A Resolved Molecular Gas Disk around the Nearby A Star 49 Ceti
aa r X i v : . [ a s t r o - ph ] M a r Accepted for publication in ApJ: March 20, 2008
Preprint typeset using L A TEX style emulateapj v. 08/22/09
A RESOLVED MOLECULAR GAS DISK AROUND THE NEARBY A STAR 49 CETI
A. M. Hughes , D. J. Wilner , I. Kamp , M. R. Hogerheijde Accepted for publication in ApJ: March 20, 2008
ABSTRACTThe A star 49 Ceti, at a distance of 61 pc, is unusual in retaining a substantial quantity of moleculargas while exhibiting dust properties similar to those of a debris disk. We present resolved observationsof the disk around 49 Ceti from the Submillimeter Array in the J=2-1 rotational transition of COwith a resolution of 1.0 × ∼
90 AUfrom the star. No 1.3 millimeter continuum emission is detected at a 3 σ sensitivity of 2.1 mJy/beam.Models of disk structure and chemistry indicate that the inner disk is devoid of molecular gas, whilethe outer gas disk between 40 and 200 AU from the star is dominated by photochemistry from stellarand interstellar radiation. We determine parameters for a model that reproduces the basic featuresof the spatially resolved CO J=2-1 emission, the spectral energy distribution, and the unresolved COJ=3-2 spectrum. We investigate variations in disk chemistry and observable properties for a range ofstructural parameters. 49 Ceti appears to be a rare example of a system in a late stage of transitionbetween a gas-rich protoplanetary disk and a tenuous, virtually gas-free debris disk. Subject headings: astrochemistry — circumstellar matter — planetary systems: protoplanetary disks— stars:individual (49 Ceti) INTRODUCTION
A key to understanding the formation of planetarysystems lies in characterizing the transitional phase be-tween the gas-rich primordial disks found around youngT Tauri stars and the tenuous, virtually gas-free debrisdisks around their main-sequence counterparts. Unfor-tunately, disks in this transitional phase are rare and dif-ficult to identify. Dust disks around young stars are com-monly identified through the “Vega-excess” phenomenon(first observed using the Infrared Astronomical Satelliteby Aumann et al. 1984; see review by Zuckerman 2001),in which an infared excess over the stellar photosphereis attributed to reprocessing of optical and ultravioletstarlight by thermally emitting circumstellar dust grains.49 Ceti was first identified in this way by Sadakane &Nishida (1986). The quantity τ = L IR /L bol is often usedas an indicator of the “optical depth” of the dust disk,as it provides a rough estimate of the quantity of op-tical/ultraviolet light intercepted and reemitted by thedust. Jura et al. (1993) correlated the IRAS Point SourceCatalog with the Yale Bright Star Catalog (Hoffleit &Jaschek 1991) and identified three A stars with τ > − ,indicative of tenuous, optically thin circumstellar dust.Two were the stars β Pic and HR4796, which are nowknown to host debris disks. The third was 49 Ceti, whichunlike the other two defies classification as a debris diskbecause it retains a substantial quantity of molecular gas,first observed in the CO J=2-1 line (Zuckerman et al.1995) and later confirmed in J=3-2 (Dent et al. 2005).At a distance of only 61 pc (Hipparcos), it is one of the
Electronic address: [email protected] Harvard-Smithsonian Center for Astrophysics, 60 GardenStreet, Cambridge, MA 02138 Kapteyn Astronomical Institute, University of Groningen, 9700AV Groningen, The Netherlands Leiden Observatory, Leiden University, P.O. Box 9513, 2300RA, Leiden, The Netherlands closest known gas-rich circumstellar disks, farther onlythan TW Hydrae (51pc; Mamajek 2005). Its outwardsimilarity to a debris disk, combined with the substan-tial quantity of molecular gas still present in the system,suggest that the disk may be in an unusual transitionalevolutionary phase.All three high- τ A stars are young: HR 4796A has anage of 8 ± β Pic hasbeen placed at ∼
20 Myr by Thi et al. (2001b), con-sistent with the age determination of 20 ±
10 Myr byBarrado y Navascu´es et al. (1999). The age of 49 Ceti isuncertain due to its isolation; unlike β Pic or HR 4796Athere are no known associated low-mass stars to providea corroborating age estimate. Jura et al. (1998) demon-strate that on an HR diagram, all three stars exhibit alow luminosity for their color, which is likely attributableto their young ages ( ∼
10 Myr). Using the evolutionarytracks of Siess et al. (2000), Thi et al. (2001b) assign anage of 7.8 Myr to 49 Ceti based on its position on theHR diagram.Few conclusive measurements have been made of thedust properties in the 49 Ceti system. HST/NICMOScoronographic observations of 49 Ceti failed to detectany scattered light in the near infrared at r > . ′′ µ m, ex-tended along a NW-SE axis and apparently inclined atan angle of 60 ◦ . Simple models of the dust emissionsuggest a radial size segregation of dust grains, with apopulation of very small grains ( a ∼ . µ m) confinedbetween 30 and 60 AU from the star, and a populationof larger grains ( a ∼ µ m) from 60 to 900 AU fromthe star. However, the outer radius of this latter com-ponent is uncertain due to its dependence on the mil-limeter flux, which is not well determined. There aretwo contradictory single dish measurements of the mil-limeter dust emission, both with modest signal-to-noise.Bockel´ee-Morvan et al. (1994) report a IRAM 1.2 mmflux of 12 . ± . µ m flux of 8 . ± . F λ ∝ λ − ) or a typical optically thin cir-cumstellar disk spectrum ( F λ ∝ λ − ) in this wavelengthregime.If we accept the lower value of the 850 µ m flux andmake standard assumptions about the dust opacity (e.g.Beckwith & Sargent 1991), then the total mass of the 49Ceti dust disk is 0.1 M ⊕ . If we compare this to othernearby dusty disks at potentially similar stages of evo-lution, we find that 49 Ceti, with an 850 µ m flux of 8.2mJy at a distance of 61 pc, has a dust mass ( ∝ F µm d )approximately 80% that of β Pic (104.3 mJy, 19.3 pc;Holland et al. 1998) but only 0.3% that of the typicalHerbig Ae star HD 169142 (554 mJy, 145 pc; Sylvesteret al. 1996). Thus the 49 Ceti disk appears to have atenuous dust disk more akin to that of the debris diskaround β Pic than a gas-rich protoplanetary disk.Studies of the distribution of gas in the 49 Ceti sys-tem have been similarly inconclusive, particularly sinceit is not obvious that a substantial reservoir of moleculargas should persist in the strong UV field of an A star atthis apparently advanced stage. Attempts to detect purerotational transitions of the H molecule have resultedin contradictory reports, with Thi et al. (2001a) report-ing a marginal detection using SWS/ISO, which Chenet al. (2006) did not confirm with Spitzer/IRS observa-tions; nor did Carmona et al. (2007) detect H emissionwith VLT/CRIRES observations. Models of the double-peaked JCMT CO J=3-2 line profile observed by Dentet al. (2005) indicated that the gas is likely distributedin either a very compact disk with ∼ ◦ inclination ora more inclined ring of radius ∼
50 AU and inclination ∼ ◦ . The latter was deemed more consistent with thedust distribution seen in the mid-infrared, although itfails to reproduce the high-velocity wings that may bepresent in the CO J=3-2 line profile.In order to obtain spatially resolved information on thedistribution of material in the system, we observed 49Ceti with the Submillimeter Array in the J=2-1 transi-tion of CO and associated continuum. We detect a rotat-ing structure of much greater extent than predicted fromthe single-dish measurements, with a large central regiondevoid of molecular gas emission. We also model the diskemission using COSTAR (Kamp & Bertoldi 2000; Kamp& van Zadelhoff 2001), a code that combines thin hydro-static equilibrium models of disks with a rich chemistrynetwork and a detailed heating and cooling balance to de-termine gas properties. The models provide some insightinto basic properties of the disk, including the region ofphotodissociation of CO in the inner disk and the spatialextent of the emission.The observations are described in §
2, and results pre-sented in §
3. In § The Submillimeter Array is a joint project between the Smith-sonian Astrophysical Observatory and the Academia Sinica Insti-tute of Astronomy and Astrophysics and is funded by the Smith-sonian Institution and the Academia Sinica. adopted from the dust emission analysis of Wahhaj et al.(2007), as well as adjustments to that fiducial model ne-cessitated by the new observations. The parameter spaceis explored in § § § §
5, and a summary is pre-sented in § OBSERVATIONS
We observed 49 Ceti with the SMA at 230 GHz dur-ing an 11-hour track on the night of October 13, 2006.Atmospheric phase was extremely stable, with typicalphase changes of < ◦ between calibrator scans (every25 minutes). Seven antennas were used in the “extended”configuration, with projected baselines between 15 and130 meters. The primary flux calibrator was Uranus, andthe passband calibrators were the quasars 3C454.3 andJ0530+135. Gain calibration was carried out using thequasar J0132-169, located just 1.3 ◦ from 49 Ceti; the fluxderived for this quasar was 0.93 Jy. The nearby quasarJ0006-063 was also included to test the quality of thephase transfer from J0132-169.Two 2-GHz sidebands separated by 10 GHz were used,yielding a continuum sensitivity of 0.7 mJy (1 σ ). Spec-tral resolution in the line was 0.26 km/s, subsequentlybinned to 2.1 km/s, with rms sensitivity 0.030 Jy in asingle 2.1 km/s channel. The LSR velocities were con-verted to heliocentric using an offset of -9.14 km/s. Thesynthesized naturally weighted beam in the CO J=2-1line was 1 . ′′ × . ′′
2, at a position angle of -78.6 ◦ . Imagingwas carried out using the MIRIAD software package. RESULTS AND ANALYSIS
Figure 1 shows the observed line emission from the re-gion around 49 Ceti. Four velocity channels are shown,with the velocity indicated by the color of the contourlines. The observations are centered on the J2000 coor-dinates of 49 Ceti; the star symbol indicates the positioncorrected for the proper motion measured by
Hipparcos .The maximum signal-to-noise ratio in the line is 8. TheCO J=2-1 emission appears to be in an extended rotat-ing structure of >
2” radius, apparently viewed close toedge-on. The symmetric distribution of the emission inthe four velocity channels implies a heliocentric velocitynear 12.2 km/s, consistent with previous determinationsof the systemic velocity (10.5 and 9.9 km/s for the diskand the star, respectively; see Dent et al. 2005, and refer-ences therein). No emission is detected outside the rangeof velocities shown. The wide separation of the emissionpeaks, combined with a lack of compact, high-velocityemission, suggests that the central regions are clear ofCO J=2-1 emission out to ∼
90 AU radius ( ∼ . ′′ TABLE 1Observational parameters for 49 Ceti
Parameter CO(3-2) a CO(2-1) CO(2-1) continuumRest frequency (GHz) 345.796 230.538 220.399 230.5 (USB b )Channel width 0.27 km s − − − × . ′′ × . ′′ . ′′ × . ′′ . ′′ × . ′′ ◦ -78.6 ◦ -78.6 ◦ rms noise (Jy beam − ) 0.22 0.030 0.017 7 . × − Dust flux (mJy) – – – < . ± ± < . − ) 9.5 ± ± < . a Dent et al. (2005) b Upper sideband frequency; lower sideband is centered at 220.5GHz. Both sidebands have 2 GHz width.
