ALMA Observations of the Inner Cavity in the Protoplanetary Disk around Sz 84
Jun Hashimoto, Takayuki Muto, Ruobing Dong, Yasuhiro Hasegawa, Nienke van der Marel, Motohide Tamura, Michihiro Takami, Munetake Momose
DDraft version September 22, 2020
Typeset using L A TEX default style in AASTeX63
ALMA Observations of the Inner Cavity in the Protoplanetary Disk around Sz 84
Jun Hashimoto ,
1, 2, 3
Takayuki Muto, Ruobing Dong , Yasuhiro Hasegawa, Nienke van der Marel , Motohide Tamura ,
7, 1, 2
Michihiro Takami , and Munetake Momose Astrobiology Center, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Subaru Telescope, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan Department of Astronomy, School of Science, Graduate University for Advanced Studies (SOKENDAI), Mitaka, Tokyo 181-8588, Japan Division of Liberal Arts, Kogakuin University, 1-24-2, Nishi-Shinjuku, Shinjuku-ku, Tokyo, 163-8677, Japan Department of Physics & Astronomy, University of Victoria, Victoria, BC, V8P 1A1, Canada Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA Department of Astronomy, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU No.1, Sec. 4, RooseveltRd, Taipei 10617, Taiwan, R.O.C. College of Science, Ibaraki University, 2-1-1, Bunkyo, Mito, Ibaraki 310-8512, Japan
ABSTRACTWe present Atacama Large Millimeter/submillimeter Array (ALMA) observations of a protoplan-etary disk around the T Tauri star Sz 84 and analyses of the structures of the inner cavity in thecentral region of the dust disk. Sz 84’s spectral energy distribution (SED) has been known to exhibitnegligible infrared excess at λ (cid:46) µ m due to the disk’s cavity structure. Analyses of the observedvisibilities of dust continuum at 1.3 mm and the SED indicate that the size of the cavity in the disk oflarge (millimeter size) dust grains is 8 au in radius and that in the disk of small (sub-micron size) dustgrains is 60 au in radius. Furthermore, from the SED analyses, we estimate that the upper limit massof small dust grains at r <
60 au is less than ∼ − M ⊕ , which is (cid:46) r <
60 au. These results suggest that large dust grains are dominant at r <
60 au, im-plying that dust grains efficiently grow with less efficient fragmentation in this region, potentially dueto weak turbulence and/or stickier dust grains. The balance of grain growth and dust fragmentationis an important factor for determining the size of large dust grains in protoplanetary disks, and thusSz 84 could serve as a good testbed for investigations of grain growth in such disks.
Keywords: protoplanetary disks — planets and satellites: formation — dust continuum emission —spectral energy distribution — stars: individual (Sz 84) INTRODUCTIONPlanet formation is believed to take place in protoplanetary disks. In its earliest stages, dust grains grow. For small(sub-micron size) dust grains, which are comparable to typical interstellar medium dust in size, van der Waals forcescause the dust grains, which exhibit Brownian motion, to stick when they collide. Beyond the millimeter size, dustgrains can grow into planetesimals a kilometer (or larger) in size via either direct collisional aggregation of dust grains(e.g., Weidenschilling & Cuzzi 1993; Kataoka et al. 2013) or some instabilities such as streaming instabilities (e.g.,Johansen et al. 2014). The accretion of such planetesimals eventually leads to the formation of planets.Grain growth in protoplanetary disks has been extensively investigated (e.g., Testi et al. 2014). Theoretically, graingrowth is limited by two processes, namely radial drift and fragmentation. Radial drift occurs when dust grains becomelarge enough to decouple from the disk gas and then experience a head wind (Weidenschilling 1977). Accordingly,dust size is limited when dust grains undergo radial drift. Fragmentation also limits grain growth. It occurs when therelative velocity of colliding dust grains becomes high enough to result in fragmentation rather than a merger.
Corresponding author: Jun [email protected] a r X i v : . [ a s t r o - ph . E P ] S e p Hashimoto et al.
Observational investigations of grain growth have been conducted at (sub-)millimeter wavelengths (e.g., Testi et al.2003; P´erez et al. 2012; Testi et al. 2014). Optical and infrared (IR) observations can trace the surface layer of thedisk due to the layer’s large optical depth, whereas (sub-)millimeter observations probe thermal emissions from thedisk midplane region, where grain growth is the most efficient. This region becomes optically thin (or thinner) atlonger wavelengths. As dust grains grow, the dust opacity ( κ λ ), which is approximated as κ λ ∝ λ β , and its index ( β )both decrease (e.g., Miyake & Nakagawa 1993; Draine 2006). Based on the Rayleigh-Jeans limit and the optically thinassumption, the observed flux can be expressed as F λ ∝ λ β +2 , and thus multiple wavelength observations can be usedto measure β even if the absolute dust opacity is unknown.In addition to determining β , comparisons of disk structures observed at near-infrared (NIR) and (sub-)millimeterwavelengths are useful for exploring grain growth. When a cavity structure in the central region of a disk (such disksare called transitional disks ; e.g., Espaillat et al. 2014) is observed directly, it may have different sizes at differentwavelengths (e.g., Dong et al. 2012; Garufi et al. 2013; van der Marel et al. 2013; Villenave et al. 2019). One explanationfor the different cavity sizes at different wavelengths is the trapping of large (millimeter size) dust grains (e.g., Riceet al. 2006) by planet–disk interactions (e.g., Zhu et al. 2012). A planet embedded in a disk reduces the surface densityof the gas and creates a gas gap at the planetary orbital radius. The gap thereby produces a gas pressure bump at itsouter edge where large dust grains are trapped. Because the small dust grains coupled to the gas can flow inside thegas pressure bump, their cavity sizes are smaller. This spatial segregation can be used as a proxy of grain growth inthe disk.Dust growth itself can also spatially segregate cavities without dust trapping. The trend of such segregation isopposite to that mentioned above. Numerical simulations of grain growth (e.g., Dullemond & Dominik 2005; Birnstielet al. 2012) show that small dust grains, which are the main components of NIR excesses in the spectral energydistribution (SED), grow into large (millimeter size) dust grains within a time scale of (cid:46) r =1 au if dustfragmentation is negligible. When small dust grains in the central region of a protoplanetary disk are removed, thecorresponding SED shows a deficit of flux at NIR wavelengths. Because grain growth proceeds in an inside-out manner,which is due to higher gas density and a faster dynamical time scale in the inner disk (e.g., Dullemond & Dominik2005; Brauer et al. 2008), the small and large dust grains are predicted to be preferentially distributed in the outerand inner regions of the disk, respectively. Such opposite distributions of small and large dust grains were reportedfor the transitional disk around DM Tau (Kudo et al. 2018; Hashimoto et al. submitted), in which the cavity in thedisk of small dust grains is inferred to be located at r =3 au. Large dust grains are present even within this cavity.These results suggest that small dust grains at a few au around DM Tau efficiently grow into large dust grains withless efficient fragmentation, possibly due to weak turbulence and/or stickier dust grains (e.g., Steinpilz et al. 2019).In this paper, we report another example of an opposite spatial segregation for a cavity in the disk around the TTauri star Sz 84 (spectral type: M5, Alcal´a et al. 2014; T eff : 3162 K, Hendler et al. 2020; M ∗ : 0.2 M (cid:12) , Alcal´a et al.2014; age: 1 Myr, Alcal´a et al. 2014; distance: 152.6 pc, Gaia Collaboration et al. 2018; disk inclination: 75 ◦ , Ansdellet al. 2016). The SED of Sz 84 shows no or very weak IR excesses at λ (cid:46) µ m, which has been interpreted asindicating the presence of an almost clean cavity in the disk of small dust grains at r ∼
