On the nature of the transition disk around LkCa 15

2 MB·English

by  Andrea Isella

Draft version January 6, 2012
PreprinttypesetusingLATEXstyleemulateapjv.5/25/10
ON THE NATURE OF THE TRANSITION DISK AROUND LKCA 15
Andrea Isella, Laura M. Pe´rez, John M. Carpenter
DepartmentofAstronomy,CaliforniaInstituteofTechnology,MC249-17,Pasadena,CA91125,USA
Draft version January 6, 2012
ABSTRACT
We present CARMA 1.3 mm continuum observations of the T Tauri star LkCa 15, which resolve
thecircumstellardustcontinuumemissiononangularscalesbetween0.2(cid:48)(cid:48)-3(cid:48)(cid:48),correspondingto28-420
AUatthedistanceofthestar. Theobservationsresolvetheinnergapinthedustemissionandreveal
an asymmetric dust distribution in the outer disk. By comparing the observations with theoretical
2 disk models, we calculate that 90% of the dust emission arises from an azimuthally symmetric ring
1 that contains about 5×10−4 M of dust. A low surface-brightness tail that extends to the northwest
(cid:12)
0 out to a radius of about 300 AU contains the remaining 10% of the observed continuum emission.
2 The ring is modeled with a rather flat surface density profile between 40 and 120 AU, while the inner
n cavity is consistent with either a sharp drop of the 1.3 mm dust optical depth at about 42 AU or a
a smooth inward decrease between 3 and 85 AU. We show that early science ALMA observations will
J be able to disentangle these two scenarios. Within 40 AU, the observations constrain the amount of
4 dustbetween10−6 and7Earthmasses, wheretheminimumandmaximumlimitsaresetbythenear-
infrared SED modeling and by the millimeter-wave observations of the dust emission respectively. In

] addition, we confirm the discrepancy in the outer disk radius inferred from the dust and gas, which
P corresponds to 150 AU and 900 AU respectively. We cannot reconcile this difference by adopting an
E exponentially tapered surface density profile as suggested for other systems, but we instead suggest
. that the gas surface density in the outer disk decreases less steeply than that predicted by model fits
h
to the dust continuum emission. The lack of continuum emission at radii lager than 120 AU suggests
p
a drop of at least a factor of 5 in the dust-to-gas ratio, or in the dust opacity. We show that a sharp
-
o dust opacity drop of this magnitude is consistent with a radial variation of the grain size distribution
r as predicted by existing grain growth models.
t
s
a
[ 1. INTRODUCTION depleted inner regions similar to those of “transition”

disks, but do not show any deficit in the infrared ex-
1 Over the past decade, the Spitzer Space Telescope
cess (Isella et al. 2010a,b; Andrews et al. 2011a). These
v has identified an increasing population of circumstellar
results demonstrate that SEDs alone cannot provide a
1 disks surrounding pre-main sequence stars that display
completepictureofthediskstructure. Highangularres-
0 a deficit of near- and mid-infrared flux compared to a
olution millimeter-wave observations are essential to re-
0 “classical” T Tauri star, while exhibiting similar levels
1 of far-infrared emission. The spectral energy distribu- movesomeofthedegeneraciesthatlimitSEDmodeling,
. tion(SED)oftheseobjectssuggeststhatthesestarslack and therefore provide a more accurate description of the
1
radial distribution of circumstellar material.
0 warm dust in the inner disks regions, while substantial
To determine the physical phenomena responsible for
2 emission at longer wavelengths indicates that the outer
disk cavities, measurements of the mass surface den-
1 diskremains quitemassive (see, e.g., Calvetet al.2005).
sity profile Σ(r) are essential. To first order, circum-
: Theseso-calledtransitiondisksmaybeintermediatesys-
v stellar disks evolve via viscous spreading, where friction
tems between young (∼1−10 Myr), optically thick, gas
i forces redistribute the material and smoothly shape the
X rich protoplanetary disks and old (> 10 Myr), optically
disk surface density (Lynden-Bell & Pringle 1974). Disk
thin, gas poor, debris disks, where significant disk evo-
r photoevaporationbyenergeticphotonsmightreducethe
a lution has occurred and a planetary system might have
amountofdiskmaterial. Modelsthatcombinethesetwo
formed.
process have been the focus of many theoretical studies
Subsequenthigh-resolutionimagesoftheopticallythin
(Alexander et al. 2006a,b; Gorti et al. 2009; Owen et al.
millimeter-wave dust emission confirm the SED model-
2010). These models suggest that viscous evolution pro-
ing predictions that the inner disk in transition disks
ceeds unperturbed by photoevaporation until the mass
is depleted of dust (Andrews et al. 2011a; Brown et al.
accretion rate throughout the disk is comparable with
2009; Hughes et al. 2009; Pi´etu et al. 2006). However,
the photoevaporation rate. After this phase, which can
spatially resolved observations of the gas emission show
last for a few Myr for typical values of the stellar radia-
thatsomeofthesedustdepletedcavitiescontainasignif-
tionanddisksurfacedensity,agapopensatfewAUfrom
icant amount of gas (Pi´etu et al. 2007) and that the size
the central star, where the photoevaporation rate is the
of the hole is not always consistent with SED modeling
largest. The material within the gap then drains quickly
(Andrews et al. 2011a). Furthermore, recent high angu-
ontothecentralstarleavingagas-freecavityinthedisk.
larresolutionobservationsofthemm-wavedustemission
Although the exact time scale for the formation of the
have also revealed that some “classical” disks have dust
cavity varies between different models, they all predict
[email protected] an order of magnitude drop in the gas surface density
2 Isella A., P´erez L., and Carpenter J.
over a 1 AU radial extent at the edge of the cavity. tion of 0.2(cid:48)(cid:48) corresponding to a spatial scale of 28 AU
Alternatively, cavities in the disk can be produced by at the distance of star, which is a factor of two improve-
the gravitational interaction between giant planets and ment with respect of existing observation of this system.
thediskmaterial(see,e.g.,Brydenetal.1999). Although InSection2and3wepresentourobservationsofLkCa15
this is a common explanation for transition disks, Zhu and discuss the morphology of the dust emission. The
etal.(2011)haveshownthatevenmultiplegiantplanets methodusedtoanalyzethedataisdiscussedinSection4,
cannot account for optically thin cavities larger than 20 andtheresultsarepresentedin5. InSection6wediscuss
AU, unless the small grains within the region perturbed the possible origin of the dust continuum cavity and of
by the planets are efficiently removed. Similarly to the thewholediskstructure. Asummaryofthemainresults
photoevaporationmodel,theplanet-diskinteractionpre- follows in Section 7.
