Detections of trans-Neptunian ice in protoplanetary disks
M. K. McClure, C. Espaillat, N. Calvet, E. Bergin, P. D'Alessio, D. M. Watson, P. Manoj, B. Sargent, L. I. Cleeves
DDraft version October 10, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
DETECTIONS OF TRANS-NEPTUNIAN ICE IN PROTOPLANETARY DISKS
M. K. McClure , C. Espaillat , N. Calvet , E. Bergin , P. D’Alessio , D. M. Watson , P. Manoj , B. Sargent ,L. I. Cleeves Draft version October 10, 2018
ABSTRACTWe present
Herschel
Space Observatory a PACS spectra of T Tauri stars, in which we detect amor-phous and crystalline water ice features. Using irradiated accretion disk models, we determine thedisk structure and ice abundance in each of the systems. Combining a model-independent comparisonof the ice feature strength and disk size with a detailed analysis of the model ice location, we estimatethat the ice emitting region is at disk radii > ∼ µ m may probe the location of the water ice snow line in the disk upper layers.This project represents one of the first extra-solar probes of the spatial structure of the cometary icereservoir thought to deliver water to terrestrial planets. Subject headings:
Protoplanetary disks — radiative transfer — astrobiology — stars: individual: AATau, DO Tau, Haro 6-13, VW Cha INTRODUCTION
As the most abundant non-refractory solid-state com-ponent in protoplanetary disks, water ice plays a key rolein the dynamics and chemistry of planet formation. Itssticking properties may enhance the efficiency of dustgrain growth and settling (Okuzumi et al. 2012), whichis important for planetesimal growth. Water is one ofthe main molecular oxygen carriers, so its ice desorp-tion fronts contribute strongly to the radial variation ofdisks’ C/O in the gas phase and on grains ( ¨Oberg et al.2011). The resulting C/O ratio in the atmospheres ofgiant planets affects these planets’ spectral signatures,which are typically hydrocarbon or water vapor absorp-tion features (Madhusudhan 2012). Delivery of ice fromdisk reservoirs by comet or asteroid impacts is likely theorigin of Earth’s water (Hartogh et al. 2011; Alexander etal. 2012). Constraining the location of water ice in diskswould enhance our understanding of all these topics. Department of Astronomy, The University of Michi-gan, 500 Church St., 830 Dennison Bldg., Ann Arbor,MI 48109; [email protected], [email protected], [email protected],[email protected] Department of Astronomy, Boston University, 725 Com-monwealth Avenue, Boston, MA 02215; [email protected] Centro de Radioastronom´ıa y Astrof´ısica, UniversidadNacionalAUt´onoma de M´exico, 58089 Morelia, Michoac´an,M´exico; [email protected] Department of Physics and Astronomy, University ofRochester, Rochester, NY 14627, USA; [email protected] Tata Institute of Fundamental Research, HomiBhabha Road, Colaba, Mumbai 400005, India;[email protected] Center for Imaging Science and Laboratory for Multiwave-length Astrophysics, Rochester Institute of Technology, 54 LombMemorial Drive, Rochester, NY 14623, USA; [email protected] NSF Graduate Research Fellow a Herschel is an ESA space observatory with science instrumentsprovided by European-led Principal Investigator consortia andwith important participation from NASA.
The distribution of water ice throughout the disk isdominated by thermal desorption (sublimation), withsecondary effects from photodesorption and settling. Inthe disk’s upper layers where most of the stellar radia-tion is deposited, icy grains are directly exposed to thefar ultra-violet (FUV) radiation field that, for low massstars, originates mostly in the stellar accretion shock(Calvet & Gullbring 1998). Water molecules should bephotodesorbed from the grain surface into the gas phase(Pollack et al. 1994; ¨Oberg et al. 2009), producing watervapor even at locations in the disk with temperaturesbelow the water ice sublimation temperature (Dominiket al. 2005). However, recent observations of water vaporemission from the DM Tau and TW Hya disks with the
Herschel
Space Observatory show that the water linesare weaker than predicted by chemical models includingphotodesorption of ice (Bergin et al. 2010; Hogerheijdeet al. 2011). The lower water vapor abundance in TWHya may be due to growth and subsequent settling of theicy grains from the upper layers, which would reduce theamount of ice available to photodesorb.The structure of water ice traces its past thermal his-tory, because it crystallizes in an irreversible reaction attemperatures of 110 to 130K (Smith et al. 1994). Pro-tostellar infall chemical models suggest that water ice isformed amorphous in a star’s natal cloud, and the bulkof the ice beyond ∼ µ m water ice in the upper lay-ers of edge-on disks (Pontoppidan et al. 2005; Teradaet al. 2007); however, Kuiper belt objects (KBOs) andsatellites of Solar system gas giants show predominatelycrystalline ice signatures (Jewitt & Luu 2004; Grundyet al. 2006). Several mechanisms exist that can crystal-ize and/or amorphize water ice in disks: desorption and a r X i v : . [ a s t r o - ph . E P ] N ov McClure et al.recondensation onto grains (Kouchi et al. 1994; Ciesla2014), irradiation by high energy particles (Moore &Hudson 1992), and collisions between large particles orplanetesimals (Porter et al. 2010). A handful of crys-talline ice detections at 3 µ m (Schegerer & Wolf 2010;Terada & Tokunaga 2012) in T Tauri disks as well as43 and 63 µ m with ISO in Herbig AeBe disks (Malfaitet al. 1998, 1999; Creech-Eakman et al. 2002) representthe missing link between primitive ices from molecularclouds and thermally processed ices in mature solar sys-tems. In our previous paper (McClure et al. 2012), weused
Herschel to observe the 63 µ m crystalline ice featurefor the first time in a T Tauri disk and suggested that thecrystalline water ice could be the result of planetesimalcollisions in the outer disk.Here we present Herschel
PACS spectra of disks aroundT Tauri stars in which we detect signatures of crystallineice and amorphous ice (Sections 2 and 3). Through com-parison of their spectral energy distributions (SEDs) withsynthetic spectra from disk structure models (Section4.1), we constrain the radial and vertical ice emittingregion (Section 4.2) and conclude that we have detecteda proto-Kuiper belt or other trans-Neptunian water icereservoir (Section 5.2) below the photodesorption layer(Section 5.3), where the crystalline ice is regeneratedthrough impacts between dust grains and/or planetes-timals (Section 6). SAMPLE SELECTION, OBSERVATIONS, AND DATAREDUCTION
The four disks in our sample, AA Tau, DO Tau,Haro 6-13, and VW Cha, were drawn from two larger
Herschel programs, OT1 mmcclure 1 (PI: McClure) andOT1 cespaill 2 (PI: Espaillat), and selected on the basisof their water ice detections, with one non-detection in-cluded as a control case (VW Cha). We note that ourcombined Herschel programs observed 50 circumstellardisks; of these, 86% did not show prominent signs of ice.The disks presented in this paper and McClure et al.(2012) represent the best detections. Three of the disksare in Taurus, and one is in Cha I. The
