to restrain particles in a confined
structures in a population of disks is thus critical to
0 area, such as a local pressure maximum in the disk
study their originandto ultimately gainanunderstand-
. (Lyra et al. 2008; Johansen et al. 2009b; Pinilla et al.
1 ing of the planetesimal formation processes during gas-
2012; Birnstiel et al. 2013).
0 rich stages.
Continuumemissionat(sub)mmwavelengthsprovides
6 Hereweinvestigatethecommonalityof10-30AU-sized
the most direct constraints on spatial distribution of
1 dust structures in a modest sample of four protoplane-
mm-sized dust grains in disks. Recent observations
: tary disks with the highest spatial resolution (sub)mm
v of some transition disks show large scale (>40AU) ra-
i dial and azimuthal inhomogeneities in continuum emis- continuum observations to date.
X
sion, providing direct evidence of dust trapping in disks 2. OBSERVATIONS AND RESULTS
r (e.g. Casassus et al. 2013; van der Marel et al. 2013;
a Our sample is composed of four protoplanetary disks:
Isella et al. 2013; P´erez et al. 2014; Zhang et al. 2014).
TW Hya, DM Tau, HD 163296 and HL Tau. Data on
Such extreme inhomogeneities are commonly attributed
TW Hya and DM Tau were acquired out as part of the
topressurebumps excitedbygiantplanet(s)inthe disk.
ALMA cycle 2 project 2013.1.00198.S,and those on HD
However, this poses a chicken-egg dilemma on the plan-
163296 were obtained in project 2013.1.01268.S(Salinas
etesimalformationproblem. Othermechanism(s)ofdust
et al., in prep). Here we mainly use the public data on
trapping therefore need to be explored with higher spa-
HL Tau (ALMA Partnership et al. 2015) as a test case
tial resolution observations in larger disk samples.
forourdataanalysismethodology. Asummaryofobser-
The Atacama Large Millimeter/Sub-milimeter Array
vations is provided in Table 1.
All visibility data were calibrated in CASA (version
1Department of Astronomy, University of Michigan,
4.2) using scripts provided by the ALMA staff. The ab-
1085 S University Ave, Ann Arbor, MI 48109, USA;
[email protected] solute uncertainty of the flux calibration is 10%. We
2Division of Geological & Planetary Sciences, MC 150-21, performed iterative self-calibration on both ∼the contin-
CaliforniaInstituteofTechnology, Pasadena, CA91125,USA uum emission phase and amplitude to reduce the atmo-
3Harvard-Smithsonian Center for Astrophysics, 60 Garden
spheric decoherence.
St.,Cambridge,MA02138, USA
4LeidenObservatory,LeidenUniversity,P.O.Box9513,2300 Figure1presentsthecontinuumvisibilityprofilesfrom
RALeiden,TheNetherlands the four disks as a function of the deprojected base-
2
Table 1
Observationlogandsourceproperties
Source νrest ∆ν tint Beam Baseline Flux Rms Obsdate
(GHz) (GHz) (minute) (′′×′′(PA)) (kλ) (mJy) (mJybeam−1)
TWHya 349 2.938 29.0 0.28×0.28(-10) 25-913 1415 0.096 6/15/2015
661 1.875 39.9 0.35×0.20(85) 33-931 5586 1.19 3/12/2014
DMTau 329 2.234 7.7 0.41×0.33(24.9) 24-861 191 0.191 6/14/2015
HD163296 233 2 154.5 0.38×0.27(64.7) 19-638 710 0.017 7/27-29/2014
HLTau 233 8 280.2 0.035×0.022(11) 12-11843 744 0.01 10/24-31/2014
Source Distance M⋆ L⋆ M˙ incl PA RCO Ref
(pc) (M⊙/yr) (L⊙) (M⊙/yr) (deg) (deg) (AU)
TWHya 54 0.55 0.23 4×10−10 7 355 17-23 1,2,3,4
DMTau 145 0.5 0.25 2×10−9 35 155 70±10 5,6
HD163296 122 2.3 27.2 7.6×10−8 224 312 90+8 7,8
−6
HLTau 145 1.3 — 1×10−6 46.7 138 63±10 9
Note. — References: 1.Qietal.2004,2.Hughesetal.2011,3.Qietal.2013,4.Schwarzetal. submitted,5.Pi´etuetal.2007,6.Berginetal.