dictasharpdropofthedustyandgasdensityattheedge
of the region cleared by the planet tidal interaction. 2. OBSERVATIONSANDDATAREDUCTION
Athirdpossibleoriginoftheinnerdiskcavitiesisthat LkCa 15 was observed with CARMA array configu-
thedustgrainshavegrownfrommicronsizedparticlesto rations A, B, C, and E, providing projected baseline
centimetersizedpebbles. Therefore,thecavitiesreflecta lengths between 6 and 1700 m. C-configuration observa-
reduced dust opacity and not a reduced matter density. tionswereobtainedinOctober2007andarediscussedin
Theory predicts that dust coagulation is more efficient Isellaetal.(2009). ObservationsinB-configurationwere
in the dense inner disk (Tanaka et al. 2005; Dullemond obtained in December 2008. The receivers were tuned
& Dominik 2005) and as the dust particles grow, the at a local oscillator frequency (LO) of 224.75 GHz and
opacity of the dust diminishes. Current models of grain the continuum emission was observed using three con-
growth anticipate a continuous radial variation of the tiguous bands of 468 MHz each in both correlator side
dust opacity within the disk (e.g., Birnstiel et al. 2010), bands, resulting in a total bandwidth of about 3 GHz.
whose observational signature corresponds to a gradual Fluxandpassbandcalibrationwerederivedbyobserving
transition between the inner and outer disk structure. Uranus and 3C84 respectively; 0510+180 was observed
Among the known stars with a transition disk, the 2- every 15 minutes to derive the atmospheric and instru-
5 Myr old star LkCa 15 represents an outstanding case. mental phase corrections. A- and E-configuration obser-
LkCa15isaK5star(L =0.74L ,M =1.0M ;Simon vations were carried out in November 2010 and January
(cid:63) (cid:12) (cid:63) (cid:12)
et al. 2000; Kenyon & Hartmann 1995) located in the 2011 respectively, using the upgraded CARMA correla-
Taurusstar-formingregionatadistanceofabout140pc tor which provides a maximum continuum bandwidth of
(vandenAnckeretal.1998). Itsdiskischaracterizedby about 8 GHz. The receivers were tuned to the same LO
a partially dust-depleted inner region of about 50 AU in frequency used for C and B-configuration observations.
radius(Andrewsetal.2011a;Espaillatetal.2007;Pi´etu The upper and lower correlator side bands were config-
et al. 2006) and a mass accretion rate of about 3×10−9 ured with eight partially overlapping bands of 494 MHz
M yr−1 (Hartmann et al. 1998). The disk SED is char- eachinordertocoverthefullbandwidth. Thebandpass
(cid:12)
acterized by the presence of an infrared excess over the shape was calibrated by observing 3C84 and 3C454.3;
stellar photosphere, which can be explained by the pres- flux calibration was set by observing Uranus and cross
ence of hot dust within few AUs from the central star checked using almost simultaneous observations of 3C84
(Espaillat et al. 2007; Mulders et al. 2010). The disk and 3C454.3 obtained with the SMA at the frequency
has a very active chemistry observed in several molecu- of 225 GHz. The estimated uncertainty in the absolute
lar transitions (Chapillon et al. 2008; Pi´etu et al. 2007; flux calibration is 10%. Atmospheric and instrumental
O¨berg et al. 2010), and also exibits keplerian rotation effects were corrected by observing the nearby quasar
0510+180 every 6-10 minutes, depending on the array
out to a radius of 900 AU (Pi´etu et al. 2007). These lat-
configuration.
ter observations suggest that gas is present at an orbital
The data taken in the four different array configura-
radius as small as 10 AU, and therefore well within the
tions were independently calibrated using the MIRIAD
cavityobservedinthedustcontinuumemission. Ground
softwarepackage. Thedatasetwereshiftedbothinright
based H-band (1.6 µm) observations reveal the presence
ascension and declination to compensate for the stellar
of an elliptical structure in correspondence to the edge
proper motion (see Appendix) and combined to increase
of the dust inner cavity (Thalmann et al. 2010). Fi-
the image sensitivity and dynamic range. Images were
nally, Kraus & Ireland (2011) has recently reported the
then obtained through standard inversion of the uv data
discovery through aperture masking of a possible 6 M
J usingdifferentweightingfunctionstoemphasizethemor-
mass proto-planet located inside the continuum cavity
phology of the dust emission on both large and small
at an orbital distance of 16 AU from the central star.
angular scales. The images were deconvolved using the
These observations suggest that the cavity might be in-
CLEAN algorithm.
deed shaped by the dynamical interaction with a giant
planet. However,Zhuetal.(2011)andDodson-Robinson
3. MORPHOLOGYOFTHECONTINUUMEMISSION
&Salyk(2011)havearguedthatacavity50AUinradius
The high dynamic range obtained by combining the
cannot be explained by a single planet, and that addi-
compact and extended array configurations enables
tional giant planets or clearing mechanisms are required
CARMA to reveal the structure of the dust emission on
to explain these observations.
both small and large angular scales. Figure 1 shows the
In this paper we present new observations of the 1.3
mapobtainedbyadoptingthreedifferentweightingfunc-
mm dust thermal emission obtained with the Com-
tions to achieve an angular resolution of (a) 3.0(cid:48)(cid:48)×2.6(cid:48)(cid:48)
bined Array for Research in Millimeter-wave Astronomy
(b)1.1(cid:48)(cid:48)×0.5(cid:48)(cid:48) and(c)0.21(cid:48)(cid:48)×0.19(cid:48)(cid:48). Inpanel(a),thedisk
(CARMA). The observations achieve an angular resolu-
emission appears fairly symmetric and centered near the
3
Figure 1. Mapsofthe1.3mmdustcontinuumemissionobservedtowardLkCa15employingthreedifferentweightingschemesoftheuv
data. (a)NaturalweightingwasadoptedtoachieveaFWHMbeamsizeof3.0(cid:48)(cid:48)×2.6(cid:48)(cid:48). Intensitycontoursstartat3σandarespacedby6σ,
wherethe1σ noiselevelis0.58mJy/beam. (b)Robustweightingwasadoptedtoachievearesolutionof1.1(cid:48)(cid:48)×0.5(cid:48)(cid:48). Contoursareplotted
every3σ,wherethe1σ noiselevelif0.53mJy/beam. (c)UniformweightingwasadoptedtoachieveaFWHMbeamsizeof0.21(cid:48)(cid:48)×0.19(cid:48)(cid:48).