55 au (i.e., negligible smalldust grains inside the cavity; e.g., Mer´ın et al. 2010). Subsequent Atacama Large Millimeter/submillimeter Array(ALMA) observations of Sz 84 with a beam size of 0 . (cid:48)(cid:48) r =20–41 au (Tazzari et al.2017; van der Marel et al. 2018). These results suggest that the size of the cavity in the disk of small dust grains( r ∼
55 au) could be larger than that in the disk of large dust grains ( r =20–41 au). The CO J = 3 → M ∼ × − M (cid:12) /yr (Manara et al. 2014), is comparable to that of typical T Tauri stars (Najita et al. 2015). These twoobservational results predict that small dust grains well coupled to the gas exist in the vicinity of the central star (theyarrive there by flowing inside the cavity), possibly explaining the smaller size of the cavity in the disk of small dustgrains. However, as mentioned above, analyses of the visibilities of the dust continuum and the SED in the literature There are two types of transitional disk in the simple classical picture based on SED analyses (e.g., Espaillat et al. 2014). One has acavity in which the central region of the disk is optically thin, and the other is an optically thick disk separated into inner and outer disksby an optically thin gap. Recent studies on transitional disks by Francis & van der Marel (2020) suggest that the existence of the innerdisk responsible for the NIR excess does not correlate with that in the dust continuum at (sub-)millimeter wavelengths, and that thisdiscrepancy may not exist for large dust grains. nner Cavity of Sz 84 Table 1.
ALMA observations and imaging parameters
ObservationsObserving date (UT) 2016.Sep.17Project code 2015.1.01301.STime on source (min) 29.7Number of antennas 38Baseline lengths 15.1 m to 2.5 kmBaseband Freqs. (GHz) 219.5, 220.4, 230.5, 232.5Channel width (MHz) 0.122, 0.122, 0.122, 15.6Continuum band width (GHz) 2.3Bandpass calibrator J1517 − − − CO J = 2 → − . uv -taper parameter 50.0 × λ with 183.0 ◦ · · · Beam shape 198 ×
195 mas at PA of − ◦ ×
161 mas at PA of − ◦ r.m.s. noise ( µ Jy/beam) 61.3 2.37 × at 1.0 km/s bin show the opposite observational results. The origin of Sz 84’s cavity in the disk of small dust grains with a moderatemass accretion rate is still unclear (e.g., Manara et al. 2014). OBSERVATIONSALMA observations of Sz 84 were carried out with band 6 in cycle 3 (ID: 2015.1.01301.S; PI: J. Hashimoto); theyare summarized in Table 1. The data were calibrated using the Common Astronomy Software Applications (CASA)package (McMullin et al. 2007) with the calibration scripts provided by ALMA. We conducted a self-calibration ofthe visibilities. The phases were self-calibrated once with fairly long solution intervals (solint=‘inf’) that combinedall spectral windows. The proper motions of Sz 84 were calculated with the function
EPOCH_PROP in GAIA ADQL(Astronomical Data Query Language ). The phase centers were corrected using fixvis in the CASA tools. The dustcontinuum image at band 6 was synthesized by CASA with the CLEAN task using a multi-frequency deconvolutionalgorithm (Rau & Cornwell 2011). In the
CLEAN task, we set the uv -taper to obtain a nearly circular beam pattern(Table 1). The synthesized dust continuum image is shown in Figure 1. The root-mean-square (r.m.s.) noise in theregion far from the object is 61.3 µ Jy/beam with a beam size of 198 ×
195 mas at a position angle (PA) of − ◦ .In addition to our own data, two archival dust continuum datasets were used for our visibility analysis in § ∼ . (cid:48)(cid:48)
3, we only show the band 6 image inFigure 1.The CO J = 2 → uv plane using the uvcontsub task in the CASA tools. A line image cube with channel widths of 1.0 km/s was produced by the CLEAN task. The integrated line flux map (moment 0) and the intensity-weighted velocity map (moment 1) are shown inFigures 1 and 2, respectively. The channel maps at − · km/s with a beam size of 235 ×
161 mas at a PA of − ◦ andthat in the moment 1 map at the 1.0 km/s bin is 2.37 mJy/beam. The peak signal-to-noise ratio (SNR) is 17.9 in thechannel map of +7.0 km/s. CO J = 2 → O J = 2 → https://gea.esac.esa.int/archive/ Hashimoto et al. RESULTSFigures 1(a) and (b) show the dust continuum image at band 6 and the CO moment 0 map, respectively. Ourobservations clearly detect the spatially resolved disk in both images. However, no cavity structure appears in thecentral region of the disk in either image. The total flux density of the dust continuum derived from the visibilityfitting in § ± ± CO integrated flux density at more than3 σ is 1.89 ± · km/s.We derived the spectral index α based on band 3, 6, and 7 data. The total flux densities at bands 3 and 6 taken fromour visibility fitting in § ± ± ± α was then calculated as 2.42 ± α ∼ CO moment 0 map (Figure 1b) at a PAof 165.71 ◦ taken from our modeling results in § r (cid:46)
50 au with a nearly flatslope at r (cid:46)
20 au. In contrast, the two brightness profiles (Figure 1c) at r (cid:38)
50 au deviate, possibly due to the largersize of the CO disk (Trapman et al. 2020) or the presence of small dust grains, which is discussed in § CO moment 1 map and its position–velocity (PV) diagram at a PA of 165.71 ◦ and a diskinclination of 75.13 ◦ taken from § M (cid:12) in the PV diagram and found that the dynamicalmass of Sz 84 is ∼ M (cid:12) . This value is consistent with the dynamical mass estimated from the CO J = 3 → ± M (cid:12) ; Yen et al. 2018). Note that these estimates are roughly 2–3 times largerthan the spectroscopically determined mass (0.16–0.18 M (cid:12) ; Alcal´a et al. 2017). This discrepancy may result from thehigh disk inclination of 75 ◦ . CO is generally optically thick and traces the surface layer of the disk, and thus thevelocity structure could be largely affected by the high inclination. The disk vertical structure must be taken intoaccount to derive a dynamical mass in the inclined disk system. ″ (152.6 au) NE 1 ″ (152.6 au) NE(b)(a) Moment 0 (mJy/beam km/s)
0 80 160
Flux density (mJy/beam)
0 2.4 4.8 (c) D u s t c on ti nuu m ( m J y / b ea m ) C O m o m e n t ( m J y / b ea m k m / s ) Offset (au)
CO (3 σ )Dust (3 σ )Dust cont.CO mom. 0 -100 -50 0 50 100 Figure 1.