Fig. 1.—
A renzogram of SMA observations of 49 Ceti in theCO J=2-1 line. The beam size is 1 . ′′ × . ′′
2, and the position angleis − ◦ . Contours are -3, 3, and 5 ×
37 mJy/beam (the rmsnoise). The position of 49 Ceti is marked with a star symbol,while the green line indicates the position angle derived by Wahhajet al. (2007) from mid-IR imaging. The contour colors indicateheliocentric line-of-sight velocity; the four distinct velocities shownare 9.0, 11.1, 13.2, and 15.3 km/s, in the order of bluest to reddestchannel. No emission was detected outside this velocity range. in CO probed by the J=2-1 transition is given by M = 4 πhν F md A x (1)where the subscript 21 refers to the CO(2-1) transition, F is the integrated flux in the line, d is the distanceto the source (61 pc; Hipparcos), m is the mass of theCO molecule, ν is the rest frequency of the transition, h is Planck’s constant, and x ≡ N N tot where N is thepopulation in the J=2 rotational level while N tot is thetotal CO population. The CO mass calculated using thismethod is 2 . × − M ⊕ . Using the canonical CO/H ratio of 10 − this yields a molecular hydrogen mass of2 . ⊕ , consistent with the value of 6 . × − M Jup =2 . ⊕ calculated by Zuckerman et al. (1995). No continuum emission was detected at this combina-tion of resolution and sensitivity. This indicates one oftwo things: either the continuum flux is concentrated atthe center of the disk but the total flux is too low to bedetected, or the total flux may be larger but spread overmany beams, so that the brightness within each beam isbelow our detection threshold. These observations weresensitive enough to detect the higher continuum flux re-ported by Bockel´ee-Morvan et al. (1994) if it were con-centrated within a few synthesized beams. However, anextrapolation of the Song et al. (2004) value for a typicalcircumstellar dust spectrum predicts a lower flux by afactor of 6, which is just below the detection threshold.The lack of an SMA continuum detection at 230 GHzis therefore inconclusive: if the Song et al. (2004) valueis correct, we would not expect to detect even centrallyconcentrated emission, and so we cannot constrain thespatial extent of dust emission through the nondetectionat 230 GHz. DISK MODELING
In order to gain insight into the physical processes atwork in the 49 Ceti system, we carried out modeling ofthe disk with COSTAR (Kamp & Bertoldi 2000; Kamp& van Zadelhoff 2001), a code which solves the chemicalequilibrium simultaneously with a detailed heating andcooling balance to determine gas properties of circumstel-lar disks. In the following, the salient features of thesemodels are summarized. The chemistry is modeled usinga network of 48 different species covering the elements H,He, C, O, S, Mg, Si, and Fe. The elemental abundancesand key parameters of these models, including the stel-lar mass, radius, effective temperature, surface gravity,and ultraviolet flux, are summarized in Table 2. The 48species are connected through 281 reactions, includingcosmic ray chemistry, photochemistry and the chemistryof excited H . We compute equilibrium chemistry using amodified Newton-Raphson algorithm. The solution thenonly depends on the element abundances and not on ini-tial conditions.We use the results of dust modeling by Wahhaj et al.(2007) and assume large 30 µ m black body grains withradiative efficiencies of Q λ = 2 πa/λ for λ > πa and Q λ = 1 otherwise. These grains are efficient absorbersand inefficient emitters, thus achieving dust radiativeequilibrium temperatures of T dust = 324 (cid:18) L ∗ L ⊙ (cid:19) . ( a µ m ) − . ( r AU ) − . K . (2)Here, L ∗ and L ⊙ are the stellar and solar luminosityrespectively, a µ m is the grain size in micron and r AU thedistance from the star in astronomical units. The gastemperature is derived from a detailed energy balanceincluding the most relevant heating and cooling processes(Kamp & van Zadelhoff 2001). TABLE 2Element abundances and parameters used in the diskmodels
Parameter a Value A He . × − A C . × − A O . × − A Mg . × − A Si . × − A S . × − A Fe . × − T eff
10 000 Klog g ∗ ⊙ M ∗ ⊙ σ UV .