Contoursareplottedevery3σ,wherethe1σnoiselevelis0.43mJy/beam. (d)Thelarge,medium,andsmallredcirclesshowtheposition
ofthecenterofsymmetryofthedustemissioncorrespondingtopanel(a), (b), and(c)respectively. Thesymbol(cid:63)marksthepositionof
thestarandthesurroundingcircleitsuncertainty,calculatedasdiscussedintheAppendix. Thedottedcurvesshowtheintensitycontours
asinpanel(c).
position of the star. The integrated flux measured in is117±10mJy. CARMAobservationsrevealforthefirst
a circular aperture of 4(cid:48)(cid:48) in radius, is 128±5 mJy, and time an asymmetric dust distribution in LkCa 15 outer
it is consistent with the value measured by Pi´etu et al. disk, while the ring-like structure presented in panel (c)
(2006). In panel (b), the emission has two peaks sepa- ofFigure1isconsistentwithearlierlowerangularresolu-
rated by about 0.3(cid:48)(cid:48). In addition, the low intensity con- tion observations of LkCa15 (Pi´etu et al. 2006; Andrews
tours show that the disk extends toward the northwest. et al. 2011a).
The integrated flux, as measured in a circular aperture To investigate the properties of the dust emission we
of2(cid:48)(cid:48) inradiusis127±15mJy, wheretheuncertaintyac- define the center of symmetry (x ,y ) of the map inten-
c c
countsonlyforrandomnoise. Finally, themapshownin sity I(x,y) such that x = ΣxI/ΣI and y = ΣyI/ΣI,
c c
panel (c) reveals that the dust emission comes from an where the sum extends over all positions brighter than 5
ellipticalringthatextendsforabout1.8(cid:48)(cid:48) alongitsmajor times the noise level in the image. Since I(x,y) depends
axis, and for about 1.2(cid:48)(cid:48) in the perpendicular direction. ontheweightingschemeadoptedintheimageformation
Assuming that the emission arises from a circular disk, process, the position of the center of the emission is a
the aspect ratio of the contour levels leads to a disk in- function of the angular resolution in the image. Panel
clination of about 50◦, a position angle measured east (d) in Figure 1 shows the center of symmetry for the
from north of about 60◦, and a disk diameter of about three maps discussed above. The stellar position and its
250 AU for the stellar distance of 140 pc. The total uncertainty, as expected from proper motion correction
integrated flux measured in an elliptical aperture with (Appendix), are shown by the star symbol and the sur-
major axis of 2.4(cid:48)(cid:48) and the same aspect ratio of the disk rounding circle respectively. We find that the center of
4 Isella A., P´erez L., and Carpenter J.
symmetryofthehighestangularresolutionmapisconsis- and Σ 1 The first modeling procedure, i.e., variable γ
t
tentwiththepositionofthestar, andbothappeartobe andfixedr ,stemsfromtheideathattransitionaldisks
in
shiftedbyabout0.1(cid:48)(cid:48) withrespecttothecenterofinner- might be shaped a global physical process, such as the
mostintensitycontourslevels. Althoughtheastrometric disk viscosity and/or the variation of the dust opacity
uncertainty on the position of the star does not allow due to the grain growth. By contrast, the second case
us to firmly conclude on the nature of this shift, we note assumes that the disk surface density profile follows the
thatapericenteroffsetofsimilarmagnitude(0.064(cid:48)(cid:48))and α-constantprescriptionoftheviscosity(Shakura&Sun-
direction has been recently derived from infrared obser- yaev 1973) which leads to γ = 1, and that the cavities
vations by Thalmann et al. (2010). observedinthedustemissionresultsfromtheinnertrun-
At lower angular resolution the center of symmetry cationofthedisk,perhapsduetoplanets,whichdoesnot
moves progressively toward the northwest up to a dis- effectthedensitydistributionatlargerradii. Inorderto
tance of about 0.3(cid:48)(cid:48) from the star. This shift of the cen- investigate the nature of LkCa 15 disk we here adopt
ter of symmetry, which results from the asymmetry ob- both approaches which we will be referred to as smooth
served at intermediate angular resolution, suggests that and truncated viscous models.
the outermost disk regions might have been perturbed. The radiation transfer equation within the disk is
However,about90%ofthedustemissionarisesfromthe solvedbyadoptingthe“two-layer”approximationofChi-
fairly symmetric ring shown in panel (c). The structure ang & Goldreich (1997), in which the disk is described
ofthisringandthesignificanceoftheobservedasymme- through a warm surface layer and a cooler midplane in-
tries are discussed in the following two sections. terior. Bothtemperaturesarecalculatedasafunctionof
the orbital radius by iterating on the vertical disk struc-
ture (see Dullemond et al. 2001). The disk is in hy-
4. DISKMODEL
drostatic equilibrium between the gas pressure and the
The disk properties were inferred using two prescrip- stellargravity, whichleadstoaflaredgeometrywiththe
tions for the disk surface density. openingangleincreasingwiththedistancefromthecen-
The first is a classical power law Σ(r) = Σ0(r0/r)p tral star. Because a flared disk geometry tends to over
characterized by four free parameters: the inner radius predictthefar-IRdiskemissioninLkCa15,weallowthe
rin, the outer radius rout, the normalization value Σ0, disk scale height Hp to be lower than the self-consistent
and the slope p. This parameterization provides the solution H˜ by introducing a settling parameter Ψ < 1,
simplest form for the disk surface density that mimics p
so that H =ΨH˜ . Following Mulders et al. (2010) and
the sharp inner disk truncation caused by disk photo- p p
Espaillat et al. (2007), we chose Ψ=0.3.
evaporation or by dynamical interaction with a giant
The dust opacity is calculated by assuming an inter-
planet, but has the disadvantage of introducing an un-
stellargraincomposition(Pollacketal.1994)andapar-
physical sharp edge of Σ(r) at the disk outer radius.
ticle size distribution between a minimum (a ) and a
To obtain a smoother form of Σ(r) we adopt a sec- min
maximum (a ) size according to n(a) ∝ a−q. The
ond parameterization given by the similarity solution max
spectral slope of the LkCa15 mm-wave disk emission is
for the disk surface density of a viscous keplerian disk
α = 3.4, as computed from the observed flux density
(seeLynden-Bell&Pringle1974;Hartmannetal.1998),
at 1.3 mm (128 mJy; see Section 2) and 7 mm (0.44
adopting the form presented in Isella et al. (2009),
mJy; Rodmann et al. 2006). Assuming that the emis-
Σ(r)=Σ (cid:16)rt(cid:17)γ ×exp(cid:40)− 1 (cid:34)(cid:18)r (cid:19)(2−γ)−1(cid:35)(cid:41). sRioanylaeitgthh-eJseeanwsavaeplpenrogxtihmsaistioopnt,ictahlilsyimthpinlieasndafdoullsotwosptahce-
t r 2(2−γ) r ity slope β =2−α=1.4, which is reproduced adopting
t
a = 0.5 µm, a = 0.5 mm, and q = 3.5. For sake
(1) min max
ofsimplicityweassumethatthedustopacityisconstant
This functional form has five free parameters, i.e., the
throughout the disk.