Observational results for the Sz 84 disk from ALMA at band 6 in cycle 3. (a) Dust continuum image. The r.m.s.noise is 61.3 µ Jy/beam with a beam size of 198 ×
195 mas at a PA of − ◦ . (b) CO moment 0 map. The r.m.s. noise is8.7 mJy/beam · km/s with a beam size of 235 ×
161 mas at a PA of − ◦ . The contours represent the dust continuum at 20,40, and 60 σ . (c) Radial cuts in panels (a) and (b) at a PA of 165.71 ◦ taken from our modeling in § MODELING nner Cavity of Sz 84 − V e l o c it y ( k m / s ) − − − ″ (152.6 au) NE (b) F l ux d e n s it y ( m J y / b ea m ) − (a) C O m o m e n t ( k m / s ) − Figure 2. (a) CO moment 1 map. The contours represent the dust continuum at 20, 40, and 60 σ . (b) PV diagram at aPA of 165.71 ◦ and a disk inclination of 75.13 ◦ taken from § M (cid:12) stars. The systemic velocity (white dotted line) is 5.2 km/s (Yen et al. 2018). In this section, we determine the radial structure of the dust disk around Sz 84 by conducting both visibility and SEDfitting. Because the high disk inclination of 75 ◦ (Ansdell et al. 2016) makes characterizing a cavity with a radius of afew tens of au in an image challenging, modeling is necessary. As mentioned in the introduction ( § Visibility fitting
The visibilities of Sz 84 show a null point at ∼
450 k λ (Figure 3b), which suggests cavity (or gap) structures inthe protoplanetary disk (c.f., Zhang et al. 2016). To confirm the cavity structures, we performed visibility fitting, inwhich observed visibilities are reproduced with a parametric model of the disk by utilizing all the spatial frequencyinformation. We describe the surface brightness distributions of the disk in our model with a simple power-law radial profile: I ( r ) ∝ C · ( r/r ) − C , (1)where C , C , and r are a scaling factor, the exponent of the power law, and the normalization factor at r cav2 ,respectively. As shown below, this simple profile is sufficient for reproducing the observations. In the radial direction,we adopt the following scaling factors and exponents: C = r < r cav1 δ for r cav1 < r < r cav2 r cav2 < r <
300 au , We originally attempted to derive the disk structure from the band 3, 6, and 7 data simultaneously to map the spatial distribution ofthe spectral index α . However, we mainly show the results from band 6 in this paper due to the insufficient baseline lengths and lowersensitivities of the band 3 and 7 data (Figures 9 and 10). Data from all three bands were used only to derive the average value of α for theentire disk in § Hashimoto et al.
Table 2.
Results of MCMC fitting for band 6 data and corresponding parameter ranges
Flux r cav1 r cav2 γ γ δ i P.A. Reduced χ (mJy) (au) (au) ( ◦ ) ( ◦ )(1) (2) (3) (4) (5) (6) (7) (8) (9)13.43 +0 . − . +4 . − . +2 . − . − . +0 . − . +0 . − . +0 . − . +1 . − . +3 . − . { } { } { } { } { -10 .. 10 } { } {
50 .. 80 } {
150 .. 180 } Note — Values in parentheses are parameter ranges in our MCMC calculations. C = NA for r < r cav1 γ for r cav1 < r < r cav2 γ for r cav2 < r <
300 au . The best-fit surface brightness profile with explanations is shown in Figure 3(a). Because the SED of Sz 84 showsnegligible NIR excess, we set no emissions at r < r cav1 ; that is, C = 0. The total flux density ( F total ) was set as afree parameter. The disk inclination ( i ) and PA were also set as free parameters. The phase center was fixed. In total,there are 8 free parameters in our model ( F total , r cav , r gap , δ , γ , γ , i , PA) .The modeled disk image was converted into complex visibilities with the public Python code vis_sample (Loomiset al. 2017), in which modeled visibilities are sampled with the same ( u , v ) grid points as those in our observations. Themodeled visibilities were deprojected with the system PA and i as free parameters, and were calculated as azimuthalmean values ( V mean ) and standard deviations ( σ ) within 20 k λ bins in the real part. The fitting was performed with theMarkov chain Monte Carlo (MCMC) method in the emcee package (Foreman-Mackey et al. 2013). The log-likelihoodfunction ln L in the MCMC fitting was ln L = − . { (Re V obsmean ,j − Re V modelmean ,j ) /σ j } , where Re V obsmean ,j , Re V modelmean ,j , and σ j are the observed and modeled visibilities and standard deviations in the real part, respectively. The subscript j represents the j -th bin. Our calculations used flat priors with the parameter ranges summarized in Table 1. Theburn-in phase (from initial conditions to reasonable sampling) employed 2000 steps, and we ran another 2000 steps forconvergence, for a total of 4000 steps with 200 walkers. These fitting procedures were also applied to the band 3 and7 data with the same parameter ranges except for that of the total flux density. However, we found multiple peaksand a nearly flat posterior probability distribution, especially for the disk inclination and flux density in band 3 and7 data, respectively, possibly due to shorter baseline lengths and lower sensitivities (Table 5 and Figures 9 and 10 inthe Appendix). Therefore, we decided to use only the flux density from band 3 data (i.e., band 7 data were not used).The fitting results with errors computed from the 16th and 84th percentiles are shown in Table 2, the radial profileof best-fit surface brightness is shown in Figure 3(a), the best-fit visibilities with a reduced- χ of 1.24 are shownin Figure 3(b), the best-fit modeled image is shown in Figure 7, and the probability distributions for the MCMCposteriors are shown in Figure 8. We found that the cavity at r =26 au (i.e., r cav2 ) is shallow with δ (cid:38) r cav1 ) due to insufficient baselinesin our observations, which have an upper limit of r cav1 ∼
10 au (Figure 8). A better constraint on this size can beobtained by the SED fitting (see § §
3, we mentioned the similarity of the radial profiles at r (cid:46)
50 au in the dust continuum and CO moment 0images. As shown here, the dust continuum emission decreases at r <