inprep,7.Rosenfeldetal.2013,8.Qietal.2015,9.ALMAPartnershipetal.2015
line length. The baselines are generally 700kλ, except As discussed above, the simplest physical models fail
∼
that those for HL Tau extend to 12,000kλ. All of our to characterize the observed visibility profiles. More im-
∼
sources appear to be axi-symmetric in synthesized im- portantly, there is no coherent physical model available
ages, as also suggested by the flat distribution of their for the surface density profile of mm-sized particles, be-
imaginary visibility components as a function of depro- cause it may differ significantly from that of a viscously
jected uv-distance. The most important feature in the evolvinggasdiskdue toradialdriftandvariouspressure
visibilityprofilesisthattheyshowawidevarietyofstruc- trapping mechanisms (Chiang & Youdin 2010; Andrews
tures. TW Hya, for example, shows a bump around 290 2015). Due to these uncertainties, we employ an em-
and 250kλ at 349 and 661GHz, respectively; while HD pirical approachto characterize spatial structures in the
163296shows two bumps and a dip below zero. HL Tau surface brightness distributions and discuss the possible
has three main bumps and extensive fine structures out origin of the observed disk structures in Section 4.
to the longest uv-distances. In contrast, DM Tau has
a smooth decay and, like HD 163296, goes below zero 3.1. Deconvolution in interferometric observations
around 400kλ. Since an interferometer acts as a spatial
Theretrievalofsourceintensitydistributionsfromvis-
frequency filter, these visibility features can be used to
ibilitiesisessentiallyadeconvolutionprocess,duetodis-
reveal the detailed radial structures of the disks.
cretesampling onthe uv-plane. Critically,withoutprior
We stress that simple disk models widely used in the
information, the deconvolution has no unique solution
literaturehavedifficultyinreproducingthevisibilityfea-
because the fine structures in the source intensity distri-
turesobservedhere(Figure1,f-i). Adiskwithatapered
bution correspond to unsampled high spatial frequency
outer edge does not bring any significant visibility fea-
components that can have a wide range of amplitudes
tures. Thatwithasharpouteredge(eventhosethatde-
(Cornwell et al. 1999).
cay over modest radial distances) does yield features in
Themostwidelyuseddeconvolutionmethodinhetero-
the visibility profile, but involves a series of bumps with
dyne interferometry is the CLEAN algorithm (Ho¨gbom
similarwidthandthatoccuratharmonicspatialfrequen-
1974; Clark 1980), in which the final deconvolved image
cies. Another widely usedmodelisa diskwith asharply
is a summation of a number of point sources convolved
truncated inner cavity. This model best fits disks that
with a CLEAN beam (usually a Gaussian). This ap-
show significant negative components in their visibility
proach suppresses the highest spatial frequencies in the
profiles,andhas been successfulin modeling many tran-
data and results in a smeared image.
sition disks (e.g. Andrews et al.2011; Zhang et al. 2014;
Another common way to derive source intensity is
van der Marel et al. 2015). This model, however, does
the so-called modeling fitting approach (Pearson 1999).
notworkwellforthedisksamplehere. Ityieldsnegative
Here,theobservedvisibilitiesarereproducedwithapara-
components that are too broad compared to the profiles
metric model of the source intensity distribution. Ad-
ofDMTauandHD163296. Morespecifically,thesecond
vantages of this method include the utilization of the
nulls of the observedvisibility profiles occur muchcloser
full spatial frequency information in data and straight-
to the first nulls than predicted. Furthermore, a cav-
forwarderror estimation. A significant drawback is that
ity solution yields a visibility profile that monotonically
the possible form of models that fit the data may not
decreases within the first null, while bumps are shown
be unique. Thus the choice of a model function requires
inside the first null in TW Hya and HL Tau. These dis-
physical justification.
crepancies suggest that a sharp truncation alone cannot
Hereweretrievethe radialsurfacebrightnessdistribu-
fitthedata,andthusotherstructureelementsareneeded
tions of our disk sample using both the image (CLEAN)
to explain the observations of the four disks.
and model fitting approaches.