diskinnerandouterradius(r andr ),thecharacter-
in out Fromthederiveddustdensity,temperature,andopac-
istic radius r , the normalization value Σ = Σ(r ), and
t t t ity we calculate the disk SED and synthetic disk images
theslopeγ,whichisrelatedtotheradialviscosityprofile
in the dust continuum at 1.3 mm. We assume that the
through the equation ν(r)∝r−γ.
center of the disk corresponds to the center of symme-
Since the limited angular resolution and sensitivity of
try of the dust emission shown in panel (c) of Figure 1.
existing observations does not generally allow to fit for
The synthetic disk images are then Fourier transformed
allfiveparameters, previousstudiesofthedustdistribu-
and sampled at the positions on the (u,v) plane corre-
tion in transitional disks based on this form of the sur-
spondingtotheCARMAobservations. Best-fitvaluesfor
face density adopted two different approaches. In Isella
the free parameters that define the disk surface density,
et al. (2009, 2010a,b), we fixed the disk inner radius at
and for the disk inclination and position angle are then
the dust evaporation radius (< 0.5 AU), and compared
derived through a χ2 minimization based on a Markov
the model to the observations to constrain the values of
ChainMonteCarlosimulationasdiscussedinIsellaetal.
γ, r , and Σ . In this way, we found that the cavities
t t (2009).
in the dust continuum emission observed in LkCa 15,
RY Tau, and MWC 758 disks might be explained with 5. RESULTS
small inner disk radii and negative values of γ, which
leads to a smoothly increasing surface density up to a 1 Andrews et al. (2011a) adopt a different parameterization of
radius r = r ×(−2γ)1/(2−γ). A different approach the similarity solution for the surface density, which depends on
max t
was adopted by Andrews et al. (2011a), who fixed the the characteristic radius rc = rt×[2(2−γ)]1/(2−γ) and on the
slopeγ =1,andderivedthediskinnerradiusrin,rt and normalizationvalueΣc=Σt×[2(2−γ)]γ/(γ−2).
5
Table 1
Best-fitparametersforthesmoothandtruncatedmodels.
Model Incl. PA rin rt rout γ Σt Md
Smoothviscous 50.5+0.9 64.4+1.5 [0.2] 60.2+0.6 [160] -2.15+0.08 10.37+0.20 [0.06]
−0.9 −1.5 −0.8 −0.10 −0.24
Truncatedviscous 52+1.0 67+1.6 52+1.3 20+1.2 [190] [1] 270+20 [0.1]
−1.2 −1.6 −2.0 −1.0 −15
Model Incl. PA rin r0 rout p Σ0 Md
Power-law 50.7+1.2 63.5+1.8 42.5+2.4 [60] 119.7+1.4 0.72+0.14 9.92+1.1 [0.05]
−1.0 −1.2 −1.2 −2 −0.28 −0.64
Note. —Thenumbersinsquarebracketsareeitherfixedvalues(i.e.,thenormalizationradiusr0)oraretheresultofthemodelfitting.
Theinclinationandpositionangleareexpressedindegrees,theradiirin,rout,rt,andr0 inAU,thedisksurfacedensitiesΣt andΣ0 ing
cm−2,andthediskmassM insolarmasses.
d
5.1. Constraints on the disk surface density truncated viscous model produces a much steeper de-
creaseinthesurfacedensityinthisradialrange. Thisre-
The best-fit parameters for both the smooth and the
sultthereforeimpliesthatthesurfacedensityinLkCa15
truncated disk models are listed in Table 1. The quoted
disk is inconsistent with the α-constant prescription at
uncertainties correspond to the 68.3% confidence level
least in the radial range probed by our observations.
and were calculated by integrating the marginalized
The power-law and the smooth viscous models repro-
probability distribution resulting from the Monte Carlo
duce equally well the ring observed in the dust emission.
fitting procedure (see Appendix A of Isella et al. 2009).
To understand why our observations cannot disentan-
In addition to the free model parameters, we list within
gle these two models, we show in Figure 4 the differ-
the square brackets some relevant values for the disk
ence between the correlated flux of the power-law and
structure, such as the inner and outer disk radius for
the smooth viscous model as a function of the spatial
thesmoothviscousmodel,theouterradiusandγ forthe
frequency (solid curve), along with the 1σ and 2σ noise
viscous truncated disk model, and the normalization ra-
level provided by our observations (blue and red boxes
dius for the power-law model. Finally, the last column
respectively). The maximum difference between the two
of the table shows the total disk mass. In addition to
models is about 6 mJy at 580 kλ and is within the 2σ
the statistical errors, the surface density Σ and the to-
t noise level. The figure also shows that our ability to
taldiskmassM areaffectedbysystematicerrorsdueto
d disentangle different surface density profiles is not ham-
the flux calibration and to the uncertainty on the dust
pered by the angular resolution (i.e., by the maximum
opacity. We estimate a 10% uncertainty from flux cal-
spatial frequency achieved by our observations), but by
ibration based upon CARMA flux calibration monitor
thenoiselevelonspatialfrequenciesbetween100kλand
programs. The uncertainty on the dust opacity is more
700 kλ where the difference between the two models is
difficulttoquantifyandmightvarybetween5%and20%
the greatest. This is an important point to consider in
oncetheslopeofthemillimeterSEDisusedtoconstrain
planning future observations and will be discussed fur-
the grain size distribution (see the discussion in Isella
ther in Section 6.2.
et al. 2009, 2010a).