Herschel
OB-SIDs,
Spitzer
AORs, and dates of observation are givenin Table 1. For absolute photometric verification of thesespectra and for the analysis in Section 4.1, we gatheredphotometry between 0.3 and 3000 µ m from the literatureto construct SEDs. The references for these photometryare listed in Table 2. The complete SEDs, including thespectra described below, are shown in Figure 1. Herschel PACS
We observed the sample using the PACS (Poglitschet al. 2010) instrument on
Herschel (Pilbratt et al. 2010)in range spectroscopy modes B2A (51-73 µ m) and R1S(102-145 µ m) at Nyquist-sampling ( λ/ ∆ λ ∼ µ m) and R1L(139-210 µ m). The data were reduced using the HIPEversion 9.0 (Ott 2010) standard data reduction pipeline,including the RSRF. The instrument is a coarse IFU with5 × TABLE 1Observations
Star
Herschel date
Spitzer dateOBSID AORAA Tau 1342240152 2012-02-17 3537152 2004-02-28Haro 6-13 1342239763 2012-02-29 3541504 2004-02-28DO Tau 1342240156 2012-02-17 3533056 2004-02-29VW Cha 1342233472 2011-12-02 12696832 2005-07-121342233471 2011-12-02 27066112 2008-06-02 observed with Nyquist sampling, which provided muchgreater spectral resolution than necessary at the expenseof signal/noise, we down-sampled the data using two ap-proaches. Before calculating equivalent widths for theanalysis, we median-filtered the spectra with sliding binsof 50 resolution elements, which removed the bulk of the[O I] emission line at 63 µ m. Therefore the [O I] linein DO Tau and AA Tau (Howard et al. 2013) does notcontribute to the broad shape of their B2A spectra. Toestimate the uncertainty in the spectral shape we did thefollowing. First we median filtered the spectrum with asliding window of 4 resolution elements, to remove anyline emission. We then rebinned the flux into 1 µ m seg-ments, with the rebinned flux being the average flux inthat segment and the uncertainty being the standard de-viation of the point-to-point variation in the 1 µ m bin.This method shows that although the spectra are noisy,the shape of the overall continuum is robust.To confirm the absolute photometric accuracy of thePACS spectrum, we compared the spectra with photom-etry from IRAS, AKARI, MIPS, and PACS when avail-able. The photometry and spectra are shown with addi-tional data in Figure 1. For AA Tau there is excellentagreement between IRAS, AKARI, ISO photometry, andthe PACS spectrum. The match between photometry, inthis case MIPS and PACS, and our PACS spectroscopy isalso within 1 σ for VW Cha. The other two disks, DO Tauand Haro 6-13, show more variation between their 70 µ mphotometry and spectroscopy, although they are nomi-nally within 3 σ of each other after taking into account the30% absolute flux uncertainty in PACS. Unfortunately,the detectors used for AKARI and MIPS 70 µ m fluxesare optimized for sensitivity and become non-linear forsource fluxes greater than ∼ ∼ µ m, the AKARI and MIPS fluxesonly provide lower limits to the actual flux. Spitzer IRS
The
Spitzer
IRS (Houck et al. 2004) spectra were takenin some combination of low- and high-resolution modes:SL (5 − µ m) and LL (14 − µ m) with λ/ ∆ λ =60 − − µ m) and LH (19 − µ m) with λ/ ∆ λ =600.Observation dates and identifying information are givenin Table 1. We reduced these data with SMART (Hig-don et al. 2004) in the same way as in McClure et al.(2010), with the exception that the SH/LH data weresky subtracted from off-source frames included in theirAORs. We estimate the spectrophotometric uncertaintyto be ∼ ISO LWS
One disk in our sample, AA Tau, was observed withthe LWS instrument on
ISO (Kessler et al. 1996). The re-etections of trans-Neptunian ice 3
Fig. 1.—
SEDs of targets in sample, not corrected for extinction. References for photometry are given in Table 2. Note that for AA Tauwe also plot its
ISO
LWS spectrum (grey line), described in § TABLE 2Ancillary photometry
Wavelength Instrument & referencesUBVRI/ugriz Kenyon & Hartmann (1995); Herbst et al. (1994); Ahn et al. (2012)JHK 2MASS (Cutri et al. 2003), DENIS, Myers et al. (1987)mid-IR WISE (Cutri & et al. 2012), AKARI IRC (Ishihara et al. 2010),
Spitzer
IRAC (Luhman et al. 2008)far-IR PACS (Winston et al. 2012; Howard et al. 2013), AKARI FIS,
Spitzer
MIPS, ISO, IRASsubmm Andrews & Williams (2005), Andrews & Williams (2008), Beckwith & Sargent (1991)mm Beckwith & Sargent (1991), Beckwith et al. (1990), Kitamura et al. (2002), Dutrey et al. (1996) sulting spectrum was published and analyzed by Creech-Eakman et al. (2002). We downloaded the spectrum fromthe ISO Data Archive as well as the reduced PHT 22photometry at 90 and 170 µ m. The LWS spectrum hadseveral relative order mismatches and an overall offset inabsolute flux from the photometry. We chose LW2 (cen-tral λ ∼ µ m) as the anchor order and scaled the otherorders to that one, using the overlap between orders. Wethen scaled the entire spectrum down to the ISO pho-tometry and trimmed the spectrum shortward of 46 µ m,between 70 and 90 µ m, and longward of 170 µ m. The finalspectrum was median filtered within sliding windows of100 spectral elements. OBSERVATIONAL RESULTS
The SEDs of all four systems have infrared excesses,indicating the presence of dust-rich disks. For two of thedisks, Haro 6-13 and DO Tau, the
Herschel
B2A spec-trum peaks at 63 µ m with a shape consistent with thecrystalline water ice feature (Bertie et al. 1969, and seeopacities in Figure 2). AA Tau displays no crystallinefeatures, but the short wavelength end of the B2A spec- trum continues up into the long wavelength shoulder ofthe 47 µ m amorphous ice feature. The ISO spectrum con-firms the existence of the amorphous 47 µ m feature. Incontrast to these three objects, VW Cha shows no ice fea-ture and is essentially smooth over its PACS spectrum.For DO Tau, Haro 6-13, and VW Cha we calculatedthe equivalent width of the over the 63 µ m region, whichcaptures potential emission from the crystalline ice fea-ture. The equivalent with is defined as: W λ = (cid:90) λ λ F obs − F continuum F continuum d λ (1)In both cases, the continuum was determined by a least-squares polynomial fit to the 25 and 32 µ m region of the Spitzer
IRS spectrum and the 105 and 140 µ m region ofthe Herschel
PACS R1S spectrum. The limits of integra-tion for the crystalline 63 µ m feature were taken to be 56and 72.5 µ m and are indicated in Figure 3. Polynomialsof the fifth degree produced continuua that were mostconsistent with the model fits found in Section 4.1.4;however, differences in W λ calculated with lower degree McClure et al. Fig. 2.—