26 au. Hence, the brightness of CO might Because the best-fit profile can be rather complex, we attempted to fit the best-fit profile with an asymmetric Gaussian profile (e.g., Pinillaet al. 2018) by eye in Figure 3(a). We found that the asymmetric Gaussian profile extends inside the inner cavity at r cav1 , which resultsin significant IR excess, as shown in model C in § The value of δ was set to zero in the initial fitting. However, we immediately found that the model with δ =0 produces visibilities withan excessively deep gap at the uv -distance of ∼ λ in Figure 3(b) and cannot well reproduce the observed visibilities. Therefore, wedecided to set δ as a free parameter. Visibilities were deprojected in the uv -plane using the following equations (e.g., Zhang et al. 2016): u (cid:48) = ( u cos PA − v sin PA) × cos i, v (cid:48) =( u sin PA − v cos PA) , where i and PA are free parameters in our visibility analyses in § nner Cavity of Sz 84 ◦ ). N o r m a li ze d s u rf ace b r i gh t n e ss Radius (au) δ r cav2 r cav1 (c)(b)(a) V i s i b ilit y R ea l ( m J y ) -4-2 0 2 4 0 200 400 600 800 1000 1200 R e s i du a l ( m J y ) uv distance (k λ ) −4σ4σ0 Figure 3. (a) Surface brightness profile for the best-fit model with notes regarding our visibility fitting (red line). Black dottedline represents an asymmetric Gaussian profile fit by eye to the best-fit profile. (b) Top panel shows real part of the visibilitiesfor the observations (red dots) and the best-fit model (black line); bottom panel shows residual visibilities between observationsand the best-fit model. (c) Residual image (2 (cid:48)(cid:48) × (cid:48)(cid:48) ). Black dotted contours represent the dust continuum at SNRs of 20, 40,and 60. SED fitting
In the previous section, our model showed that the innermost cavity ( r cav1 ) is located at r (cid:46)
10 au. Because Sz 84’sSED has negligible IR excess at λ (cid:46) µ m (Figure 4e), we need to confirm that our model does not produce significantIR excess. Furthermore, we found a shallow cavity at r =26 au in the disk of large dust grains in the previous section.This size is roughly consistent with the r = 20 au estimated by van der Marel et al. (2018), who suggested that the20 au cavity can reproduce the SED of Sz 84. However, this size is smaller than the cavity size derived from the SEDanalysis by Mer´ın et al. (2010), namely 55 au in radius. Therefore, we revisited the SED analyses to constrain theradial distributions of both large and small dust grains by running radiative transfer modeling using a Monte Carloradiative transfer (MCRT) code ( HOCHUNK3D ; Whitney et al. 2013).The MCRT code follows a two-layer disk model with small (up to micron size) dust grains in the upper diskatmosphere and large (up to millimeter size) dust grains in the disk midplane (e.g., D’Alessio et al. 2006). Themodeled disk structure and dust properties in the MCRT code are described in our previous studies (Hashimoto et al.2015). Briefly, small dust grains are from the standard interstellar-medium dust model (a composite of silicates andgraphites with a size distribution of n ( s ) ∝ s − . from s min = 0 . µ m to s max = 0 . µ m) in Kim et al. (1994) andlarge dust grains (a composite of carbons and silicates with a size distribution of n ( s ) ∝ s − . from s min = 0 . µ m to s max = 1000 µ m) are from Model 2 in Wood et al. (2002). The radial surface density was assumed to have a simplepower-law radial profile similar to the equation in § r ) = C · Σ ( r/r ) − C ,C = r < r cav1 δ for r cav1 < r < r cav2 r cav2 < r <
300 au C = NA for r < r cav1 q for r cav1 < r < r cav2 q for r cav2 < r <
300 au . Hashimoto et al. where r is the normalization factor at r cav2 , Σ is the normalized surface density determined from the total (gas + dust)disk mass ( M disk ) assuming a gas-to-dust mass ratio of 100, C is the scaling factor for the surface density (whichis set to the same value as C in § C is the radial gradient parameter. The scalingfactor for small dust grains ( δ small ) was assumed to be zero at r < r smallrcav2 . The radial gradient parameters q and q (which are the same for disks of large and small dust grains) were fixed to reproduce the surface brightness derived in § r largercav2 =26 au was taken from the result in § r largercav1 and r smallrcav2 were freeparameters. We set M disk to reproduce a flux of 13.43 mJy at 1.3 mm. The scale heights ( h ) of large and small grainswere assumed to vary as h ∝ r p . For simplicity, we assumed p = 1.25 with a typical midplane temperature profile of T ∝ r − . . We fixed the scale heights of 1 au at r = 100 au for the disk of large dust grains ( h large r =100au ). Those ofsmall dust grains ( h small r =100au ) were varied to reproduce the flux at λ ∼ µ m. The mass fraction ( f ) of large dustgrains in the total dust mass was set to 0.9. The disk inclination was set to 75 ◦ , as derived in our visibility analyses( § HOCHUNK3D code calculates the accretion luminosity from the star based on the mass accretion rate. Halfof the flux was emitted as X-rays (which heat the disk) and half as stellar flux at a higher temperature. We set a massaccretion rate of ˙ M = 1.3 × − M (cid:12) /yr (Manara et al. 2014). In the code, we varied four parameters, namely r largercav1 , r smallrcav2 , h small r =100au , and M disk , as shown in Table 3, along with the χ calculated at λ =1–100 µ m.Figure 4 shows the surface densities and the SEDs for each model. Photometry and spectroscopy data used here aresummarized in Table 5. Our fitting procedure included the following four steps.1. We first tentatively set r largercav1 =10 au, q = − q =4.0 (which are derived in § r smallrcav2 =55 au(which is taken from Mer´ın et al. 2010) with varying values of h small r =100au and M disk , and found that the values of h small r =100au =5.0 au and M disk =2.5 M Jup well reproduce far-IR flux at λ ∼ µ m and millimeter flux at 1.3 mmin the SED (Figure 4e to g).2. We iteratively varied the radial gradient parameters q and q to reproduce the radial surface brightness of thedust continuum at band 6 derived in § q = − q =4.5 (fiducial model)well reproduce the surface brightness, as shown in Figures 11(a) and (b). The bumps at r ∼
10 and ∼
60 au in thesurface brightness of the MCRT modeling are attributed to those of the midplane temperature in Figure 11(c)due to irradiated cavity walls. We fixed these two values in the following procedures.3. To constrain the cavity size of small dust grains, r smallrcav2 was set to 40 (model A), 50 (model B), 60 (fiducialmodel), 70 (model C), and 80 au (model D), as shown in upper panels in Figure 4, with iterative adjustment of h small r =100au . The SED can be well reproduced by a cavity in the small dust with a size of 60 ±