Althoughwecannotachieveamodel-independentcon-
Figure 2 presents the comparison between the best-fit
straint of the disk surface density, our observations pro-
models and observations. Panels (a) show the real part
videanupperlimitoftheamountofsmallsolidparticles
of the observed correlated flux (points with error bars),
presentintheLkCa15innerdisk. Wefindthattheupper
the visibility profile of the best-fit model (solid line) and
limit is set by the best-fit smooth viscous model, since
theresidualsobtainedbysubtractingthemodelvisibility
any additional amount of dust in the inner disk provides
to the observations. Panels (b) and (c) show the maps
a worse fit to the data. Integrating this density profile
of the residuals obtained adopting the same weighting
between 3-42 AU, we calculate a dust mass of 7 Earth
functions and color scale of panels (b) and (c) of Fig-
masses(M ), orabout2M ofgasassumingastandard
ure 1 respectively. Finally, the surface density profiles ⊕ J
gas-to-dustratioof100. Additionalconstraintsofthegas
corresponding to the best-fit models are shown in Fig-
density come from spatially resolved observations of the
ure 3, along with the corresponding uncertainties.
12CO and 13CO (2-1) line emission (Pi´etu et al. 2007).
We find that the smooth viscous and the power-law
These observations are characterized by an angular res-
models provide acceptable fits to the observations. The
olution between 1(cid:48)(cid:48)-2(cid:48)(cid:48), and were compared to power-law
first model is characterized by γ =−2.15, which is more
disk models to derive the gas density and temperature
negative, although consistent within the uncertainties,
radial profile. Pi´etu et al. (2007) find that CO might
with the γ value derived in 2009 by fitting only the
be present down to a radius of 10 AU, and that a sharp
smaller spatial frequencies. Both models suggest a disk
inclination of 51◦±1◦ and a position angle of 64◦±2◦, truncation of the gaseous disk at 50 AU is excluded at
the 7σ level. These observations also suggest the pres-
that agrees with the values derived by Andrews et al.
enceofabout2M ofgaswithin42AUfromthecentral
(2011a). By contrast, the truncated viscous model char- J
star. The amount of dust within 42 AU from the central
acterized by γ = 1 does a worse job in reproducing the
star is also constrained by the infrared SED modeling,
structure of the dust emission and leads to significative
which is discussed in Section 5.3.
residualsbothinsidethecontinuumcavityandalongthe
Finally, we confirm the discrepancy found by Pi´etu
dusty ring (second row of Figure 2). The comparison
et al. (2007) between the disk outer radius inferred from
between the best-fit surface densities (Figure 3) shows
the dust continuum emission, i.e., about 160 AU, and
that the first two models are characterized by rather flat
that derived from the observations of the molecular line
densityprofilesbetweenabout50and120AU,whilethe
6 Isella A., P´erez L., and Carpenter J.
Figure 2. Comparisonbetweentheobservationsandthebest-fitmodelscalculatedassumingasmoothviscous(toppanels),atruncated
viscous (middle panels) and a power-law (bottom panels) surface density profile. Panels (a) show the real part of the correlated flux
observed at 1.3 mm (square points with error bars), along with the best-fit model (solid line) and the residuals. To account for the disk
geometry,thedatahavebeendeprojectedusingthevaluesfortheinclinationandpositionanglelistedinTable1. Panels(b)and(c)show
mapsoftheresidualsobtainedwiththeweightingfunctionsusedinpanels(b)and(c)inFigure1. Thecolorscale,themapsizeandnoise
level are also the same as in Figure 1. Solid contours are plotted every 3σ, while the dotted contours in panels (c) stars at 2σ and are
spacedby1σ. Thedashesellipsesshowtheinnerandouterdiskradiuscorrespondingofthebest-fitmodelslistedinTable1.
emission, which, depending of the observed molecule, smooth and truncated viscous best-fit models for the
varies between 550 AU (13CO) and 900 AU (12CO). dust continuum emission. The 12CO surface density is
Gaseousdisksarefoundsystematicallylargerthandusty described by Equation 1, with γ and r as in Table 1,
t
disks in almost all the objects observed at high angular andassumingaCO/H2abundanceof10−4,asmeasured
resolution (Isella et al. 2007; Pi´etu et al. 2005, 2007). In in the molecular clouds. By assuming that the 12CO
some cases this discrepancy can be reconciled by adopt- molecules are in thermal equilibrium with the dust, we
ing an exponentially tapered surface density profile, as find that the 12CO emission should be confined within
theoneresultingfromthediskviscousevolution(Hughes 300AUand550AUfromthecentralstarforthesmooth
et al. 2008; Isella et al. 2009). This model predicts that and truncated viscous model respectively, despite the
dust is present up to the outer radius inferred from the factthatthe12COdensityextendsinpracticetoinfinity.
gas but the millimeter-wave dust emission coming from The fact that 12CO is observed out to a radius of 900
the outer disk is too low to be detected by existing ob- AU suggests therefore that the exponential taper that
servations. In the case of LkCa 15, we have used the characterizes the viscous surface density is not a good
gas emission model discussed in Isella et al. (2007) to explanation for the different radial extent of the gas and
calculate the 12CO J=2-1 emission corresponding to the dust emission in LkCa 15. Other possible explanations
7
0.9
100 Smooth viscous model
Truncated viscous model
0.8
2) Power-law model
-m
c 0.7
nsity (g 10 y/beam) 0.6
de mJ
ce ((cid:109) 0.5
a
urf 0.4
S
1
0.3
0 20 40 60 80 100 120 140 160 180 200 0 2 4 6 8 10 12 14
Radius (AU) Radius (arcsec)
Figure 3. Surface density profiles corresponding to the smooth Figure 5. Radialvariationofthenoiseinthemappresentedin
andtruncatedviscousbest-fitmodels(greenandbluerespectively), panel(c)ofFigure2. Thecirclesshowthestandarddeviation(σ)
and to the power-law model (red). The colored regions represent oftheintensitymeasuredinconcentric0.2(cid:48)(cid:48)wideannuli. Thefilled
the3σ uncertaintyinterval. circles correspond to annuli in which the intensity distribution is
consistentwithastandardnormaldistribution,asexpectedifthe
emission is due to gaussian noise. The open circles indicate the
radii where the intensity distribution is dominated by true emis-
sion. Thesolidcurverepresentsthetheoreticalnoiseascomputed
10 fromtheweightsonthevisibilitydata.
y) 5 is identified with the letter A and has peak flux of 2.4
J
m mJy. It is located along the major axis of the disk at
e ( the physical distance of 140 AU from the center, and
c
en 0 thereforeveryclose,orjustoutside,theouterdiskradius
Differ itnhfeerlraerdgefrodmashoeudr delilsikpsmesodineliFnigg,uwrehi2c.h iAstretphriessednitsetadnbcye
-5
from the central star, the dust is expected to have a
temperature of about 40 K, which leads to a mass of
-10 dust of about 1.3 MJ.