Detail of the far-infrared region of the hybrid waterice opacities used in the models. Plus symbols denote the trimboundaries for the inclusion of the Curtis et al. (2005) amorphous(dashed line) and crystalline (solid line) ice opacities. Characteris-tic wavelengths of the far-infrared ice emission maxima are noted(with c for the crystalline features and a for the amorphous fea-tures). These opacities are for a power law grain size distributionwith a maximum grain size of 0.25 µ m, power of -3.5, and a massfraction of ice, relative to gas, of 0.002. polynomial continuua was not greater than 3 σ . This fig-ure also shows the polynomial continuum fits for the twodisks in which we detect the 63 µ m feature, DO Tau andHaro 6-13, and the disk in which there is a non-detectionof ice, VW Cha. For comparison, we include GQ Lup, theT Tauri disk in which we first detected the 63 µ m crys-talline ice feature in McClure et al. (2012). In Figure3 we list as well the 1 σ uncertainties for the equivalentwidths, calculated from the individual error bars in thespectra over which they were taken. Spectral energy dis-tributions of disks have intrinsic curvature in the 55 to120 µ m region due to optical depth and temperature ef-fects, leading to a systematic uncertainty in the locationof the continuum underlying the feature. We use thecalculated value of the equivalent width for VW Cha,in which ice is not detected, to represent the this un-certainty. This systematic uncertainty is less than threetimes the flux-based uncertainties. ANALYSIS
The goal of this study is to deduce the water ice distri-bution and abundance in these systems. In an opticallythick disk, the relative strength (i.e. equivalent width)of any dust feature depends on the abundance of theemitting dust species, grain geometry and size distribu-tion, degree of dust settling, disk temperature and den-sity structures, and inclination of the disk along the lineof sight (Furlan et al. 2009). It is therefore possible touse the observed 63 µ m and 47 µ m features to infer theseproperties by constructing a model disk structure andusing radiative transfer to produce a synthetic spectrumto compare with the observed data.Our approach to the analysis of these objects is as fol-lows. First, we fit the SEDs of each system with an TABLE 3Equivalent width of 63 µ mregion Star W µm σ a µm ( µ m) ( µ m)VW Cha b Note . — a Statistical uncertainty cal-culated from the spectralflux uncertainties. b Ice wasnot detected in VW Cha.This equivalent width rep-resents the systematic un-certainty arising from theintrinsic curvature in diskcontinuua over the far-infrared spectral region. emergent spectrum from the D’Alessio et al. (2006) diskstructure models using specific dust opacities (Section4.1). This allows us to constrain the grain size distri-bution of the ice, the degree of dust settling, and disktemperature structure. We can also use the radiativetransfer calculation to determine where the emitting re-gion is for the water ice (Section 4.2). To assess the effectto the overall ice distribution of photodesorption of icemantles from grains, we run a separate model to com-pute the UV radiation field and combine the results withthe density structure found from the D’Alessio modelsto determine the disk location where water ice has beencompletely photodesorbed (Section 4.3).
Disk structure models
The detailed physics of the D’Alessio irradiated accre-tion disk models is described in D’Alessio et al. (1998,1999, 2001) and D’Alessio et al. (2004, 2006). For thebenefit of the reader, we briefly highlight the main fea-tures of the code, and our updates to it, as it pertains tothis study.
General description
The D’Alessio et al. (2006) codes calculate self-consistently both the density and temperature structuresof a disk heated by both stellar irradiation and viscousdissipation. The mass accretion rate, ˙ M , is constantthroughout the disk. Viscosity is parameterized through α (Shakura & Sunyaev 1973), which is also held constant.The disk consists of gas and dust, with the dust dividedinto zones to simulate spatial variation in its propertiesand composition.Vertically, there are two dust populations: the upperdisk layer population has a smaller maximum grain size, a max , while the midplane population has much larger a max . Settling from the upper layers to the midplane isparameterized through depletion of the upper layer popu-lation, (cid:15) = ξ/ξ standard , where the denominator is the sumof the mass fraction of the different components relativeto gas and the numerator is the mass fraction in the smalldust population. The midplane dust abundance is cor-respondingly enhanced to account for material removedfrom the upper layers.etections of trans-Neptunian ice 5 non-detection of VW ChaGQ Lup DO TauHaro 6-13
Fig. 3.—
Determination of W for the three disks in this sample, plus GQ Lup from McClure et al. (2012). Continuum regions (darkgray fill), continuum fit (red dashed line), and limits of integration (light grey fill) are indicated. Error bars in W are 1 σ uncertainties. Updates
Radially, we have updated the D’Alessio code to in-clude multiple dust populations with discrete transitionsat cut-off radii ( R C ). A more comprehensive explorationof the effects of radial zoning is left to future work; herewe consider a two-zone model only in the event that athe standard D’Alessio single-zone model fails to repro-duce simultaneously the PACS ice feature and the IRSslope. The two-zone model allows us to vary the dustproperties in the upper or lower layer population inte-rior or exterior to R C . In any zone, radial or vertical,the dust properties, such as the grain size distribution,abundance, and opacity can be changed individually foreach of three main grain types: silicates, pure, solid car-bon, and water ice. The details of the dust are described in Section 4.1.3.At the inner edge of the disk, we implement a verticaldust sublimation wall with an atmosphere following theprescription of D’Alessio et al. (2004) with the two-layercurvature proposed by McClure et al. (2013b). To recapbriefly, there is a lower-layer, with height h wall, and arim z coordinate of z wall, , and an upper layer of height h wall, = z wall, − z wall, to produce a simple box-functionshape. Each wall layer is characterized by its grain sizedistribution and sublimation temperature. Beyond eachlayer’s radius, R wall defined by those two properties, dustis present. We allow the dust properties of the wall layersto vary independently of those in the disk to simulate theeffects of a radial gradient in the inner disk mineralogy. Opacities
McClure et al.The dust opacities are calculated from optical con-stants using Mie theory under the assumption of seg-regated, spherical grains. The grain size distribution ofeach grain type is of the form n ( a ) = n a p , where a is thegrain radius with limits of 0.005 µ m and a max . The abun-dance of each species is input as a mass fraction relativeto gas. For the silicate and graphite grains, we assume p = − . M g − x F e x SiO ) andpyroxenes ( M g − x F e x SiO ), where x = F e/ ( F e + M g )indicates the iron content. Opacities for the amorphousolivine and pyroxene are computed with optical constantsfrom Dorschner et al. (1995) that have x = 0 . .