68 10 − cm − H − atom − Gas-phase abundances ( A ) are relative to hydrogen. The radiation field consists of both stellar and interstel-lar components. The stellar properties are determinedby a Kurucz model fit to photometric points collectedfrom the literature (Wahhaj et al. 2007; Sylvester et al.1996; Bockel´ee-Morvan et al. 1994; Song et al. 2004); us-ing T eff =10000 K and log g = 4.5, consistent with thevalues quoted by Chen et al. (2006), the derived stel-lar luminosity is L ∗ = 26 . L ⊙ and the radius is 1.7 R ⊙ .The spectral energy distribution and Kurucz model areplotted in Figure 2, including dereddening according toextinction derived by Sylvester et al. (1996) and usinga Cardelli et al. (1989) extinction law. The solid line inthe figure denotes the fit to the photometry of a Kuruczstellar atmosphere model at the Hipparcos distance of 61pc. The dashed line shows the spectral energy distribu-tion of the best-fit model of the outer disk as describedin § . × cm − s − (Habing 1968).A basic model of the dust disk was constructed accord-ing to the Bayesian analysis of mid-infrared emission car-ried out by Wahhaj et al. (2007). Their model consistsof an inner disk extending from 30 to 60 AU, composedprimarily of small grains ( a ∼ . µ m) with a surfacedensity of 5 × − g/cm , and an outer disk extendingfrom 60 to 900 AU composed of larger grains ( a ∼ µ m) with a surface density of 3 × − g/cm . Theyderive a surface density distribution for the outer diskthat is constant with radius, yielding a total disk massof 0.35 M ⊕ . From the mid-IR images, they also deter-mine a position angle of 125 ◦ ± ◦ (indicated in Figure1) and an inclination of 60 ◦ ± ◦ . We use this model as astarting point for the disk structure, since it reflects the best available information on the dust density distribu-tion. However, since the molecular gas emission providesbetter constraints on some aspects of disk structure, in-cluding the vertical density distribution and the surfacedensity structure of the outer disk, we introduce refine-ments to this initial model where justified, as describedin § § µ m grains instead of 15 µ m grains, al-though the grain size used in this simple model is highlydegenerate with other disk properties, as discussed in § H =2 AU, sincethere is no information on disk scale height from the dustmodel of Wahhaj et al. (2007); we also begin by retainingthe inner and outer radii and radially constant surfacedensity structure from the Wahhaj et al. (2007) model,although these assumptions are modified in § − toavoid model densities dropping to unrealistically low val-ues near the boundaries of the numerical grid.To compare our models with the SMA data, we use theradiative transfer code RATRAN (Hogerheijde & van derTak 2000) to generate a sky-projected image of the COJ=2-1 emission predicted for the physical model. Wethen use the MIRIAD task uvmodel to sample the imagewith the combination of spatial frequencies and visibilityweights appropriate for our SMA data. We allow theinclination and position angle of the system to vary inorder to best match the data. Fig. 2.—
Spectral energy distribution (de-reddened according toextinction derived by Sylvester et al. 1996 and Cardelli et al. 1989extinction law) for 49 Ceti using available optical, infrared, andsubmillimeter photometry. The solid line denotes a Kurucz stellaratmosphere model fitted to the photometry using the Hipparcosdistance of 61 pc. The dot-dashed line shows the SED for thebest-fit model of the outer disk see text of § Inner Disk
In the inner disk, inside 60 AU, composed primarilyof small grains, the stellar radiation field raises the dusttemperature to 1000-2000 K and dissociates most of themolecular gas. In this region, the dominant form of car-bon is C + , and even hydrogen is predominantly atomic.We therefore ignore the inner disk component in subse-quent modeling and focus on reproducing the observedCO emission with only the outer disk component.This lack of molecular gas in the inner disk is consis-tent with the non-detection of warm H by Chen et al.(2006) and Carmona et al. (2007), and with the lack ofhigh-velocity CO emission in Figure 1. The lack of COemission more than 4.3 km/s from the stellar velocityis consistent with an absence of CO within a radius of ∼
90 AU, for gas in Keplerian rotation around a star of2.3 M ⊙ . Outer Disk
There are three primary features of the observed COemission from the outer disk that we attempted to repro-duce with this modeling effort: (1) the separation of theemission peaks in the outer channels ( ∼ ∼ r − ǫ den-sity profile. We simultaneously relax the constant scaleheight assumption, introducing a scale height H that in-creases linearly with radius r , with proportionality con- stant h = H/r . The full 2-D density structure then be-comes n ( r, z ) = r − ǫ exp ( − z / H ), where the exponent ǫ and scale height constant h are varied to obtain thebest fit to the CO data.The power-law surface density profile results in a muchbetter match between the model and the observed emis-sion peak separation. It also curbs the elongation of theemission to some extent, as the vertical column densityof the outer disk drops and the material far from thestar becomes subject to dissociation by interstellar ra-diation. However, even steep power law indices for thesurface density profile do not result in a completely pho-toevaporated outer disk and consequently produce emis-sion that is much more elongated than observed. In anext step, we therefore reduce the outer radius from 900to 200 AU. While this is at the lower end of the range al-lowed by Wahhaj et al. (2007), their derived outer radiuswas based largely on the uncertain millimeter flux mea-surement, and the gas geometry is likely a better probeof the disk extent. Grid of Disk Models