10 au.4. Finally, we set r largercav1 at 1 (model E), 8 (fiducial model), and 26 au (model F), as shown in lower panels inFigure 4, to constrain the size of the inner cavity in the disk of large dust grains. The 8 au cavity, which isconsistent with the results of MCMC modeling in § r largercav1 (cid:46)
10 au), is suitable for the fiducial model.In summary, our modeling suggests that the small dust grains are located at r (cid:38)
60 au and the large dust grains aredistributed at 10 au (cid:46) r (cid:46)
60 au. There is a dust-free region at r (cid:46)
10 au.Because we used two independent disk models in the visibility fitting ( § § . (cid:48)(cid:48) ∼ µ Jy/beam (1.9 σ ). This residual is insignificant and thus the two models are mutually consistent.Our picture of the disk with small dust grains residing only at large radii is supported by gas observations. As shownin §
3, the radial profile of the CO moment 0 deviates from that of dust at r (cid:38)
50 au. Small dust grains are the mainsource of heating as they are present in the upper layer of the disk and are thus directly irradiated by the stellar lightand effectively absorb it. Therefore, the outer disk is heated more effectively than the inner disk, which contains onlya small amount of small dust grains. Because small dust grains do not emit effectively at (sub-)millimeter wavelengthsand the amount of large dust grains rapidly decreases at outer radii ( ∝ r − . ), these two facts do not greatly affectdust continuum emission. However, the CO gas emission mainly traces the temperature of the disk and therefore itsmoment 0 emission profile should be affected by the presence of small dust grains.4.3.
Upper limit on amount of small grains inside cavity nner Cavity of Sz 84 Table 3.
Parameters in our MCRT modeling
Model r largecav1 r smallcav1 r largecav2 r smallcav2 δ large δ small p q q h large r =100 au h small r =100 au M disk ˙ M i χ (au) (au) (au) (au) (au) (au) ( M Jup ) ( M (cid:12) yr − ) ( ◦ ) ( ◦ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)fiducial 8.0 — 26.0 60.0 0.59 0 1.25 − × −
75 151.0A 8.0 — 26.0 40.0 0.59 0 1.25 − × −
75 662.4B 8.0 — 26.0 50.0 0.59 0 1.25 − × −
75 200.0C 8.0 — 26.0 70.0 0.59 0 1.25 − × −
75 180.7D 8.0 — 26.0 80.0 0.59 0 1.25 − × −
75 299.6E 1.0 — 26.0 60.0 0.59 0 1.25 − × −
75 312.4F 26.0 — 26.0 60.0 0.59 0 1.25 − × −
75 478.2 − − − − Wavelength ( µ m) - - -12 - - λ F [ e r g s c m ] − − λ - - -12 - - -9 (c) Large dust grains (h)(g) SED (f)(e) SED(d) Small dust grains − − − − S u rf ace d e n s i s it y o f du s t g r a i n s [ g c m ] − (a) Large dust grains (b) Small dust grains fiducial τ =1 at 1.0 µ m τ =1 at 1.0 mm model E model F fiducialmodel E model F fiducial τ =1 at 1.0 µ m τ =1 at 1.0 mm Figure 4.
Results of MCRT modeling. Upper and lower panels show models in which the distributions of small and largedust grains are varied, respectively. (a to d): Surface density profiles of large (millimeter size) and small (sub-micron size) dustgrains. The surface density profiles of large dust grains in the models shown in the upper panels are same, while the surfacedensity profiles of small dust grains in the models shown in the lower panels are same. Horizontal dotted black lines representthe values of τ = 1 in the vertical direction at λ =1.0 mm and 1 µ m in panels (a and c) and (b and d), respectively. (e to h):SEDs for our modeling. The models are described in Table 3. Following Beichman et al. (2005), we converted the upper limit on the measured IR ( λ (cid:46) µ m) flux at a certainwavelength λ into an upper limit on the amount of small dust grains inside the 60 au cavity, M smallcav . At NIRwavelengths, the emission from large dust grains at r >
26 au is negligible, as shown in our SED fitting ( § M smallcav is expected to be very small because the NIR flux is consistent with stellar photospherical emission. Weassumed that the excess emission at NIR wavelengths is optically thin (i.e., a transitional disk with a cavity, Espaillatet al. 2010). The surface density of small dust grains inside the cavity, Σ smallcav , was assumed to vary with the radius asΣ smallcav ( r ) = Σ smallcav ( r )( r/r ) α for r min < r < r max Hashimoto et al. where r =1 au and Σ smallcav ( r ) is the surface density at 1 au. The total dust mass is thus M smallcav = (cid:90) r max r min Σ smallcav ( r )2 πrdr. We calculated the equilibrium temperature of optically thin dust at each radius inside the cavity, T ( r ), using the HOCHUNK3D code. The total NIR flux from the cavity dust at a given wavelength is I ( λ ) = (cid:90) r max r min B ( T ( r ) , λ ) κ small ( λ )Σ smallcav ( r )2 πrdr, where B ( T ( r ) , λ ) is the Planck function at T ( r ) and λ , and κ small ( λ ) is the absorption opacity of small dust grains.Note that because our purpose is to derive the total mass of small dust grains from the upper limit of the observedflux, disk inclination is not needed to take into account in the calculation.At λ =10 µ m, the upper limit on the IR excess of the system λF ( λ ) is 2 . × − ergs s − cm − . Assuming that r min is the dust sublimation radius at 0.03 at, r max is 60 au, and α = − ∝ radius, Lynden-Bell & Pringle 1974), the upper limit on M smallcav is 4 × − M ⊕ (Σ small r =26au = 1 . × − g cm − ,equivalent to δ small = 4 × − ). We note that the value of M smallcav is only weakly affected by the chosen wavelength.For example, using λ =3.35 µ m, the associated upper limit on the disk flux λF ( λ ) < . × − ergs s − cm − yields M smallcav = 1 × − M ⊕ . Decreasing r max reduces M smallcav (e.g., setting r max =5 au results in M smallcav = 4 × − M ⊕ )and increasing r min has the opposite effect (e.g., setting r min =1 au results in M smallcav = 8 × − M ⊕ ). Flatteningor reversing the dependence of Σ smallcav ( r ) on radius yields a higher value of M smallcav (e.g., setting α = 1 results in M smallcav = 1 × − M ⊕ ).We conclude that the amount of small dust inside the millimeter emission cavity is tiny, less than a lunar mass underreasonable assumptions. The mass of large dust grains at r <
60 au is ∼ M ⊕ , and thus the ratio of the mass of smalldust grains to that of large dust grains is smaller than ∼ − . DISCUSSION5.1.