05 to 0 . ∼
15 - 200 µ m range and the Warren & Brandt (2008) op-tical constants outside of that wavelength range. Thedetails of the opacity slicing are shown in Figure 2.The amorphous ice is characterized by a single peak at ∼ µ m with a broad wing towards 100 µ m, while thecrystalline ice has two peaks at 43 µ m and 63 µ m. Asshown in Curtis et al. (2005), these peaks are shifted toshorter wavelengths with decreasing temperature. Models for individual disks
For each object, we varied (cid:15) , α , the maximum grainsize in the upper layers, a max,s , and the ice mass fractionrelative to the gas to determine the best-fitting range tothe SED and the observed ice feature. Other essentialinputs are the stellar, accretion, and disk parameters,i.e. T eff , R ∗ , M ∗ , ˙ M , A V , i , and R d . These were takenfrom the literature and held fixed. We describe below ourchoices for the fixed properties and describe briefly eachdisk’s specific modeling challenges. The final properties,fixed and fitted, are listed in Table 4. VW Cha : This is a triple system composed of a pri-mary separated by 0 . (cid:48)(cid:48)
65 - 0 . (cid:48)(cid:48) . (cid:48)(cid:48) α , W Hα , of 79 ˚A, while the emission from the secondaryand tertiary has a combined K7 spectral type (SpT) and W Hα of 4.8 ˚A. Additionally, the primary is a factor of4 brighter at K -band than the total emission from thesecondary and tertiary components (Ghez et al. 1997).Together this suggests that emission from an accretingcircumprimary disk dominates the SED. Consequently,we do not correct for the contribution of the combinedsecondary and tertiary stellar components to the totalemission. For the stellar and accretion parameters, we Fig. 4.—
Best-fitting model fit to VW Cha. Spectral and photo-metric observations are plotted in thick black; photometric errorsare 3 σ . Light gray band around PACS spectrum represents theabsolute flux calibration uncertainty of 30%. The dark gray bandrepresents the point-to-point 3 σ uncertainty in the spectrum, i.e.the uncertainty in the shape. Total model fit (red) includes thefollowing components: accretion excess (dash-dotted line), stellarphotosphere (dotted line), curved wall (dashed line), and disk (solidline). Best-fitting parameters are given in Table 4. The best fittingmodel does include ice, but no feature is visible, consistent withthe feature arising in the outer disk. take the values for the primary given by Hartmann et al.(1998) and the A V found by G´omez & Mardones (2003).The inferred circumprimary disk has not been spatiallyresolved. Uncertainty in R ∗ and v sin i makes definitiveestimates of the inclination angle difficult; after test-ing several values, we find that models between 20 and45 ◦ produce a good fit to the data. We assume 45 ◦ forthe remainder of the paper, similar to the inclinationsof Haro 6-13 and DO Tau. The upper limit to the outerradius, R d , predicted from disk-binary interaction theoryis 0.4 times the AB separation, assuming a circular orbit(Artymowicz & Lubow 1994). With a de-projected sep-aration of 147AU, R d =59AU. Smaller values of R d , e.g.10 to 30AU, fit better suggesting some eccentricity in thesystem. This may be an effect of the tertiary component.The appearance of the 10 and 20 µ m silicate complexes issimilar to disks with strong crystalline silicate indices inWatson et al. (2009) and the IRS region is well-fit withforsterite in our model, consistent with a smaller, hotterdisk. The best-fitting model is given in Figure 4. DO Tau : This is a marginally resolved system. Weuse the radius and inclination found by Koerner & Sar-gent (1995). Taking the spectral type given by Kenyon& Hartmann (1995), we use an IRTF SpeX spectrum(McClure et al., in prep.) to compute the veiling, extinc-tion, luminosity, and mass accretion rate as described inMcClure et al. (2013a), using the weak-line T Tauri starLkCa 14 as a photospheric template. DO Tau displayssigns of radial variation in its gas and dust content; themillimeter dust continuum has a smaller radial extentetections of trans-Neptunian ice 7
Fig. 5.—
Best-fitting model fit to DO Tau. Plotting styles arethe same as in Figure 4. The red curve is the model fit with iceand the blue curve is the model fit with only silicates and graphite. than the gas line emission or scattered light from smalldust grains (Koerner & Sargent 1995; Kitamura et al.2002; Itoh et al. 2008). The scattered light images showan asymmetric arc at ∼ L F UV =0.0325 L (cid:12) (Yang et al. 2012).The best fit to DO Tau is shown in Figure 5. In fittingthe SED of DO Tau, we were able to fit simultaneouslythe shape of the IRS spectrum and the PACS spectrumwith a radially uniform disk model, but not the strengthof the 63 µ m ice feature. Models that fit the ice featureunderfit the 20-30 µ m observed flux. To mimic the effectof the dust arc in the outer disk observed by Itoh etal. (2008), we used the modified version of our code tosimulate an outer ring of water ice. Although the modelthat fits best the strength of the ice feature still producestoo little flux from 20 to 30 µ m, this effect is weaker forthe 2-zone model fit than for the radially uniform case(see Figure 6). Haro 6-13 : We take the spectral type found by White& Hillenbrand (2004) and extinction correct the opti-cal and NIR photometry to match those of LkCa 14.This yields an A V of 7.6 magnitudes; however, includingthe four veiling estimates given by White & Hillenbrand(2004) and Folha & Emerson (1999) in the extinctioncalculation using the method described in McClure et al.(2013a) yields A V =6 magnitudes. Due to discrepanciesbetween the dwarf and WTTS colors and uncertainty inthe A V of LkCa14, we adopt an A V of 7.0 magnitudes.The stellar luminosity and radius then follow; the massis calculated from the Siess et al. (2000) tracks, and themass accretion rate calculated from Br γ using the cali-bration of Muzerolle et al. (1998) and the Br γ luminosityfound by Greene & Lada (1996).The spectral slopes of Haro 6-13 between 6, 13, and Fig. 6.—
Effect on the shape of DO Tau’s SED of lowering to0.00001 the water ice mass fraction in the disk upper layers interiorto some radius, R C . Exterior to R C , ice is present in the upperlayers with a mass fraction of 0.002. Ice in the midplane layer hasthe same mass fraction in both the R < R C and R > R C zones. Fig. 7.—
Best-fitting model fit to Haro 6-13. There are two wallcomponents; one for the inner wall and one for the outer wall. Bothare plotted as dashed lines. Other plotting styles are the same asin Figure 4. µ m (Watson et al. 2009) are consistent with those ofpre-transitional disks in Taurus and Ophiuchus (McClureet al. 2010), suggesting that this disk may have a gap(Espaillat et al. 2014). Attempts to fit Haro 6-13 with aradially uniform disk were unsuccessful; a gap of ∼ Fig. 8.—