After these initial studies of the outer disk, it becameclear that several model parameters were ill-constrainedby previously existing data. Specifically, the disk mass isconstrained only by the weakly-detected and contradic-tory millimeter flux measurements; similarly, the densitypower law index ǫ is ill-determined by the infrared ob-servations, which are primarily sensitive to inner diskemission. The scale height h is also completely uncon-strained by the continuum or single-dish measurements,neither of which is sensitive to disk structure in the ver-tical direction. The disk geometry (PA and inclination)quoted by Wahhaj et al. (2007) is also subject to largeuncertainties, due to the irregular shape of the emissionobserved in the infrared. We therefore attempt to bet-ter constrain these disk parameters by using our resolvedCO gas line observations. Gas lines are generally moresensitive than dust emission to temperature and densitygradients, and can thus provide means to break modeldegeneracies. We ran grids of models for the three struc-tural parameters (disk mass, density index, scale height)and two geometrical parameters (PA, inclination), find-ing the best-fit values by calculating and minimizing a χ value comparing the model to the observed emissionfrom the disk. Due to the computational intensity of thecalculations necessary to determine the chemistry andradiative transfer solutions for each model, we ran onlya sparsely sampled grid of models. In order to ensurethat the final model reflects all available observationalconstraints, we centered the grid on the fiducial modelof § CO Chemistry Across the Model Grid
The CO chemistry is dominated by photodissociationin a number of UV bands and thus the abundance of COin each model is mostly dependent on the radial and ver-tical column densities being able to shield the stellar andinterstellar UV radiation respectively. In the followingwe briefly discuss some basic characteristics of the modelgrid.The surface density in the models is independent ofthe scale height and hence the radial mass distributionin each model can be written as M ( R ) ∝ R − ǫ +3 , where M ( R ) denotes the mass inside a radius R . So, as weincrease the density power law exponent ǫ , the inner re-gion of the outer disk harbors a larger fraction of thetotal mass. The densities in this region of the disk be-come higher and hence it is easier to obtain the criticalcolumn densities necessary for UV shielding in the radialdirection. On the other hand, a shallower gradient forthe density distribution translates into higher densitiesin the outer parts of the disk, thus enhancing the verti-cal shielding in the outer disk compared to models withhigh ǫ . None of our models is optically thick in the dustcontinuum, so the UV shielding is mainly H shielding ofthe CO bands due to their overlap in wavelengths; COself-shielding also plays a role.With this basic picture, we can understand the COchemistry displayed in Fig. 3 as a function of disk mass(right column) and density gradient ǫ (center column).As the total disk mass is increased, CO first starts tobuild up in the radial direction. It can still be dissoci-ated by the vertically impinging interstellar UV radiationfield in the outer regions of the disk (150-200 AU) un-til the disk reaches a mass of ∼
17 M ⊕ , at which pointit becomes opaque in the CO bands even in the verti-cal direction. A shallow density gradient always leads tosmaller radial column densities at the same reference ra-dius, thus pushing the C + /C/CO transition further outin radial distance. In our best-fit model of 13 M ⊕ , achange in ǫ from 2.5 to 1.1 changes the radius for theC + /C/CO front from close to 40 AU to 190 AU.The scale height h of the models affects only the verti-cal density structure in the models. However, since den-sity and chemistry are closely intertwined, it can stronglyimpact the overall radial and vertical structure of the COchemistry. From a comparison of the center panel withthe bottom left panel in Figure 3, we see that a factor2 lower scale height with respect to the best fit model( h = 0 . From Chemistry to Observables
The predicted CO J=2-1 emission for the models inFigure 3 is displayed in Figure 4; a comparison of thesefigures illustrates the ways in which differences in chemi-cal structure are manifested in the observable propertiesof the CO emission. The CO emission is sampled with the same spatial frequencies and visibility weights as theSMA data and displayed in renzogram form with thesame velocity structure as in Figure 1. In order to em-phasize the relative structural differences between mod-els, the contour levels are 15% of the peak flux for eachmodel, with the absolute flux indicated by the thicknessof the contours, and also printed explicitly at the top ofeach panel.The decreased shielding in the inner disk caused by re-ducing the density gradient ǫ is visible as a lengtheningof the emission in the central channels and a wideningof the emission peaks in the outer channels in the low-epsilon model (bottom center panel). Increasing ǫ (topcenter panel) leads to enhanced shielding at the disk in-ner edge, causing much higher CO fluxes in the outerpart of the disk and extremely high contrast between theinner and outer velocity channels.The primary observable consequence of adjusting themass (right panels, top and bottom) is that the increasedor decreased shielding from extra gas leads to a cor-responding increase or decrease in the total CO flux;changes to the shape of the emission are minimal, andthe primary difference between models of different massover the mass range under consideration is simply in therelative brightness of the emission.Differences in the scale height of the disk similarlymanifest as differences in the flux scale; however, de-creasing the scale height (bottom left panel) also causesgreater shielding at the inner disk edge, leading to greaterelongation of the outer velocity channels and causing theinner velocity channels to draw together and overlap asthe CO flux rises throughout the inner areas of the disk.An increase in scale height (top left panel) leads to agreater area in the front and back of the disk, projectedalong our line of sight, which increases the flux in thecentral channels and leads to a lower contrast betweenthe inner and outer channels of the disk. Spectral Energy Distribution
After converging initially on a model that was able toreproduce the observed CO J=2-1 emission, we used thatmodel to predict the spectral energy distribution. Thisserves as an a posteriori test of the consistency betweenthe gas and dust properties in the models and the avail-able observables.We integrate over the disk volume to obtain the fluxas a function of wavelength F λ = ( πa /d ) Z Z πr B λ ( T dust ( r, z )) n dust ( r, z ) Q ( λ ) dz dr , (3)where d is the distance to the source and n dust is the num-ber density of dust grains in cm − . We assume through-out a grain density of 2.5 g/cm .While the predicted shape of the spectral energy distri-bution matches the observations well, the absolute fluxesare too high by a factor of ∼