3. MODELING 3.2. Model fitting approach
3
1.4 0.8
0.25
(a) (b) (c)
1.2 TW Hya DM Tau 0.7 HL Tau
0.20
1.0 349GHz 329GHz 0.6 233GHz
]
y 0.15 0.5
[ J 0.8
y 0.4
bilit 0.6 0.10 0.3
Visi 0.4 0.05 0.2 500100015002000
0.2
0.00 0.1
0.0 0.0
−0.05
0 200 400 600 800 1000 0 100 200 300 400 500 600 700 0 2000 4000 6000 800010000
5
(d) 0.7 (e)
TW Hya HD 163296
4 0.6
661GHz 233GHz
] 0.5
y
J 3
[ 0.4
y
t
bili 2 0.3
si 0.2
Vi
1 0.1
0.0
0
−0.1
0 200 400 600 800 1000 0 100 200 300 400 500 600
uv distance [kλ] uv distance [kλ]
101 101
(f) 1.0 (g) (h) 1.0 (i)
y y 3.narrow ring
ed surface densit 111000−−021 2. psohwa1erpr.S- leeadlwfg- sedimiskilar disk alized Visibility 000...468 1 ed surface densit 100 45ca..bsvhritoayalldo wring alized Visibility 0000....4682 3
ormaliz 10−3 Norm 00..02 ormaliz 10−1 Norm 0.0 5
N 2 N −0.2
4
10−4 −0.2 10−2 −0.4
100 101 102 0 200 400 600 8001000 101 102 0 200 400 600 8001000
R [AU] uv distance [kλ] R [AU] uv distance [kλ]
Figure 1. Panel(a-e): VisibilityprofilesofcontinuumemissionfromTWHya,HD163296,DMTauandHLTau. TheReal(blackdots)
andImaginary(lightbluediamonds)partsofthevisibilitiesareplottedasafunctionofdeprojecteduv-distance,andthestatisticalerrors
aresmallerthan the sizeofsymbols. The redlinesareour best fitting models fromSection 3. Panel (f,h): model surfacedensityprofiles
foradiskat 140pc; Panel (g, i): visibilityprofiles of the simpledisks models in(f,h). The data of panel (a-e) areavailable fordownload
fromarXivsource.
4
For circularly symmetric disk emission, the link be- using a step size of 0.1AU from 400AU.
tween the deprojected uv-distance and radial brightness UsingHL Tauasanexample,Figure4(a-b)showhow
distribution is a Hankel transform (Pearson1999): including more visibilities changes the derived radial in-
tensity distribution. In particular, by fitting only two
′ Gaussians out to 500kλ, we find a broad gap around
u =(ucosφ vsinφ) cosi (1)
′ − × 60AU. Extending the data to 1000kλ then demands fits
v =usinφ+vcosφ (2) with three Gaussians, and a second but narrower gap
∞ is found around 30AU. When we include data within
V(ρ)=2π Iν(θ)θJ0(2πρθ)dθ, (3) 2000kλ, an innermost gap is seen at 13AU.
Z0 ∼
whereiandφarethediskinclinationandpositionangle,
3.3. Image approach
ρ=√u′2+v′2 is the deprojected uv-distance in units of
Here we obtain radial intensity profiles from the
λ, θ is the radial angular scale from the disk center, and
CLEANed images directly. The visibilities are depro-
J is a zeroth-order Bessel function of the first kind.
0 jected using eqs. (1-2), and deconvolved through the
Here we adopt an analytical function for I(θ) that is
CLEANalgorithmusinguniformweighting,andrestored
inspired by the multi-peak features seen in the visibility
with a synthesized Gaussian beam. We then derive an
profiles (Figure 1). A peak in visibility indicates that
azimuthally averaged I(θ) from the images. An illus-
some spatial frequencies, corresponding to some partic-
trative comparisonof radial intensity profiles of HL Tau
ular spatial scales, have more contribution than other
is plotted in Figure 2(c). Clearly, the three major gaps
scales. Specifically, we model the disk surface inten-
(13, 32 and 63AU) are reproduced nicely by the model
sitydistributionI(θ)withagroupofGaussianfunctions,
fittingapproachusingtheρ 2000kλdata,ascompared
eachofwhichismodulatedbyasinusoidalfunctionwith ≤
with the I(θ) derived from a CLEANed image based on
a spatial frequency of ρi (eq. 4). The number of Gaus-
visibilities of ρ 12000kλ.