Best-fitting model fit to AA Tau. Plotting styles arethe same as in Figure 4. The red curve is the model fit including iceand the blue curve is the model fit with only silicates and graphite.Additional dark gray spectrum from 43 µ m to 160 µ m is the archiveISO LWS spectrum, trimmed and scaled. tween 13 and 31 µ m. As with DO Tau, we were able toreproduce well the overall SED, but not in conjunctionwith the 63 µ m ice feature. It appears that either theabsolute flux of the PACS spectrum is too high or thephotometry is too low, although the 30% absolute fluxuncertainty and 3 σ error bars of the far-infrared photom-etry overlap. The SED may also dip near 40 µ m, which wedo not attempt to reproduce. The models demonstratethat there is ice detected in this disk, but the poor fitover the far-infrared suggests additional structure thatwe cannot take into account with our current models.The best-fitting model is displayed in Figure 7. In Table4, we include the parameters of the outer disk wall as afootnote, for the sake of uniform formatting. AA Tau : This is a spatially resolved system at a higherinclination than our other targets (Kitamura et al. 2002).We assume the stellar luminosity and effective temper-ature given by Hartmann et al. (1998), recompute themass using the Siess et al. (2000) tracks, and calculate themass accretion rate from the luminosity of the Br γ linevia the relation given by Muzerolle et al. (1998), using theequivalent width of Br γ given by Fischer et al. (2011)and the maximum K band flux given by Eisner et al.(2007). We take A V from Fischer et al. (2011) and theinclination and outer disk radius from Cox et al. (2013).We note that the radius found by Cox et al. (2013) fromcoronographic images is smaller than that found fromsubmillimeter observations (Andrews & Williams 2007);the former authors attribute the difference to contam-ination from a background source in the submillimeterimage.There is still a small discrepancy between the best-fitting model and data at the end of the IRS range, butthis difference may arise due to a number of convergenteffects that are difficult to account for. In particular, the location of the peak of the 47 µ m feature between theIRS and ISO spectra, the difference in epochs betweenthese spectra, and potential radial or vertical variationin the ice grain size could all affect the shape of thisfeature relative to the continuum. Despite this issue, themodel fit to AA Tau is the best out of the three diskswith ice detections and, overall, fits well both the SEDand feature strength. The best-fitting model is given inFigure 8. Ice emitting region
Even though our spectral features are spatially unre-solved, and therefore in theory sample the whole disk,in practice certain regions of the disk contribute morethan others to the features we detect. For example, ifthe optical depth along the line of sight exceeds ∼
1, re-gions at higher optical depths (e.g. on the opposite sideof the midplane) are invisible to us. Likewise, regionsthat are very cold or hot will emit at longer or shorterwavelengths, respectively, than our PACS spectra. Usingthe opacity, density, and temperature of our best-fittingdisk structure models, we can determine the contributionof each point in the disk to the observed intensity at agiven wavelength. This contribution is quantified by theintegrand of the solution to the transfer equation for theemergent intensity: I ν (0) = (cid:90) + ∞ S ν e − τ zp d τ zp (2)where τ zp is the optical depth calculated along the lineof sight towards the observer, taking into account theinclination of the disk. Since we are interested in thedust, the source function, S ν , is the Planck function. Werewrite the integrand in terms of the coordinate alongthe ray in the line of sight, z p and define a ‘contributionfunction’ of z p as: C ( ν, z p ) = B ν ( T ) e − τ zp d τ zp d z p d z p (3)where the differential expression is simply equal to theopacity at z p . By definition this function will be negli-gible in regions of the disk where τ zp is either very largeor relatively constant. It also will be smaller in coolerregions of the disk. As τ zp is dependent upon the in-clination angle along the line of sight, the contributionfunction will be asymmetric between the near and farsides of the disk. Water ice contributes to both the fluxon either side of the feature and the feature itself. There-fore to identify the emitting regions probed specificallyby the 47 and 63 µ m features, one can subtract the con-tribution to the emission at 72 µ m from the contributionto the emission at the peak wavelength of each ice featurefor each spatial grid point in the disk structure model.Of the three new ice detections, Haro 6-13 has thepoorest model fit, potential radial disk structure, and noancillary UV data (for use in 4.3). We exclude it from fur-ther analysis and concentrate our efforts on AA Tau andDO Tau. For both of these disks, we compute the opticaldepth along the line of sight, the temperature structure,and the final, differenced contribution function using theuniform disk model that best-fit the ice feature. We notethat in the case of DO Tau, the model used is not theetections of trans-Neptunian ice 9 R d i s k , y - a x i s z d i s k (a) AA Tauλ=47μm(b) DO Tauλ=63μm R d i sk , y - a x i s z d i sk τ λ , z p Optical depth disk boundarydisk plane axesdisk surface, z s inner 150x150 AUobserver Fig. 9.—
Comparison of the optical depth along the line-of-sight (zp) in the plane of the sky for AA Tau (top) and DO Tau (bottom)for the 47 µ m amorphous ice and 63 µ m crystalline ice features, respectively. The isocontour of τ λ,zp =1 is indicated. The optical depthstructures are overlaid with the disk geometry, including the maximum extent of the disk models in our calculations, and the mid planeand disk rotation axis. The disk surfaces, where τ =1 to stellar radiation, are also displayed. Linestyles and symbols are defined in thelegend. l og T ( K ) l og C - thermal snowline l og T ( K ) l og C - thermal snowline (a) AA Tau: 47μm (b) DO Tau: 63μm Emitting regionTemperature TemperatureEmitting region disk boundarydisk plane axesdisk surface, z s observerphotodesorbed layerisotherms Fig. 10.—
Comparison of the temperature structure and emitting area contributing to the ice features for AA Tau (left) and DO Tau(right). The emitting region is calculated by subtracting the contribution to the total intensity of each point at 72 µ m from that at either47 or 63 µ m, as described in the text. Note that the red regions contribute most to the flux while purple or white regions contribute theleast. The regions of the disks above the assumed equilibrium ice crystallization temperature, 130K, are indicated, along with the regionsbelow 80K, where high energy particles will re-amorphize crystalline ice after 0.1 Myr. The photodesorption layer, where ice is completelyremoved from the grains, is indicated. For AA Tau, the latter is a barely visible thin skin in the upper layers of the disk. etections of trans-Neptunian ice 11overall best-fitting model, but a uniform upper layer iceabundance is required for this comparison. Figures 9 and10 show the results. UV radiation field models