5. Adjusting the tempera-ture of the dust grains alters the shape of the SED curve,causing it to deviate from the observed shape; we weretherefore required to increase the gas:dust ratio from 100to 500 in order to reproduce the observed photometry.This unusually high ratio is likely an artifact of the sim-ple assumptions of the model, since little information isavailable about the dust distribution in this system (and
M=13 M_E eps=2.5 h=0.02h=0.01h=0.03
50 100 150 200 r [AU]0246810 z [ AU ]
50 100 150 200r [AU]0246810 z [ AU ] -10-8-6-4-20 l og ε C O
50 100 150 200r [AU]02468 z [ AU ]
50 100 150 200r [AU]02468 z [ AU ] -10-8-6-4-20 l og ε C O
50 100 150 200r [AU]02468 z [ AU ]
50 100 150 200r [AU]02468 z [ AU ] -10-8-6-4-20 l og ε C O
50 100 150 200r [AU]02468 z [ AU ]
50 100 150 200r [AU]02468 z [ AU ] -10-8-6-4-20 l og ε C O
50 100 150 200r [AU]02468 z [ AU ]
50 100 150 200r [AU]02468 z [ AU ] -10-8-6-4-20 l og ε C O eps=3.5eps=1.1 M=9 M_E
50 100 150 200r [AU]02468 z [ AU ]
50 100 150 200r [AU]02468 z [ AU ] -10-8-6-4-20 l og ε C O
50 100 150 200r [AU]02468 z [ AU ]
50 100 150 200r [AU]02468 z [ AU ] -10-8-6-4-20 l og ε C O M=17 M_E
Fig. 3.—
Two-dimensional CO abundances in a subset of disk models. The center panel shows the best-fit model ( M = 13M ⊕ , ǫ = 2 . h = 0 . h (left column) , ǫ (center column) , and M disk (right column) .The values of the parameters shown are h = 0 .
01, 0 . ǫ = 1 .
1, 3 .
5; and M = 9, 17 M ⊕ . TABLE 3Derived quantities from a subset of the 49 Ceti disk models M a disk ǫ h N (CO) b radial N (CO) , cvertical M d CO I CO (J=2-1) e (M ⊕ ) (10 cm − ) (10 cm − ) (10 − M ⊕ ) (Jy km s − )13 2.5 0.020 2.76 4.23 9.66 2.69 2.5 0.020 0.32 1.82 2.46 1.217 2.5 0.020 13.5 9.06 37.2 6.913 3.5 0.020 15.1 4.47 98.0 11.713 1.1 0.020 0.13 0.91 3.74 2.313 2.5 0.010 42.8 78.4 96.6 14.513 2.5 0.030 0.12 2.20 2.97 1.5 a Total disk gas mass b Total radial CO column density through the midplane c CO vertical column density at 100 AU d Total CO mass in the disk e Integrated CO(J=2-1) line emission none at all from our data). For example, the mass of thesystem is likely not all in 30 µ m grains, and a significantfraction of the mass may be in larger grains that con-tribute little to the infrared emission. Another possibil-ity is that the overall gas:dust ratio is consistent with thestandard value, but that gas and dust are not well-mixed:for example, much of the excess emission may arise fromthe inner edge of the disk, which will be directly illumi-nated and heated by the stellar radiation. Resolved ob-servations of the dust continuum emission would test thishypothesis by placing constraints on the spatial distribu-tion of the emitting region. Including effects such as thiswould significantly complicate the model presented here,as the H formation rate would be affected by varying the abundance of the dust on which it forms. In general, thedust size and gas:dust mass ratio are strongly related bythe total dust surface required to maintain the observedquantity of molecular gas; these are in turn dependenton the stellar properties determining dust grain temper-atures. None of these dust-dependent quantities are wellconstrained by available data. Given the observationsavailable and the extremely simplified dust model, whichnot only neglects the size distribution but also the possi-bility of a mixture of compositions and opacities, we usethe simplest assumption of an altered gas:dust ratio inorder to conduct a consistency check of the temperatureand density structure of the gas model.Decreasing the total dust mass in the model to match Fig. 4.—
CO J=2-1 emission predicted for the subset of models shown in Figure 3, sampled with the same spatial frequencies andvisibility weights as the SMA data in Figure 1. The center panel shows the best-fit model, while the rows of models above and belowshow the effects of incrementing and decrementing, respectively, each of the three structural parameters that we allowed to vary during thefitting process: h (left column) , ǫ (center column) , and M disk (right column) . The contour levels are displayed in the upper left corner ofeach panel; they are set at 3 and 5 ×
15% of the peak flux for each model. The thickness of the contours is proportional to the absoluteflux: thicker contours indicate that the source is brighter than the data, while thinner contours indicate that it is fainter than the data.The contour levels in the center panel are identical to those in Figure 1. Table 4 gives the full list of parameters for the best-fit model. the SED reduces the grain surface area for H formation.Thus molecular hydrogen begins to form at larger radiiand greater depth, compared to the initial model withthe canonical gas:dust ratio of 100. As a consequence ofless effective UV shielding, the total CO mass decreases.Hence the total mass of the best-fit model has to be in-creased slightly to compensate for the lower moleculargas fraction. As a secondary effect, the overall gas tem-perature of the dust-depleted model also decreases dueto the diminished photoelectric heating in the disk. Thecorresponding SED predicted for these parameters is in-dicated by the dashed line in Figure 2. The mid-infraredflux points are underestimated by this model becausewe do not include the inner disk component of Wahhajet al. (2007); as our data provide no constraints on the properties of the inner disk, we ignore this componentand concentrate on the fit to the outer disk. The fluxpredicted by the model SED is consistent with our owncontinuum upper limit reported in Table 1. Best-Fit Disk Model
The center panel of Figure 4 shows the best-fit modelfrom the grid, with the minor modifications introducedby reproducing simultaneously the spectral energy distri-bution. The structural and geometric parameters for thismodel are listed in Table 4. The errors given in the tableare the approximate 1- σ uncertainty range interpolatedfrom the χ grid.This model reproduces the basic features of the COJ=2-1 emission well, including the strength of the emis- TABLE 4Parameters for Best-Fit Disk Model h . +0 . − . ǫ . +0 . − . M gas ± ⊕ M dust . ± .