siansisdecidedbythenumberofdistinctivepeaksinthe max ∼
visibility profile, and a0,σ0,ai,σi,ρi are free parame- 3.4. Results
{ }
ters. Thus, we choose
The retrieved radial intensity distributions of the four
disks from both the image and modeling fitting ap-
a θ2 proachesarepresentedinFigure3. Consistentresultsare
I(θ)= 0 exp foundoverlargerscales,but(asexpectedbytheHLTau
√2πσ (cid:18)−2σ2(cid:19)
0 0 example) the modeling fitting results clearly show more
ai θ2 detailed structures. The continuum emission from all
+ cos(2πθρi) exp (4)
Xi × √2πσi (cid:18)−2σi2(cid:19) fourdisksisrichinradialstructureswithatypicallength
scale of 10-30AU. For TW Hya, both approaches show
This analytic function is empiricalbut consistent with thatthe349and661GHzemissionhasaturningpointin
realistic disk emission in several aspects. It insures that the slope around 25AU, followed by a plateau and then
I(θ) goes to zero at infinity. Further, the amplitudes of a gradual decay out to 70AU. Nomura et al. (2015)
∼
components associated with unsampled high spatial fre- recently reported similar structures in the 336GHz con-
quency go to zero quickly, meaning no fine structure in- tinuum emission of TW Hya. For HL Tau, its known
formationisadded. Becauserealdiskemissionneverbe- major gaps at 13, 32 and 63AU are well recovered. HD
comes negative, the amplitude of V(ρ) should gradually 163296andDMTauaretwodisksthatshowsignsofcen-
decay with spatial frequency. Thus, adding new visibil- tralflux decrementin ourmodeling (see alsoDM Tauin
ity data with higher spatial frequency coverage will not Andrews et al. 2011). For these two, we show the best
changetheknownstructuresinI(θ)drastically. Thisap- fittingresultsoftwoanalyticalmodels: (1)asmoothdisk
proach is suitable for I(θ) functions without hard edges (no sharp inner edge), and (2) a disk with a sharp inner
and its utility is supported by the fact that no har- edge (R , δ). Both types of models retrieve consistent
cav
monic features associated with sharply truncated disks structures beyond 30AU – HD 163296 has two de-
∼
are found in the four disks. As the largest recoverable pressedzonescenterednear55and100AU,andDMTau
spatialscale(determinedby the shortestbaseline)issig- has a shallowly depressed emission zone around 70AU.
nificantly larger than the disk emission, the total flux The two depressed zones in HD 163296 are also notice-
recoveredfrom the analytic function is conserved. ablein its synthesizedimage alongthe beamminor axis.
After initial fitting, we find that HD 163296 and DM Thetwotypesofmodelsgiveslightlydifferentstructures
Taushowafluxdecrementinside 20AU.Toinvestigate in the central region of HD 163296 and DM Tau, but
∼
if including a sharpinner edge wouldchangethe derived both suggest that the central regions are probably just
disk structures, we run additional models for the two shallowly depleted. It is likely that there are unresolved
disks, by adding two extra free parameters to simulate emissionfromthecentralregionsandthefluxdecrement
aninnercavity—asharpinneredgeR andadepletion is possibly due to gaps rather a central cavity.
cav
factor δ (0 δ 1). We assume the source intensity is Itisimportantto notethatourproposedsolutionsare
≤ ≤
flat inside the cavity since fine structures inside 20AU consistent with the data but other disk structures may
are unresolved. also be possible. This is a nature of deconvolution that
We use the Levenberg-Marquardtχ2 minimization al- the solution is not unique without a restrictive physical
gorithm to search for the optimal value of free param- framework,a framework we currently lack in interpolat-
eters. The initial guesses of the ρi are the centers of ing mm-sized particle distribution in disks. Under this
{ }
peaks in visibility profiles and values of ai can be ei- condition, the simplest solutions are preferred. Our pro-
{ }
therpositiveornegative. Theintegralineq.(4)issolved posed solutions belong to the the simplest group since
5
2.0 2.0 0.40
HL Tau (a) (b) 0.35 (c)
1.5 1.5 0.30
d Visibility1.0 V2(ρ)+1.0 d Intensity1.0 I2(θ)+1.0 d Intensity00..2205 mimoadgeel If(itθt)i,n ρg< I1(θ2)0, 0ρ0<k2λ0 00kλ
alize alize alize0.15
m m m
Nor0.5 V3(ρ)+0.5 Nor0.5 I3(θ)+0.5 Nor0.10
1
2 3 4 0.05
0.0 V4(ρ) 0.0 I4(θ) 0.00
0 500 1000 1500 2000 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160
UV distance [ kλ] R [ AU ] R [ AU ]
Figure 2. HL Tau as an example of the model fitting approach. Panels (a) and (b) show how the derived surface intensity profile
I(θ) changes when visibilities from larger uv-distances are included. The functions V2, V3 and V4 in (a) correspond to the number of
Gaussianfunctions inthe model fitting, and the threevertical dashed linesin(b) highlightthe centers ofthree majordiskgaps reported
by ALMAPartnershipetal. 2015. (c) A comparison of the surface brightness derived from fitting the ρ <2000kλ visibilities and that
resultingfromaCLEANedimageusingallρ<12000kλdata.