0 200 400 600 800 1000 1200 The significance of this residual depends critically on
B (k(cid:104)) knowing the value of the noise in our map and how it
uv
varies with the distance from the center due to the an-
tennaprimarybeamattenuation. Atheoreticalvaluefor
Figure 4. Differencebetweenthe1.3mmcorrelatedfluxes(solid
the noise can be obtained from the weights on each visi-
curve) of the best-fit power-law and smooth viscous models. The
blue and red triangles show the 1σ and 2σ noise level of the bilitypoint,whicharemeasuredatthetimeoftheobser-
CARMA observations. The figure shows that the sensitivity of vationsanddependsontheeffectiveareaofthetelescope
CARMA observations is not sufficient to distinguish between the and the system temperature (see, e.g, Thompson et al.
twosurfacedensityparameterizations.
1991). However, if the observed source is bright, this es-
are discussed in Section 6.3. timate does not take into account possible effects due to
theimagedeconvolution,suchasthepresenceofresidual
5.2. Sub structures and asymmetries
side lobes in the final map, and dynamic range limita-
Figure 2 shows the map of the residuals obtained by tions due to the atmospheric decorrelation (i.e., seeing)
subtracting the best-fit models from the observations in and calibration errors.
the Fourier domain, and by adopting different weighting We estimated the noise in the images as follow. We
functionsintheimagereconstructionprocess. Panels(b) divide the intensity map in concentric annuli character-
and(c)adoptthesameweightingfunctions,usethesame ized by a width of 0.2(cid:48)(cid:48). For each annulus we calculate
color scale, and have the same size of the maps shown in the mean intensity and the standard deviation σ. If the
the panel (b) and (c) of Figure 1. emission is due only to gaussian noise, then the mean is
Panel(b)clearlyshowstheasymmetricemissioninthe 0 and the standard deviation of the intensity is equal to
northwest side of the disk discussed in Section 3. The the noise. For each annulus, we check that the distribu-
integrated flux is about 8 mJy, which corresponds to a tionis gaussianby creatinga histogramforthe intensity
dust mass between 5 and 10 M for a dust temperature and fitting a normal distribution. Otherwise, if the an-
J
between 20-40 K. nulus contains true emission, the intensity distribution
Asfortheresidualsalongthedustyringandinsidethe will deviate from the normal profile. In this case σ will
cavity, we discuss only the case of the smooth viscous give an upper estimate of the noise.
and power-law model, since we have concluded in the Figure5showstheradialvariationofthestandardde-
previous section that the truncated viscous model does viation of the intensity, σ. At radii larger than 6(cid:48)(cid:48) (filled
not provide as good of a fit to the observations. For circles), the intensity distribution is well described by a
these two models, the brightest residual in panels (c) standardnormalfunction; σ increaseswiththeradiusas
8 Isella A., P´erez L., and Carpenter J.
the inverse of the antenna primary beam profile and it
is equal to the theoretical noise indicated by the solid
-9 Smooth viscous model
curve. Within6(cid:48)(cid:48),theintensityisacombinationofgaus-
siannoiseandtrueemissionanditsdistributiondeviates 2)
-m
fnrooimse tinhethsetamndaaprdmanyoramssaulmperovfialelu.esInbetthwiesenregthioent,htehoe- -1s c -10
retical noise and σ. This implies a noise upper limit of erg
01(cid:48).(cid:48)4)7, wmhJiych/bleeaamdsattotahesipgnoasilt-itoon-noofisethreatrieosiodfua5l.1A, g(iiv.een., F) ((cid:105) -11
(cid:105)
the measured peak flux of 2.4 mJy. g (
The significance level of residual A can be estimated Lo -12
by multiplying the normal probability corresponding to
a 5.1σ residual (3.4 × 10−7) by the number of inde-
-13
pendent pixels in our map. If each resolution element
-0.5 0 0.5 1 1.5 2 2.5 3
(0.21(cid:48)(cid:48)×0.19(cid:48)(cid:48)) is accounted as independent pixel, then
Log (cid:104) (µm)
the number of independent pixels within the 1.3 mm
CARMAfieldofview(27(cid:48)(cid:48))isabout18000,andtheprob-
abilitythattheresidualmightbeduetorandomnoiseis
smaller than 0.6%, or about 2.8σ. This result suggests -9 Power-law model
thattheresidualmighttracearealcompactover-density 2)
in the dust distribution with respect to the best-fit sur- -m
face density profile, but more sensitive observations are 1 c -10
-s
required to investigate the nature of this emission. g
wiAthllinth±e4o.t5hetirmreessidtuhaelsnoinispealnevelel(.c)TohfeFipgruorbea2bihliatvyetflhuaxt ) (er(cid:105) -11
F
any one of these residuals could originate from random g ((cid:105)
noise is greater than 10%. Lo -12
5.3. Understanding the SED
Figure6comparestheobservedSEDforLkCa15with -13
theSEDinferredfromthebest-fitmodelstothemillime- -0.5 0 0.5 1 1.5 2 2.5 3
terdata. Boththesmoothviscous(upperpanel)andthe Log (cid:104) (µm)
power-law (lower panel) provide a good agreement with
the observations at millimeter wavelengths. At infrared Figure 6. SED of LkCa 15. Filled squares present photomet-
ricdatafromtheliterature(Kenyon&Hartmann1995;Hartmann
wavelengths, the model SED strongly depends on the
etal.2005;Espaillatetal.2007;Rebulletal.2010;Kitamuraetal.
disk surface density profile. In the case of the smooth 2002; Dutrey et al. 1996; Andrews & Williams 2005, 2007; O¨berg
viscous model, the disk is optically thick to the stellar etal.2010)andfromournewCARMAobservations. Infraredpho-
radiation starting from 3 AU, and the agreement with tometry at 9 µm, 19.6 µm, and 90 µm is from the Akari archive,
the observation extends to about 20 µm. At shorter and the infrared spectrum from 5 µm to 14 µm is from archival
Spitzer IRS observations. The solid curves show the SED of the
wavelengthsthemodelSEDunderestimatestheobserved
best-fitmodelsforthesmooth(toppanel)andthepower-law(bot-
emission from the disk. This is due to the fact that the tom panel) surface density parameterization. The dashed curves
surface density within a few AU from the central star indicate the SED required to reproduce the observed near- and
is lower than 10−6 g cm−2 and the near-infrared disk mid-infraredexcess. Asdiscussedinthetext,thisadditionalcom-
ponentcanariseeitherfromanarrowringofopticallythickdust,
emission is negligible with respect to the stellar photo-
orfromamoreextendedopticallythinregion.
sphere. Inthecaseofthepower-lawmodel,thepredicted
andwouldthereforehaveanegligibleeffectontheoverall
SED agrees with the observation only at wavelengths
disk millimeter emission. The same two models for the
longer than 50 µm due to the cut-off of the dust den-
near-infrared emission can be applied to the case of the
sity at 42.5 AU. Independently on the adopted model,
smooth viscous surface density profile. However in this
the near-infrared emission observed toward LkCa 15 re-
case the outer disk is brighter in the mid-infrared than
quiresthepresenceofmaterialwithtemperaturebetween
in the power-law case, and therefore the region emitting
1000-2000 K in excess of what predicted by our models.
the infrared emission has to be smaller.