Comparison with other systems
The sizes of the cavities of large and small dust grains have been discussed by combining NIR direct imaging andradio interferometry (e.g., Dong et al. 2012; Villenave et al. 2019). Additionally, assuming that small dust grains arewell coupled to the gas, measured CO gas distributions might serve as a proxy of the spatial distribution of small dustgrains. CO gas observations with sufficient spatial resolution and sensitivity have been conducted with ALMA (e.g.,van der Marel et al. 2015, 2016, 2018). The general trend of the cavity sizes in the disk of large dust grains vs. smallones (or CO gas) indicates that the cavity size in the disk of large dust grains is largest. The ratios of r smallcav to r largecav and those of r COcav to r largecav from the literature are compiled in Figure 5. These results can be interpreted as outcomesof planet–disk interactions (e.g., Zhu et al. 2012; de Juan Ovelar et al. 2013; Facchini et al. 2018), as described in § §
4. As far as we know, such structures can only be found in DM Tau ( r smallcav ∼ r largecav ∼ r smallcav vs. r largecav or r COcav vs. r largecav ) for 24 objects and found that all the disks have larger cavities of large dust grains (Figure 5). Thereare currently two objects (Sz 84 and DM Tau) that have a larger cavity in the disk of small dust grains, accounting for7.7 % of objects observed with NIR direct imaging and ALMA. However, current NIR observations are biased towardbrighter objects ( R band (cid:46)
12 mag) due to the limitations of the adaptive optics system. Future observations withextreme adaptive optics systems such as VLT/SPHERE and Subaru/SCExAO would increase the number of samples(especially faint objects) and thus further constrain the statistics.5.2.
Origin of cavities
Although systems with large dust grains inside the cavity in the disk of small dust grains may be rare, Sz 84 datahave important implications for understanding planet formation. Here, we discuss the possible origins of such cavitystructures. Some formation mechanisms of the cavity have been proposed, including photoevaporation (e.g., Clarkeet al. 2001; Alexander et al. 2014), planet–disk interactions (e.g., Kley & Nelson 2012), grain growth (e.g., Dullemond nner Cavity of Sz 84 R a ti o o f r t o r ca v l a r g e ca v s m a ll S z D M T a u V S g r UX t a u T C h a S z S z S R S AO R Y L up R X J . - P D S O ph I R S M W C L k C a J - J HD HD HD HD HD HD HD D o A r C Q T a u Villenave et al. van der Marel et al. Hashimoto et al.
Figure 5.
Cavity ratio of r smallcav (small dust grains) to r largecav (large dust grains). Black dots denote the cavity ratios calculatedusing the NIR and (sub-)millimeter dust continuum observations taken from (Villenave et al. 2019), and gray dots are thosecalculated using the CO gas and dust continuum observations taken from (van der Marel et al. 2016, 2018). We assumed thatthe cavity sizes of the gas and small dust grains are identical. In the samples from van der Marel et al. (2018), we use threeobjects with constrained cavity sizes of CO gas. Red dots represent our two objects (Sz 84 from this work and DM Tau fromHashimoto et al. submitted) with r smallcav > r largecav mentioned in § & Dominik 2005), radiation pressure (e.g., Krumholz et al. 2019), and a combination of these mechanisms (e.g., planet+ grain growth; Zhu et al. 2012). Photoevaporation —
The basic idea of photoevaporation is that high-energy radiation (UV/X-ray) from the centralstar heats the surface of the disk, and the hot gas ( ∼ –10 K) escapes from the disk as a photoevaporative wind.Because small dust grains are well coupled to the gas, they flow with the gas, possibly resulting in similar sizes of thecavities in the disks of small dust grains and gas. However, CO emissions can be clearly seen at r <
60 au (Figure 1).Furthermore Sz 84 has a moderate mass accretion rate (Manara et al. 2014). Thus, photoevaporation does not seemto be a viable mechanism for creating the cavity in the disk around Sz 84 (e.g., Ercolano & Pascucci 2017).2
Hashimoto et al.
Planet–disk interactions —
This mechanism is commonly considered as a potential origin of transitional disks (e.g.,Espaillat et al. 2014). However, the robust detection of young planets that possibly induce cavity/gap structures iscurrently very limited (e.g., PDS 70b & c; Keppler et al. 2018; Haffert et al. 2019), and no planets have been detectedaround Sz 84. Additionally, as mentioned above ( § (cid:38) Grain growth —
To account for a transitional disk system with negligible NIR excess in the SED and a moderatemass accretion, only small dust grains in the vicinity of the central star need to be removed. For this purpose, Zhuet al. (2012) introduced grain growth in addition to planet–disk interactions. Dust grains grow faster in the innerregion of the disk because of a faster dynamical time scale (e.g., Brauer et al. 2008), and thus small dust grains aredispersed from the inside out. However, large dust grains are expected to fragment into small dust grains dependingon disk turbulence (e.g., Weidenschilling 1984) and/or their stickiness (e.g., Wada et al. 2009), and thus weak dustfragmentation is required to efficiently remove small dust grains. Numerical simulations of grain growth with no/lowfragmentation show a deficit of flux at NIR to MIR wavelengths in the SED (e.g., Dullemond & Dominik 2005; Birnstielet al. 2012). Moreover, as grain growth does not affect gas distribution, the mass accretion would be unchanged. Hence,grain growth with less efficient fragmentation would explain both the spatial distributions of dust grains at r (cid:38)
10 auand the moderate mass accretion rate of Sz 84. We note that our modeling in § r (cid:46)
10 au is optically thin at λ (cid:46) µ m for both small and large dust grains, which could be interpreted as meaningthat dust grains are large enough to radially drift to the central star (e.g., Brauer et al. 2008) or have already growninto planetesimals (e.g., Okuzumi et al. 2012; Kataoka et al. 2013).As mentioned in § (cid:46) r ∼