they are the smoothest models that fit the data (least eithersmallorabsent,ascomparedtostructuressuchas
high spatial frequency components needed). the sharply truncated narrow rings or edges often seen
in disks with a large central cavity.
4. DISCUSSION
4.1. Origin of disk structures 4.3. Correlation between CO snowlines and enhanced
continuum emission
The richness of small scale features in the sur-
face brightness profiles shown in Figure 3 is strik- With sufficient spatial resolution to resolve CO snow-
ing. One possibility is that they are results of pres- lines, current ALMA observations have enabled the first
sure bumps in protoplanetary disks. Possible mecha- directinvestigationsofthe role ofcondensationfronts in
nisms proposed for generating pressure bumps include: the evolution of solids in nearby protoplanetary disks.
zonal flows (Johansen et al. 2009a; Simon et al. 2012), Sofar,N2H+ cationandC18Oemissionhavebeenused
planet-disk interaction (Lyra et al. 2009), or a (water) as two independent tracers of the mid-plane CO snow-
snowline-induced jump in surface density/ionization de- line. ThetwotracersshowconsistentresultsinTWHya,
gree (Kretke & Lin 2007). where the mid-plane CO snowline is found to lie at 17–
On the other hand, disk structures in (sub)mm con- 23AU(Qi et al.2013,Schwarzetal. submitted),andfor
tinuum emission may also be produced by spatial vari- HD 163296where RCO=90+−86AU (Qi et al. 2015). Since
ations in the dust opacity κν(R). For example, grain nosimilarobservationsareavailableforHLTauandDM
growthitself, willalterthe dustopacity,andif localized, Tau,hereweadoptCOsnowlineradiibasedonradiative
the change in opacity can mirror the effects of a change transfermodelsofthetwodisks,whichyieldRCOclatherate
in the surface density profile. As but one example of = 63 10AU for HL Tau (Men’shchikov et al. 1999;
±
a local effect that dust growth near the water snowline Zhang et al. 2015) and RCO = 70 10AU for DM Tau
±
frommillimeter todecimeter-sizedpebbles ispossibleon (Bergin, in prep).
a timescale of only 1000 years (Ros & Johansen 2013). Figure3presentsthemid-planeCOsnowlinelocations
on top of the surface brightness distributions in the four
4.2. Commonality of smooth disk structures disks. The data suggestthat thereis possibly arelation-
shipbetweenthe snowline locationandenhancements in
Sofar,ALMAhighspatialresolutionobservationshave
the continuum emission.
been only carriedout for severalwell-studied classicalT
Tauri or Herbig star disks or transition systems (disks
4.4. Efficient selection of disk candidates for long
withalargecentraldustcavity). Themajorityoftransi-
baseline ALMA observations
tiondisksobservedshowsomeaxi-asymmetryandsharp
edges (van der Marel et al. 2015). The fraction of tran- The HL Tau observations demonstrate that ALMA
sition disks is estimated to be 10-20% in nearby star- long baseline observations are critical to revealing struc-
∼
forming regions, based on the spectral energy distri- tures within the nominal planet-forming disk radii
bution statistics (Kim et al. 2009; Mer´ın et al. 2010); a (<30AU). However,a preliminary selectionof sources is
greater fraction of 30% (Andrews et al. 2011) is given desiredduetothelongintegrationtimesandexcellentat-
∼
based on resolved sub-mm imaging. Nevertheless, cur- mosphericstabilityneededforlongbaselineobservations.