For a power-law surface density profile truncated at
42.5 AU, the near infrared emission can be explained
6. DISCUSSION
by two different models, as discussed in Mulders et al.
(2010). Inthefirstcase,theemissioncomesfromasmall 6.1. On the origin of the continuum cavity
optically thick disk that extends from the dust sublima- The results presented so far suggest at least two pos-
tionradius(∼0.1AU)uptoabout1AU(seealsoEspail- sible scenarios for the radial distribution of the circum-
latetal.2007,2008). Fortypicalinfrareddustopacities, stellar material around LkCa 15.
this model requires a minimum dust mass of 3×10−5 In the first case, most of the circumstellar dust is con-
M . Alternatively, the LkCa15’s infrared SED can be fined in a sharply truncated ring extending between 42-
⊕
fittedwithanopticallythinregionthatextendsfrom0.1 120 AU. Since no discontinuity is observed in the gas
AU to 5 AU. In this case, the mass of dust would be density at the edges of this dusty ring, this scenario re-
3×10−6 M . Theopticallythinregionandtheoptically quiresadropofthedust-to-gasratio,orofthedustopac-
⊕
thick diskwould produce a1.3mmfluxbelow 10−6 mJy ity, outside the ring. As discussed in Section 1, a sharp
9
internal disk truncation can be the result of dynamical
4 0.14
interactions with one, or more, giant planets (see, e.g.,
Bryden et al. 1999) or be due to the disk photoevapora- 3.5 0.12
tioncausedbythestellarradiationfield(see,e.g., Gorti
evthtereaegl.pas2reo0ob0ul9es)m.asn.TdhFdisiursslatty,ttiedtrispkmr,eowddiheclitcsshu,affaetsrrudhniosccwautesivoseenrditniwnobSoestech-- mm) 2. 53 00..018 2-1m g)
tviaotnio5n.s1,oifttihsenmotmc-ownasviseteCnOtwemithisssipoant.iaSlleycornesdo,lvitepdroebdsicetrs- (1-3(cid:96) 2 0.06 (c3mm
that the accretion of material on the central star stops 1.
1.5 (cid:103)
assoonasthecavityisopened, whilethemassaccretion 0.04
rate measured toward LkCa 15 is about M˙ = 3×10−9 1
M yr−1 (Hartmann et al. 1998). 0.02
(cid:12)
Whetherlarge(>20AU)dustdepletedcavitiescanbe 0.5
producedbythedynamicalinteractionwithgiantplanets 0.01 0.1 1 10 100
is still subject of debate. Zhu et al. (2011) showed that Maximum grain size (mm)
for large values of the viscosity parameter (α > 0.01), a
Figure 7. Dependence of the slope of the dust opacity β mea-
systemwith3or4Jupitermassplanetsorbitingbetween suredbetween1.3and3mm(solidcurve)andofthedustopacityκ
5 and 20 AU can lead to a largely depleted gap in the at1.3mm(dashedcurve)onthemaximumgrainsize,foragrain
disksurfacedensity. However,themassaccretionrateon size distribution n(a) ∝ a−q, where q = 3.5 and the minimum
thecentralstarispredictedtodropbelow5×10−10 M grainsizeis5×10−6 mm.
(cid:12)
yr−1inlessthat1Myraftertheformationoftheplanets.
thecavityradiusof42AU,atleastanotherplanetclear-
Furthermore, a discontinuity in the gaseous disk surface
ingthediskwithin12AU,andothertwoplanetsclearing
density will not be consistent with the CO observations.
theregionbetween20and42AUwouldberequired(see,
Alternatively,alowerviscosity(α≤5×10−3)wouldlead
e.g., Dodson-Robinson & Salyk 2011).
to larger values of M˙ and less depleted cavities. While
Inanalternativescenario,whichdoesnotrequiremul-
this latter model might be consistent with the observa-
tipleplanets, thedisksurfacedensityisdescribedbythe
tion of the CO emission, it fails to explain the lack of
smooth viscous model shown in Figure 3. In this case,
mid-infrared dust continuum emission observed toward
the gas density decreases within 80 AU but it remains
LkCa 15. To reconcile the measured values of M˙ with
high enough to explain the small inner disk radius de-
theinfraredSEDintheframeworkofplanet-diskinterac-
rivedfromtheCOobservations. Thissituationissimilar
tion,Zhuetal.(2011)arguethatlowvaluesofαhaveto tothatproposedforMWC758,wherethe12COemission
be coupled with a decrease by at least one order of mag-
is centrally peaked while the dust emission traces a par-
nitude of the near- and mid-infrared dust optical depth
tially dust depleted disk within 70 AU from the central
in the region partially depleted by the planets. A drop
star(Isellaetal.2010b). Itisimportanttonotethatthe
of this magnitude in the dust opacity can be achieved
smooth best-fit model was derived in the assumption of
throughthecoagulationofsmall,micronsizedgraininto
constant dust opacity throughout the disk. By relaxing
larger bodies. In the particular case of LkCa 15, we find
this assumption, we can interpret our results in terms of
that the dust opacity at 10 µm will decrease from about
radial variation of the dust opacity, due, for example, to
3 cm2 g−1 to 0.2 cm2 g−1 by increasing the maximum
grain growth. Radial variations in the grain size distri-
grain size from the adopted value of 0.5 mm (Section 4)
butionareindeedpredictedbytheoreticalmodelsforthe
to10cm. Itisthereforepossiblethattheactualstructure
dust evolution (Brauer et al. 2008) and can be observed
oftheLkCa15innerdiskistheresultofanearlierphase
by measuring radial variations of the mm-wave opacity
characterizedbytheformationoflargepebblesandboul-
slopeβ throughspatiallyresolvedmulti-wavelengthsob-
dersintheinnermostdiskregions(see,e.g.,Braueretal.