The weakness of cold water vapor detections from
Her-schel (Hogerheijde et al. 2011) may indicate that most ofthe grains exposed to the UV radiation field are not icy.Rather it is likely that the icy grains lie just below theUV-exposed layer. To investigate the effect of ultravio-let radiation on the distribution of water in these disks,we wish to compare the emitting region identified by thecontribution function (Section 4.2) with the disk regionin which water ice would be completely photodesorbedfrom grains. Using the Bethell & Bergin (2009) code,we calculate the UV radiation field at each point in thedisk, taking our best-fitting disk structure as input andassuming an input UV spectrum of TW Hya, scaled tothe luminosities of AA Tau and DO Tau given by Yanget al. (2012). The location at which photodesorption ofice from a grain overwhelms H O freeze-out on a grainin molecular clouds can be modeled as A V ∝ ln ( G Y /n ),where where G is the mean interstellar flux in units ofHabing (1 Habing = 1 . × − erg/cm /s ), Y is the pho-todesorption yield, and n is the gas density (Hollenbachet al. 2009; Boogert et al. 2013). If we assume that thisrelation holds for the upper layers of protoplanetary disksas well, then the surface in the disk where ice no longerexists should be the set of points (R, z) that satisfy: G ,disk ( R, z ) = n disk ( R, z ) G ,cloud n cloud (4)We calculate G ,disk ( R, z ) from the Bethell & Bergin(2009) flux; combining these G ,disk ( R, z ), with the as-sumption of 1 and 10 cm − (Hollenbach et al. 2009) forthe values of G ,cloud and n cloud , respectively, we derivethe photodesorption surface for both disks (see Figure 9,bottom right panel). RESULTS OF ANALYSIS
The details of how we fit each source are given above(Section 4.1.4). In general good fits to the data wereobtained with radially uniform disks for VW Cha andAA Tau, while radial variations were required to fit Haro6-13 and DO Tau. The modifications still do not produceideal fits. Despite this, we can extract useful informationabout the the ice distribution from the sample as a whole.
Dust settling vs ice abundance
To fit the overall far-infrared fluxes and slopes of theirSEDs, these disks required a local enhancement of thedust/gas ratio at the midplane of a factor of ∼
10 (cor-responding to (cid:15) ∼ .
1) and midplane grain growth tomillimeter size pebbles in order to fit the SED submil-limeter slopes. However, to fit the absolute flux of the
Spitzer and
Herschel spectra of the two disks in which thecrystalline 63 µ m feature was detected, the upper layersrequired less depletion than the mean depletion valuefor disks in Taurus and Ophiuchus (McClure et al. 2010, (cid:15) =0.01-0.001), meaning these disks are less settled. Thisresult is consistent with the suggestion by Hogerheijdeet al. (2011) that water ice has typically settled out ofthe disk upper layers. The fact that AA Tau, the disk with the amorphous 47 µ m detection, was best fit by anaverage degree of dust depletion does not contradict theseresults; the strength of the 47 µ m feature increases withhigher inclination for a fixed degree of dust settling, andAA Tau is inclined at 71 ◦ , ∼ ◦ more than the othertargets.All three of the disks with ice detections were fit bestby ice mass fractions of 0.002 based on the peak-to-continuum ratio of the feature, which increased with totalice abundance. Although the strength of this feature alsodepends on the degree of dust settling, we can constrainthe latter from the overall flux and slope from ∼
31 to100 µ m. This mass fraction of ice is only 36% of the massfraction predicted to be in the disk (Pollack et al. 1994),which may suggest that icy-coated grains do preferen-tially grow and settle to the midplane better than baregrains. Despite the non-detection of an ice feature, VWCha could be equally well-fit by either an iceless disk oran disk with the same ice mass fraction as the other disks.Significantly, its disk appeared to be truncated close to7AU, which we assume to be a result of its secondary andtertiary companions and viscous evolution. In § µ m crystalline ice feature itself cannotoriginate primarily from the inner disk. Radial distribution of ice
In Section 4.2 we calculated the contribution of eachpoint in the disk to the 47 µ m amorphous ice feature inAA Tau and the 63 µ m crystalline feature in DO Tau, rel-ative to the emission at 72 µ m for each disk. Comparingthe results for both disks (Fig. 10), we see that the amor-phous ice feature for AA Tau samples exclusively theupper layers of the whole disk; the midplane remains op-tically thick over the entire radial range. In contrast, al-though the primary contribution of the crystalline 63 µ mice feature in DO Tau is still from the upper layers, itis concentrated below the disk surface and includes faintemission from z disk < ◦ . However, these tests do confirm that the de-tected ice in both disks is trans-Neptunian ( R > µ m crystalline icefeatures (see Section 3) against the disk sizes. In gen-eral for optically thick disks the strength of a featuredepends not only on the dust properties but also on thedisk temperature structure and geometry in the regionswhere the continuum and feature arise. However, thethree disks with crystalline features (DO Tau, Haro 6-13, and GQ Lup) and our control system, VW Cha, haveroughly similar central stars, inclinations, and disk pa-rameters, simplifying the comparison. Barring any differ-ences in dust properties between these disks, the equiv-alent widths should track the outer radii of the disks if,for example, the feature emission were dominated by theouter disk due to its increased solid angle or larger frac-tion of the total disk mass.These outer radii are quasi-independent of model as-sumptions. For example, although their adopted diskradii of 7AU and 50AU come from the best-fitting model2 McClure et al. Fig. 11.—
The equivalent width, W λ , of the 63 µ m feature versusthe outer disk radii for the two disks in which the 63 µ m featureis detected, the disk in which the feature is not detected (VWCha), and our previously published feature detection in GQ Lup(McClure et al. 2012). The disks of VW Cha and GQ Lup havehard outer limits imposed by the presence of their companions of0.4 times their de-projected separations of 147 and 163AU, respec-tively, while the adopted value comes from the model fits to theSED. For DO Tau and Haro 6-13, the open circle symbols indicatethe radius derived for their CO disks (and presumably smaller, en-trained grains), while the solid circles are for the millimeter graindisks. The equivalent width clearly correlates with the disk radius,suggesting the ice emission region is beyond 30AU. of their SEDs, the disks of VW Cha and GQ Lup havehard outer limits imposed by the presence of their com-panions of 59 and 65AU, or 0.4 times their de-projectedseparations of 147 and 163AU, respectively (assumingcircular orbits Artymowicz & Lubow 1994). The dustand gas in DO Tau and Haro 6-13 have been imagedat submillimeter wavelengths, which provides a range ofradii as the dust emission tracks millimeter grains whilethe gas emission tracks submicron grains that are cou-pled to the gas. In Figure 11 we plot W against thedisk radii. The equivalent width shows a clear increasefrom a ∼ µ m non-detection in VW Cha, R disk =7AU,to 2.1 µ m for DO Tau, R disk =350AU. Our test suggeststhat the disks with larger outer radii have stronger icefeatures, likely due to a larger total ice mass. Vertical distribution of ice