rent statistics indicates that disks with a large cavity The modeling fitting analysis above shows that distinc-
(>20AU) are probably not the majority of disks. tive features at visibility profiles are useful predictors of
The four disks studied here perhaps provide a better fine structures in disks. To search for 10AU scale struc-
matchtothestructureofthemajorityofdisks,i.e.,‘full’ tures in disks of nearby star forming regions ( 140pc),
∼
disks or disks with small holes. One prediction from our we propose that an initial survey with 2000kλ base-
∼
sample is that circularly symmetric and smoothly vary- line (e.g. 2.6kmat1.3mm) shouldbe sufficientto select
ingstructureswith 10-30AUscalelengthsarelikelyto sources with significant features in deprojected visibil-
∼
be more common in disks in which the central cavity is ity profiles to then be imaged with full baseline (16km)
6
1.0
ty TW Hya HL Tau HD 163296 DM Tau
si
n0.8
e
nt 349GHz smooth model smooth model
d I0.6 660GHz model with Rcav,δ model with Rcav,δ
e
aliz0.4
m
r0.2
o
N
0.0
1.0
y
sit averaged
n0.8 minor axis
e
t
n
d I0.6
alize0.4 beam FWHM beam FWHM beam FWHM beam FWHM
m
r0.2
o
N
0.0
0 20 40 60 80 100 0 20 40 60 80 1001201400 50 100 150 200 0 50 100 150 200
R [ AU ] R [ AU ] R [ AU ] R [ AU ]
Figure 3. Radialsurfacebrightnessprofilesofthefourdisks,derivedfrommodelingfitting(upperrow)andsynthesizedimages(bottom
row). Theresultsofeachdiskarederivedfromthesamevisibilities,exceptforHLTau,forwhichthemodelingfittingresultusesvisibilities
withamaximumuv distancethat ismuchshorterthanthose usedintheimage(ρmax∼2000kλv.s. 11843kλ). Forthemodelingfitting
results of HD 163296 and DM Tau, we show two I(θ) profiles derived from a smooth model as well as a model with a sharplytruncated
centraldepletionzone. Thelightblueregionshighlighttheexpected mid-planeCOsnowlineregion,includinguncertainties.
0.00 0.21 0.46 0.73 1.00 0.00 0.14 0.37 0.66 1.00 0.00 0.12 0.34 0.64 1.00 0.00 0.03 0.18 0.49 1.00
1.5
TW Hya 349GHz 1.0 HL Tau 233GHz 2 HD 163296 233GHz DM Tau 329GHz
2
1.0
0.5 1
0.5 1
c]
e
arcs 0.0 0.0 0 0
[∆δ−0.5 −1
−0.5 −1
−1.0
−2
−1.0 −2
−1.5
1.5 1.0 0.5 0.0 −0.5 −1.0 −1.5 1.0 0.5 0.0 −0.5 −1.0 2 1 0 −1 −2 2 1 0 −1 −2
∆α[arcsec] ∆α[arcsec] ∆α[arcsec] ∆α[arcsec]
Figure 4. Prediction of long-baseline ALMA images (at 0.′′035 resolution). The surface brightness distributions are based on our best
modelfittingofobservedvisibilities(Figure3,toprow). Theintensityisnormalizedtothebrightestpixelineachimage.
ALMA observations. In Figure4, we show simulated ALMA data sets: ADS/JAO.ALMA#2011.0.00015.SV,
long-baseline ALMA images of our sample. The signif- ADS/JAO.ALMA#2013.1.00198.S& ADS/JAO.ALMA
icant contrast in the HD 163296 image is induced by #2013.1.01268.S. ALMA is a partnership of ESO (rep-
the visibility null near 450kλ. The structures proposed resenting its member states), NSF (USA) and NINS
here can easily be confirmed or ruled out in long base- (Japan),togetherwithNRC(Canada),NSCandASIAA
line observations,and similarly the potential association (Taiwan),andKASI(RepublicofKorea),incooperation
betweenCOsnowlinesandcontinuumemissionenhance- with the Republic of Chile. The Joint ALMA Observa-
ments. tory is operated by ESO, AUI/NRAO and NAOJ.
This work was supported by funding from the Na- REFERENCES
tional Science Foundation, grants AST-1344133 (IN-
SPIRE) and AST-1514670. The authors thank John
ALMAPartnership,Brogan,C.L.,P´erez,L.M.,&Hunter,e.a.
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