01 M ⊕ i ◦ ± ◦ PA − ◦ ± ◦ R in
40 AU a R out
200 AU a a For a description of the constraints on the inner and outer radii,see § sion, the separation of the emission peaks, and the spatialextent of the emission. There are still several importantdifferences between the model and the data, however, in-cluding (1) an inability to reproduce the changes in po-sition angle with radius evident in the data (the “wings”of emission extending to the southeast and northwest ofthe position angle axis), and (2) the separation of theinnermost, low-velocity channels. Both of these may beindicative of departures from azimuthal symmetry in thedisk structure, the former possibly indicating a warp inthe disk and the latter apparently pointing to a deficit ofemission along the minor axis of the disk. In none of ourmodels were we able to reproduce the wide separation be-tween the inner channels; while the signal-to-noise ratioin these channels is low, the observed CO morphology isdifficult to reproduce in detail with a simple, azimuthallysymmetric disk model. The CO emission for this best-fit model is optically thin in both the J=2-1 and J=3-2transitions, even for the edge-on disk orientation, andtherefore traces the full column density of disk material.The densities in the disk are too low for efficient gas-dust coupling and thus the gas finds its own equilibriumtemperature determined mainly by photoelectric heatingand line cooling. The most important cooling lines fromsurface to midplane are [C ii ], [O i ], and H . CO abun-dances are only high in a region between 45 and 70 AU(Fig. 3). Outside that region, CO cooling is less impor-tant for the energy balance. Fig. 5 summarizes the mostimportant heating and cooling processes and also showsthe resulting gas temperature structure. The disk surfacestays well below 100 K due to efficient fine structure linecooling. The molecular cooling is however less efficient incompeting with the photoelectric heating from the largesilicate grains (Kamp & van Zadelhoff 2001), leading totemperatures of a few 100 K in the disk interior.In order to test the robustness of the best-fit modelto the gas properties, we used this model to predict theCO J=3-2 spectrum. It compares favorably with thespectrum observed by Dent et al. (2005), reproduced inFigure 6. The heavy solid line shows the J=3-2 spectrumpredicted from the best-fit disk model, while the lightsolid line shows the observed JCMT spectrum. Althoughthe observed spectrum is noisy and likely subject to anabsolute calibration uncertainty, the overall agreementis within ∼ a priori to determine thesemodel parameters. DISCUSSION
50 100 150 200r [AU]0246810 z [ AU ] Γ PE Γ H2diss Γ H2form Γ g-g Γ C Γ CR Γ OI
50 100 150 200r [AU]02468 z [ AU ] T g a s [ K ]
50 100 150 200r [AU]0246810 z [ AU ] Λ CII Λ CH Λ H2 Λ OI Λ CO
60 K 50 K 40 K
Fig. 5.—
Two-dimensional gas temperatures in the best fit diskmodel ( M disk = 13 M ⊕ , ǫ = 2 . h = 0 .
02. Shown are the most im-portant heating (top panel) and cooling (middle panel) processesas well as the gas temperature (bottom panel). The dust temper-ature, which depends only on radius, is overlaid in white contourlines (steps of 10 K).