100 au within 1 Myr (see model F2 inFigure 6). This picture is roughly consistent with Sz 84 ( r smallcav =60 au in § § ∼ r =1 au via grain growth is predicted to be ∼ Radiation pressure —
Another possible mechanism for the selective removal of small dust grains is radiation pressure(e.g., Krumholz et al. 2019; Owen & Kollmeier 2019). Stellar radiation radially and rapidly pushes away small dustgrains, whereas large dust grains persist for a longer time, when the radiation pressure force on dust grains is strongerthan the drag force of the gas. To suppress this drag force, Krumholz et al. (2019) reduced the gas density to lessthan 1 % of the minimum mass solar nebula (e.g., Weidenschilling 1977; Hayashi 1981). Additionally, because thedust disk needs optically thin conditions to avoid shielding stellar radiation, a dust-to-mass ratio of less than 10 − ispreferable. Consequently, radiation pressure could efficiently remove small dust grains on gas-poor systems, i.e., debrisdisks. Conversely, the protoplanetary disk of Sz 84 is likely to be a gas-rich system, as detected in CO (Figure 1), andtherefore, radiation pressure can be safely ruled out as the dominant mechanism for cavity formation around Sz 84. nner Cavity of Sz 84 CONCLUSIONWe observed the transitional disk around the T Tauri star Sz 84 at band 6 ( λ ∼ . (cid:48)(cid:48) CO J = 2 → λ (cid:46) µ m, indicating a cavity structure with a size of ∼
100 auin diameter, the dust continuum image does not show any cavity structures. In contrast, the observed visibilities ofthe dust continuum clearly show a null point at the uv -distance of ∼
450 k λ , suggesting a cavity structure in dustcontinuum. These observational results motivated us to conduct analyses of the visibilities and the SED to explorethe structures of the dust disk. Our main findings are as follows.1. The spectral index ( α ) at bands 3, 6, and 7 (0.9 to 3 mm) is 2.42 ± α ∼ r (cid:38)
60 au, and that large dust grains are present inside the cavity in the disk of small dust grains at r ∼
60 audown to ∼
10 au. Gas is also present at r <
60 au in the CO moment 0 map.3. A transitional disk in which the size of the cavity in the disk of small dust grains is larger than that in the diskof large dust grains may be rare (to our knowledge, only Sz 84 and DM Tau), accounting for 7.7 % of objectsobserved with NIR direct imaging and ALMA (Villenave et al. 2019; van der Marel et al. 2016, 2018). Note thatwe assumed that the cavity sizes in disks of gas and small dust grains are identical in the modeling of CO gastaken from van der Marel et al. (2016, 2018).4. To account for the observational results for Sz 84 (spatial distributions of dust grains and gas in the disk, SEDwith negligible IR excess, and moderate mass accretion), grain growth and less efficient fragmentation (i.e., notphotoevaporation, planet–disk interactions, or radiation pressure) are the likely mechanisms for cavity formationaround Sz 84. Grain growth is thought to be an important first step in planet formation, and dust fragmentationprevents dust grains from growing into larger bodies. Therefore, Sz 84 is a good testbed for investigating graingrowth with inefficient fragmentation of dust grains.ACKNOWLEDGMENTSWe thanks an anonymous referee for a helpful review of the manuscript. This paper makes use of the following ALMAdata: ADS/JAO.ALMA
Software : vis_sample (Loomis et al. 2017), HOCHUNK3D (Whitney et al. 2013),
CASA (McMullin et al. 2007), emcee (Foreman-Mackey et al. 2013) APPENDIX4
Hashimoto et al.
Table 4.
ALMA observations of archive data
Band 3 Band 7Observing date (UT) 2016.Oct.06 2015.Jun.14Project code 2016.1.00571.S 2013.1.00220.STime on source (min) 6.0 2.2Number of antennas 42 41Baseline lengths 18.6 m to 3.1 km 21.4 m to 0.78 kmBaseband Freqs. (GHz) 90.6, 92.5, 102.6, 104.5 328.3, 329.3, 330.6, 340.0, 341.8Channel width (MHz) 0.98, 0.98, 0.98, 0.98 15.6, 0.122, 0.122, 0.244, 0.977Continuum band width (GHz) 7.5 4.8Bandpass calibrator J1517 − − − − − Note — Because bands 3 and 6 data are mainly used for visibility analyses in § Table 5.
Results of MCMC fitting for band 3 and 7 data and their parameter ranges
Band Flux r cav1 r cav2 γ γ δ i P.A.(mJy) (au) (au) ( ◦ ) ( ◦ )(1) (2) (3) (4) (5) (6) (7) (8) (9)Band 3 1.70 +0 . − . +4 . − . +7 . − . +3 . − . +2 . − . +0 . − . +8 . − . +22 . − . { } { } { } { } { -10 .. 10 } { } {
50 .. 80 } {
150 .. 180 } Band 7 30.88 +5 . − . +2 . − . +16 . − . +2 . − . +0 . − . +0 . − . +9 . − . +8 . − . { } { } { } { } { -10 .. 10 } { } {
50 .. 80 } {
150 .. 180 } Note — Values in parentheses are parameter ranges in our MCMC calculations.
Here, we provide additional supporting tables and figures. ALMA observations of archive data from bands 3 and 7used in this paper are summarized in Table 4.Figure 6 shows the CO J = 2 − − § § § r <
150 au based on MCMC model fitting and MCRTmodeling in § § Alcal´a, J. M., Natta, A., Manara, C. F., et al. 2014, A&A,561, A2, doi: 10.1051/0004-6361/201322254Alcal´a, J. M., Manara, C. F., Natta, A., et al. 2017, A&A,600, A20, doi: 10.1051/0004-6361/201629929 Alexander, R., Pascucci, I., Andrews, S., Armitage, P., &Cieza, L. 2014, in Protostars and Planets VI, ed.H. Beuther, R. S. Klessen, C. P. Dullemond, &T. Henning, 475,doi: 10.2458/azu uapress 9780816531240-ch021 nner Cavity of Sz 84 Table 5.
Photometric and spectroscopic values of Sz 84
Wavelength λF λ Reference( µ m) (10 − erg s − cm − )0.44 132.0 USNO-B1.0 (Monet et al. 2003)0.64 400.8 USNO-B1.0 (Monet et al. 2003)0.80 1388.1 USNO-B1.0 (Monet et al. 2003)1.235 2042.6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Note — The value of A V =0.5 mag (Manara et al. 2014) is applied here. Hashimoto et al.
Linear scaled flux density (mJy/beam)
0 45.0 + + + + + + + + +10 .0 km/s + − + ″ (152.6 au) NE Figure 6.
Channel maps of CO J = 2 −
1. The r.m.s noise at the 1.0 km/s bin is 2.37 mJy/beam with a beam size of235 ×
161 mas at a PA of − ◦ . nner Cavity of Sz 84 ″ (76.3 au) F a i n t B r i gh t Figure 7.