Having determined that the 47 and 63 µ m ice featuresprimarily sample the outer disk, we want to know wherethis ice is located vertically. That these disks are lesssettled suggests that the water grains may be exposedto photodesorbing UV radiation. On the other hand,ultraviolet radiation is extinguished at smaller penetra-tion depths in the disk than visible light, and less settlingmeans more optically thick disk upper layers, so the pen-etration depth should be even smaller than in more set-tled disks. For AA Tau, it is clear that photodesorptiondoes not significantly effect the ice distribution at large radii: in Figure 10 the complete photodesorption surfaceis a thin skin of at most 5AU in vertical depth with a ra-dial range out to 80AU. This region is located well abovethat contributing to the 47 µ m ice emission feature.However, the L F UV of DO Tau is a factor of 16 greaterthan that of AA Tau (Yang et al. 2012). As demonstratedin the bottom right panel of Figure 10, this amount of UVradiation is enough to photodesorb ice out to 140AU inthe disk, with a vertical depth of ∼ µ m ice feature and to the contin-uum between 20 and 30 µ m (D’Alessio et al. 2006). Theseareas should be ice free, and although the majority of the63 µ m contribution comes from below the photodesorp-tion layer the abundance of ice in the lower disk layersmay also be less than if it were below a region unaffectedby photodesorption. The combination of turbulence andphotodesorption may reduce the amount of midplane wa-ter ice by moving midplane ice to the disk surface, whereit is desorbed and reacts with other molecules (Furuyaet al. 2013). Over time this cycle could deplete ice fromthe solid phase at given radius for all disk heights, asshown by Furuya et al. (2013) for the inner 30AU of adisk. Future spatially resolved studies probing the gasphase abundance of water and other molecules are nec-essary to confirm or refute this scenario. DISCUSSION
Is crystalline ice a signature of planetesimalcollisions?
To place these results in context, we can compare theinferred properties of our disk water ice detections withthose of other disks at shorter wavelengths and solar sys-tem comets. Ice has been detected in absorption at 3 µ min protostars and edge-on systems by Pontoppidan et al.(2005), Terada et al. (2007), Honda et al. (2009), Terada& Tokunaga (2012), and Aikawa et al. (2012). These au-thors are able to fit the 3 µ m feature best with grain sizesof 0.5 to 1 µ m and an abundance relative to hydrogen of9 × − (Pontoppidan et al. 2005), similar to the massfraction of 2 × − found in this work. In only two ofthese detections was the water ice crystalline (Terada &Tokunaga 2012; Schegerer & Wolf 2010). This result isconsistent with protostellar collapse models, which pre-dict that the bulk of the disk ice in the upper layers ofthe outer disk arrives unprocessed from its initial chemi-cal formation on grains in the parent molecular cloud orprotostellar envelope (Visser et al. 2009), so it should beamorphous. Significantly, in one of the two disks withprevious crystalline ice detections, YLW16A, the diskand envelope water ice were spatially resolved, with crys-talline ice only in the upper layers of the outer disk andamorphous ice in the inner disk and in falling envelope(Schegerer & Wolf 2010).In contrast, near- and far-infrared spectral observa-tions of solar system objects find compositions domi-nated by crystalline ice. Jewitt & Luu (2004) detecteda 1.65 µ m crystalline ice signature towards Kuiper beltobject (KBO) Quaoar, while Grundy et al. (2006) foundthe same feature in satellites of Uranus, placing an upperlimit of 20% on the amorphous content of the observedwater ice. At longer wavelengths, ISO SWS/LWS spectraof comet Hale-Bopp show both crystalline features at 43etections of trans-Neptunian ice 13and 63 µ m, which are best-fit with 15 µ m sized ice grains(Lellouch et al. 1998), an order of magnitude greater thanthe size inferred in edge-on disk features. It is possibleto crystalize amorphous ice on large bodies through col-lisions of planetesimals or differentiation (Brown 2012).Depending on the initial phase of ice in the disk, thereare processes by which it can be amorphized or crys-tallized. Ice which is initially crystalline can recondenseamorphously after being photodesorbed in the upper lay-ers of the outer disk (Ciesla 2014). Alternatively, itscrystalline structure can be damaged by high-energy ra-diation or particles when the disk temperature is lessthan 80K (Grundy et al. 1999, and references therein),which should amorphize these regions completely on theorder of 10 -10 years (Cook et al. 2007). On the otherhand, local heating events, such as shocks or collisionswith other dust grains or large bodies, can crystallizeamorphous ice (Porter et al. 2010; Marboeuf et al. 2009)and ice can be crystallized as material moves into warmerregions near the star.Our finding of amorphous ice in the upper layers ofAA Tau’s outer disk is consistent with the predictionthat ice below 80K should become amorphous by 10 years, if it was not already inherited that way from itsnatal cloud. The region where crystalline ice could bethermally generated is much smaller than the contribu-tion region of the 47 µ m amorphous feature. However,the case of DO Tau is more complicated. The vast ma-jority of its outer disk is below 80 K and should, there-fore, be amorphous. The remaining regions above 80Kare almost entirely within the complete photodesorptionzone, so crystalline ice should not exist in the upper lay-ers of its disk. Our detection of crystalline ice in thissystem suggests that there has been replenishment ofthe crystalline ice population in the outer disk at somepoint within 10 years. Replenishment by warm ice fromthe inner disk would require transport through the disk.However, in the disk’s upper layers this would require thecrystalline ice to pass through regions where turbulenceshould circulate grains into the photodesorption zone,which would have the effect of amorphizing the grains(Ciesla 2014). Therefore our detection strongly suggestsregeneration by in situ crystallization of icy grains, e.g.by micrometeorite/planetesimals collisions or a desorp-tion/recondensation event. We note that these resultsconfirm the conclusions of McClure et al. (2012). Can we trace the radial extent of the water icesnowline?