The processes determining the amount and distribu-tion of gas and dust in transition disks like that around49 Ceti are the same processes that shape the featuresof emergent planetary systems around these young stars.Resolved observations of individual disks in this phaseare desirable to address such basic questions as when inthe lifetime of a star its disk disperses, whether the gasclears before the dust, and whether the disk clears fromthe center or in a radially invariant manner.In the 49 Ceti system, the infrared dust properties ap-pear similar to those of a debris disk (Wahhaj et al.2007). Yet observations presented here indicate that asubstantial quantity of molecular gas persists in the outerdisk, between radii of 40 and 200 AU, where photochem-istry from stellar and interstellar radiation dominates.The lack of molecular gas emission interior to this radiusas indicated by our observations, combined with the lackof dust emission within a radius of 30 AU inferred byWahhaj et al. (2007), implies that the 49 Ceti systemappears to be clearing its gas and dust from the centerout. The mechanism responsible for this central clearingis not indicated; in general, the best-developed theoriesto explain this transitional morphology are (1) centralclearing through the influence of a massive planet and(2) photoevaporation by radiation from the central star.The clearing of gaps and inner holes has long been pre-0
Fig. 6.—
CO J=3-2 spectrum predicted for the model that pro-vides the best fit to the resolved J=2-1 emission (heavy solid line),compared with the Dent et al. (2005) JCMT CO J=3-2 spectrum(light solid line). The x-axis shows heliocentric velocity while they-axis gives the JCMT main beam brightness temperature. dicted as a consequence of the formation of massive plan-ets in circumstellar disks (e.g. Lin & Papaloizou 1986;Bryden et al. 1999). In the case of 49 Ceti, the for-mation of a Jupiter-mass planet would be required at adistance of ∼
40 AU from the star, roughly the inner ra-dius of the observed hole in the gas distribution. Such ascenario could also help to explain the size segregation ofdust grains observed by Wahhaj et al. (2007); a predictedconsequence of inner disk clearing by gravitational influ-ence of a massive planet is a filtration of dust grains bysize, with only those below a certain threshold (typically1-10 µ m) accreted across the gap along with a reducedamount of gas (Rice et al. 2006). However, this scenarioultimately requires the accretion of substantial amountsof gas into the inner disk, and searches for molecular gasin the inner disk of 49 Ceti (Chen et al. 2006; Carmonaet al. 2007) have not detected such a population. An-other indication that an inner hole is likely caused by amassive planet in formation would be non-axisymmetricfeatures resulting from its gravitational influence, such asspiral waves. While the CO emission from 49 Ceti doesnot appear asymmetric within the limits of the SMA ob-servations, more sensitive spatially resolved observationscould address this hypothesis.The absence of gas in the inner disk is, however, consis-tent with a photoevaporation scenario: as the photoevap-orative wind produced by stellar radiation becomes com-parable to the accretion rate in the disk, material withinthe gravitational radius R g = GM ⋆ /c s will quickly drainonto the star, leaving an evacuated inner hole free of gasand dust (e.g. Hollenbach et al. 1994; Alexander et al.2006). The gravitational radius for 49 Ceti is roughly 20AU, which is comparable to the inferred inner radius of40 AU for the outer disk. The larger outer radius mayin fact be consistent with the later stages of photoevap-oration, after the inner disk has become optically thin to ultraviolet radiation and the inner disk radius slowly in-creases under the influence of the photoevaporative wind(Alexander et al. 2006). Alexander & Armitage (2007)propose a method of discriminating between inner holescaused by photoevaporation and those caused by the for-mation of a giant planet, involving a simple comparisonbetween two observables: the disk mass and the accre-tion rate. As there is no measured accretion rate for49 Ceti, we cannot apply the criteria presented by theseauthors; however, we note that the low disk mass doesindeed fall within the parameter space consistent witha photoevaporative scenario. Further observations arenecessary to determine the origin of the inner hole; inparticular, stringent limits on the accretion rate couldsuggest a photoevaporative mechanism.There are few disks which appear to be in a similarevolutionary stage to that of 49 Ceti; a rare example isthe disk around the A star HD 141569. Like 49 Ceti,it hosts a disk composed primarily of sub µ m-size grainswith infrared properties approaching those of a debrisdisk (Wahhaj et al. 2007; Marsh et al. 2002), while stillretaining a substantial quantity of molecular gas withcentral region clear of gas emission, in this case out to aradius of ∼
11 AU (Goto et al. 2006; Brittain et al. 2007).It exhibits a transitional SED (Mer´ın et al. 2004), andobservations of the rovibrational CO spectrum reveal gaswith disparate rotational and vibrational temperatures(200 K and 5000 K respectively; Brittain et al. 2007),indicative of UV fluorescence on the outer edges of aninner disk region cleared of gas and dust. An analysis ofthe chemistry and gas properties of the system similarto the one presented here for 49 Ceti was conducted byJonkheid et al. (2006). While the presence and extent ofthe inner hole are clearly indicated, the physical origin ofthis clearing is less obvious. The Br γ profile is indicativeof substantial accretion, and Brittain et al. (2007) deem aphotoevaporative clearing mechanism unlikely due to thelarge column density outside the cleared region and thelack of evidence for a photoevaporative wind in the FUV(Martin-Za¨ıdi et al. 2005). However, Mer´ın et al. (2004)place a much lower limit of 10 − M ⊙ /yr on the accretionrate, based on the assumed gas:dust ratio of 100 and thelow optical depth of the inner disk, which would be muchmore consistent with a photoevaporation scenario. Gotoet al. (2006) note that the rough coincidence of the innerrim of the disk with the gravitational radius suggests thatphotoevaporation in concert with viscous accretion is alikely cause for the inner disk clearing.Whatever the origin of their morphology, the observedgas and dust properties indicate that the disks surround-ing both 49 Ceti and HD 141569 appear to be in a transi-tional state of evolution during which the dust propertiesare beginning to appear more like those of a debris disk,while the gas is in the process of being cleared from thedisk from the center out. CONCLUSIONS