Best-fit model image at band 6 with row resolution. White circle represents the beam shape of 198 ×
195 mas at aPA of − ◦ in our ALMA observations.Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner,D. J. 2013, ApJ, 771, 129,doi: 10.1088/0004-637X/771/2/129Ansdell, M., Williams, J. P., van der Marel, N., et al. 2016,ApJ, 828, 46, doi: 10.3847/0004-637X/828/1/46Ansdell, M., Williams, J. P., Trapman, L., et al. 2018, ApJ,859, 21, doi: 10.3847/1538-4357/aab890Beichman, C. A., Bryden, G., Gautier, T. N., et al. 2005,ApJ, 626, 1061, doi: 10.1086/430059Birnstiel, T., Andrews, S. M., & Ercolano, B. 2012, A&A,544, A79, doi: 10.1051/0004-6361/201219262 Brauer, F., Dullemond, C. P., & Henning, T. 2008, A&A,480, 859, doi: 10.1051/0004-6361:20077759Clarke, C. J., Gendrin, A., & Sotomayor, M. 2001,MNRAS, 328, 485, doi: 10.1046/j.1365-8711.2001.04891.xCutri, R. M., & et al. 2014, VizieR Online Data Catalog,II/328Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003,VizieR Online Data Catalog, II/246D’Alessio, P., Calvet, N., Hartmann, L., Franco-Hern´andez,R., & Serv´ın, H. 2006, ApJ, 638, 314, doi: 10.1086/498861de Juan Ovelar, M., Min, M., Dominik, C., et al. 2013,A&A, 560, A111, doi: 10.1051/0004-6361/201322218 Hashimoto et al.
Band 6 γ − −0.46+0.85 γ −0.13+0.16 r cav1 = 6.45 −4.29+4.12 r cav2 = 25.90 −1.85+2.01 δ = 0.59 −0.25+0.26 PA = 165.71 −2.58+3.22 i = 75.13 −0.46+1.74 F = 13.43 −0.13+0.13
12 14 16 1860 66 72 78156 168 180.2 .4 .6 .818 24 30 363 6 9 122 4 6 8-8 -4 0 4 8 δ P A PA r cav2 r cav1 F i γ γ F i δ r ca v2 r ca v1 γ Figure 8.
Corner plot of the MCMC posteriors calculated in the visibility fitting for band 6 data in § σ confidence intervals of parameters computed from the16th and 84th percentiles. The off-diagonal plots show the correlation for corresponding pairs of parameters.Dong, R., Rafikov, R., Zhu, Z., et al. 2012, ApJ, 750, 161,doi: 10.1088/0004-637X/750/2/161Draine, B. T. 2006, ApJ, 636, 1114, doi: 10.1086/498130Dullemond, C. P., & Dominik, C. 2005, A&A, 434, 971,doi: 10.1051/0004-6361:20042080 Ercolano, B., & Pascucci, I. 2017, Royal Society OpenScience, 4, 170114, doi: 10.1098/rsos.170114Espaillat, C., D’Alessio, P., Hern´andez, J., et al. 2010, ApJ,717, 441, doi: 10.1088/0004-637X/717/1/441 nner Cavity of Sz 84 Band 3 -2-1.5-1-0.5 0 0.5 1 1.5 2 0 200 400 600 800 1000 V i s i b ilit y R ea l ( m J y ) uv distance (k λ ) γ −5.38+3.89 γ −2.12+2.11 r cav1 = 8.70 −5.83+4.67 r cav2 = 23.71 −4.15+7.74 δ = 0.54 −0.36+0.32 PA = 152.43 −1.88+22.92 i = 64.73 −10.94+8.15 F = 1.70 −0.05+0.06 δ PA r cav2 r cav1 F i γ γ P A F i δ r ca v2 r ca v1 γ Figure 9.
Same as Figure 8 but for band 3 data. The top-right panel is the real part of visibilities in observations (red dots)and the best-fit model (black line).Espaillat, C., Muzerolle, J., Najita, J., et al. 2014,Protostars and Planets VI, 497,doi: 10.2458/azu uapress 9780816531240-ch022Facchini, S., Pinilla, P., van Dishoeck, E. F., & de JuanOvelar, M. 2018, A&A, 612, A104,doi: 10.1051/0004-6361/201731390 Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman,J. 2013, PASP, 125, 306, doi: 10.1086/670067Francis, L., & van der Marel, N. 2020, arXiv e-prints,arXiv:2003.00079. https://arxiv.org/abs/2003.00079Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al.2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051 Hashimoto et al. γ −5.35+2.46 γ −0.30+0.42 r cav1 = 12.65 −6.94+2.12 r cav2 = 20.39 −4.12+16.73 δ = 0.69 −0.35+0.23 PA = 165.30 −3.16+8.26 i = 68.29 −2.37+9.18 F = 30.88 −7.24+5.44
24 32 4060 66 72 78156 168 180.2 .4 .6 .818 24 30 363 6 9 122 4 6 8-8 -4 0 4 8 δ PA r cav2 r cav1 F i γ γ P A F i δ r ca v2 r ca v1 γ -10 0 10 20 30 40 0 200 400 600 800 1000 V i s i b ilit y R ea l ( m J y ) uv distance (k λ ) Band 7
Figure 10.
Same as Figure 8 but for band 7 data. The top-right panel is the real part of visibilities in observations (red dots)and the best-fit model (black line).Garufi, A., Quanz, S. P., Avenhaus, H., et al. 2013, A&A,560, A105, doi: 10.1051/0004-6361/201322429Haffert, S. Y., Bohn, A. J., de Boer, J., et al. 2019, NatureAstronomy, 329, doi: 10.1038/s41550-019-0780-5Hashimoto, J., Tsukagoshi, T., Brown, J. M., et al. 2015,ApJ, 799, 43, doi: 10.1088/0004-637X/799/1/43 Hayashi, C. 1981, Progress of Theoretical PhysicsSupplement, 70, 35, doi: 10.1143/PTPS.70.35Hendler, N., Pascucci, I., Pinilla, P., et al. 2020, ApJ, 895,126, doi: 10.3847/1538-4357/ab70ba nner Cavity of Sz 84
100 10 100 10 100 10 S u rf ace b r i gh t n e ss ( m J y / b ea m ) Radius (au)
MCRT modeling MCMC model fitting MCRT modeling MCMC model fitting (b) Convolution (a) Raw resolution
10 100 M i dp l a n e t e m p e r a t u r e ( K ) Large dust grainSmall dust grain (c)
Figure 11.
Radial profiles of modeled dust continuum images at (a) raw resolution and (b) convolution with the ALMA beamshape of 0 . (cid:48)(cid:48) § r ∼