As seen by DO Tau, photodesorption can have a signif-icant effect on the curvature of the snow line in the upperlayers, releasing water ice from grains at larger radii thanthermal desorption alone. Our attempts to fit DO Tauwith a radially constant disk model suggest that inclu-sion of ice inside this region in our disk structure models(which do not self-consistently account for photodesorp-tion) causes the decrease in flux from 20 to 30 µ m, whichprevents us from fitting the IRS and PACS spectra si-multaneously. We confirmed the general effect on thatwavelength region of truncating radially the water icein the disk upper layers inwards of some critical radius R C in Figure 6, using the new 2-zone model. AlthoughDO Tau was not fit perfectly with the new model pre-scription, the broader mid- to far-IR SED fit is improved by models with less ice in the inner 100AU. Including acurved desorption zone rather than a step function mayimprove the fit.These results suggest that with updated modeling, in-cluding a self-consistent account of photodesorption, itmay be possible to constrain the location of water icein the upper layers of the inner ∼ µ m feature with the absolute fluxand slope of the SED over the end of the Spitzer
IRSspectrum. Combining this type of analysis with a morephysical settling parameterization, and potentially dataaround 45 µ m with FIFI on SOFIA, SPICA, or near-infrared scattered light spectroscopy (e.g. with GPI orSPHERE) may allow a more complete picture of the 2Dlocation water ice depletion front, or ‘snowline’, takinginto account both thermal and photo-chemical effects. CONCLUSIONS
We present four new
Herschel
PACS spectroscopic ob-servations of disks around T Tauri stars in the Taurusand Cha I star-forming regions. Two of the Taurus disksshow crystalline water ice features at 63 µ m, while we in-fer the presence of the red wing of the amorphous 47 µ mwater ice feature in the third system. A fourth disk,in Cha I, exhibits an ice non-detection and is used as acontrol.Using detailed irradiated accretion disk models, we ex-tract basic constraints on the abundance, grain size, andradial and vertical location of the water ice in the disk,finding that: • both of the amorphous 47 and crystalline 63 µ mfeatures are dominated by emission at trans-Neptunian radii, R > • the emitting region of the crystalline ice is muchlarger than the region that is hotter than the crys-tallization temperature, suggesting local heating ortransport; • both features were well-fit by an ice mass fractionof 0.002 relative to gas, or half the predicted solarnebula value, consistent with a depletion of ice fromthe disk upper layers; • comparing the ice feature strength with continuumshape in Spitzer
IRS may yield more detailed in-formation regarding the location of the snowline inthe upper layers.Through this work, we probe the main reservoirthought to provide water ice to terrestrial planets,namely the proto-Kuiper Belt. However, larger disk sam-ple sizes and more physically motivated model ice distri-butions are necessary to characterize better the proper-ties of this reservoir and determine the innermost spatialextent of water ice in disks, i.e. the snowline, both ofwhich are essential to constraining how Earth acquiredits water.M.K.M was supported by the National Science Founda-tion Graduate Student Research Fellowship under GrantNo. DGE 0718128. N.C. acknowledges support fromNASA Origins grants NNX08AH94G.4 McClure et al.
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TABLE 4Stellar and Model Properties
Parameter AA Tau Haro 6-13 a DO Tau VW Cha T eff (K) 4060 3850 3850 4350 A V (mag) 1.34 7.0 3.0 2.8 M ∗ ( M (cid:12) ) 0.80 0.56 0.56 1.1 R ∗ ( R (cid:12) ) 1.80 2.45 1.90 2.7˙ M ( M (cid:12) /yr) 6 × − × − × − × − i ( ◦ ) 71 40 42 45 b d (pc) c
140 140 140 160Wall, lower T wall, (K) 1600 1400 1600 1600 a max ( µ m) 1 5 2 3sil. comp. 100% PyMg60 100% PyMg60 100% PyMg60 100% PyMg60 R wall, (AU) 0.12 0.15 0.17 0.21 h wall, = z wall, (AU) 0.009 (2.25H) 0.024 (4H) 0.021 (3H) 0.018 (2.5H) z s,disk ( R wall ) (AU) 9.7 × − × − × − . × − Wall, upper T wall, (K) 750 800 700 1200 a max ( µ m) 5 3 3 0.75 sil. comp.
60% OlMg50 100% PyMg60 60% OlMg50 50% OlMg5040% Forst. 40% Forst. 50% Forst. R wall, (AU) 0.32 0.36 0.57 0.35 h dwall, (AU) 0.035 (3H) 0.05(3.5H) 0.07 (2.75H) 0.012 (1H) z wall, (AU) 0.044 0.074 0.085 0.030 z s,disk ( R ) (AU) 3.4 × − × − × − . × − Disk α e (cid:15) e R d (AU) 140 180 350 7 M d ( M (cid:12) ) 3.06 × − × − × − × − a max,midplanef g a max,upper ( µ m) 0.25 0.25 0.25 0.5sil. species 100% PyMg80 90% OlMg50 100% OlMg50 50% PyMg8010% Enst. 30% Forst.20% Enst.H O ice a max,upper ( µ m) 0.25 15 0.25 0.25-15 m/m H × − × − × − up to 2 × − power Note . — a Our model for Haro 6-13 has a gap between 0.36AU and 7.5AU, with an outer wallof 4 H and a composition the same as that of the disk. b VW Cha lacks definitive inclination information, so we assumed i =45 ◦ . c Distance references: Taurus: Kenyon et al. (1994), Chamaeleon I: Whittet et al.(1997), references for stellar and accretion parameters are given in § d The wall height is expressed in terms of the gas pressure scale height, H , at thewall radius. e VW Cha lacks data beyond ∼ µ m; without that additional constraint, α and (cid:15) can vary as indicated. f The maximum grain size in the midplane was taken to be the same for silicates,graphite, and water ice, which are assumed to be present in the midplane with thesame abundance as in the upper layers. g Silicates and graphite were assumed to have a power of -3.5 and m/m H =4 × − and 2.5 × −3