servations of the dust emission (Isella et al. 2010a; Guil-
2008),followedbytheformationofgiantplanets. Ifthat
loteau et al. 2011). In the case of LkCa 15, the com-
happenedinalowviscosityenvironment,thegasdensity
parison of 1.3 and 3 mm observations suggests that β
within 40 AU would be high enough to explain both the
increases from 0.7-1.0 to 1.5-1.7 between 30 AU and 150
measured mass accretion rate and the CO observations,
AU (Guilloteau et al. 2011). As shown in Figure 7, this
and perhaps to allow the planetary cores to accrete the
variation would correspond to a decrease of the maxi-
gas required to reach the Jupiter mass.
mum grain size from about 8-30 mm to 0.3-3 mm, or to
This scenario is compatible with the recent discovery
an increase of about a factor of 2 in the dust opacity at
of a possible proto-planet orbiting at about 16 AU from
1.3 mm. The observed variation in the grain size might
thecentralstardiscoveredthroughaperturemaskingob-
thereforeexplaintheobservedcavityinthe1.3mmdust
servations in the K(cid:48) (∼2.1 µm) and L(cid:48) (∼ 3.8µm) bands
emission without invoking multiple giant planets, but
(Kraus & Ireland 2011). The K(cid:48) magnitude and K(cid:48)−L(cid:48)
moresensitiveobservationsatlongerwavelengthsarere-
color of the planet are consistent with a temperature of
quired to investigate the presence of large grains in the
1500Kandamassof6M ,orsmaller. InadditiontheL(cid:48)
J 1.3 mm continuum cavity.
observations trace extended emission interpreted as ev-
idence of circumplanetary material. However, following 6.2. Investigating the origin of transition disks with
theoretical models for the planet disk interactions, this ALMA
planet would be able to open only a relatively small gap
Several experiments can be set up to investigate the
in the dust distribution between 12-20 AU. To explain
origin of the inner cavities in transition disks by taking
10 Isella A., P´erez L., and Carpenter J.
0.2
0.1
y)
e (J 0
c
n
e -0.1
er
Diff -0.2
-0.3
-0.4
100 200 300 400 500 600 700 800
B (k(cid:104))
uv
Figure 9. Differenceinthevisibilityprofilebetweenthepower-
lawandsmoothviscousbest-fitmodels(solidcurve),comparedto
the3σ sensitivityofALMAearlyscienceobservationsat0.44mm
(shaded region). This figure demonstrates that ALMA observa-
tionscanreliablydistinguishbetweentwoplausiblegeometriesfor
transitions disks to identify the mechanism likely responsible for
innercavities.
tainties from the simulated observations. At the wave-
Figure 8. SimulatedALMAobservationsof0.44mmcontinuum
lengthadoptedforthesimulation,thetwomodelscanbe
emission corresponding to the smooth viscous (top panels) and
power-law(bottompanels)best-fitmodelsdiscussedinSection5.1. disentangled at high significance level on almost all spa-
Thepanelsontheleftshowthemodelwhilethesimulatedobserva- tialfrequenciesshorterthan600kλ,whichcorrespondto
tionsareshownontherightcolumn. Thesimulationsassumea30 baselines shorter than 270 m.
min on source integration and the default weather conditions for
Band9. ALMAwilldeterminewhethertheinneredgeofthedisk
is sharply truncated (possibly due to dynamical interactions with 6.3. The LkCa 15 outer disk structure
a planet), or varies smoothly with radius (possibly due to grain
The discrepancy in the outer radius of the dusty and
growthintheinnerdisk).
gaseousdiskremainsanunsolvedissuesince,asdiscussed
in Section 5.1, it cannot be reconciled by adopting an
advantage of the superb imaging capabilities of the Ata-
exponentially tapered surface density profile. A caveat
cama Large Millimeter Array (ALMA). Here we explore
to this analysis is that our observations constrain the
the possibility to use relatively low angular resolution
dustdensityonlybetween40-120AU.Theextrapolation
observations, achievable during ALMA early science, to
of Σ to larger radii relies therefore on the assumption
constrain the profile of the dust distribution at the edge
thattheprescriptionofEquation1isvalidacrosstheall
of the dust continuum cavity. These observations can
disk radial extent.
be used to disentangle the two possible scenarios dis-
To test this assumption we compare our results with
cussed above. As shown in Figure 4, and discussed in
thegasdensityinferredfromtheanalysisofthe13CO(1-
Section 5.1, CARMA observations fail to distinguish be-
0)emissionbyPi´etuetal.(2007). InLkCa15,the13CO
tween a sharp and smooth edge of the continuum cavity
(1-0) line is nearly optically thin and traces the density
because they do not provide enough sensitivity on the
in the disk mid-plane. By comparing the observations
spatial frequencies where the difference between the two
to a power-law disk model, Pi´etu et al. (2007) find that
models is the largest, namely between 100 and 700 kλ.
Ontheotherhand, Figure8showsthatconstrainingthe the 13CO surface density decreases as r−3/2 from about
radial density profile at the edge of the continuum cav- 1.4×1016 cm−2 at100AUto1.2×1015 cm−2 at500AU.
ity is within the capabilities of ALMA in the early sci- If the 13CO abundance is constant throughout the disk,
ence phase. The left-most panels of Figure 8 show the then the decrease of the gas density is less steep than
model of the dust emission corresponding to the best-fit what is predicted by an exponentially tapered profile.
solutions for the smooth viscous and power-law surface To check whether the disk surface density profile de-
density profile discussed in Section 5.1. The maps in the rived from CO observations is consistent with the dust
right-mostpanelsrepresentALMAband9(λ=0.44µm) continuum emission, we show in Figure 10 simulated
simulated observations obtained using the array specifi- CARMA observations of the 1.3 mm dust emission cor-
cations for Cycle 0 observations and 30 min on source responding to a dust surface density Σd(r) = 0.13 ×
integration. The structural differences between the two (r/100AU)−3/2 that extends between 42.5 AU and 550
models are evident in these images: the smoothly vary- AU. The surface density normalization is derived in or-
ing Σ(r) shows trace amounts of emission in the inner derto reproduce thepeakflux measuredinour map. To
disk that is detectable with ALMA, while the inner re- facilitate the comparison with the observations, the sim-
gion in the truncated disk model is devoid of emission ulatedemissionisobservedatthesameresolutionandis
and resolved. More quantitatively, Figure 9 shows the affected by the same noise as in panel (c) of Figure 1.
differencebetweenthevisibilityprofilesofthetwodiffer- We find that only the dust emission within about 200
ent models as a function of the spatial frequency, where AU would have been clearly detected while the flux aris-
the colored region indicate the 3σ measurement uncer- ing from larger radii would have been lost in the noise.