ALMA Observations of the Asymmetric Dust Disk around DM Tau
Jun Hashimoto, Takayuki Muto, Ruobing Dong, Hauyu Baobab Liu, Nienke van der Marel, Logan Francis, Yasuhiro Hasegawa, Takashi Tsukagoshi
DDraft version February 12, 2021
Typeset using L A TEX default style in AASTeX63
ALMA Observations of the Asymmetric Dust Disk around DM Tau
Jun Hashimoto ,
1, 2, 3
Takayuki Muto, Ruobing Dong , Hauyu Baobab Liu , Nienke van der Marel , Logan Francis , Yasuhiro Hasegawa, and Takashi Tsukagoshi 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 Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU No.1, Sec. 4, RooseveltRd, Taipei 10617, Taiwan, ROC Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA Division of Science, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
ABSTRACTWe report an analysis of the dust disk around DM Tau, newly observed with the Atacama LargeMillimeter/submillimeter Array (ALMA) at 1.3 mm. The ALMA observations with high sensitivity(8.4 µ Jy/beam) and high angular resolution (35 mas, 5.1 au) detect two asymmetries on the ring at r ∼
20 au. They could be two vortices in early evolution, the destruction of a large scale vortex, ordouble continuum emission peaks with different dust sizes. We also found millimeter emissions with ∼ µ Jy (a lower limit dust mass of 0.3 M Moon ) inside the 3-au ring. To characterize these emissions,we modeled the spectral energy distribution (SED) of DM Tau using a Monte Carlo radiative transfercode. We found that an additional ring at r = 1 au could explain both the DM Tau SED and thecentral point source. The disk midplane temperature at the 1-au ring calculated in our modeling isless than the typical water sublimation temperature of 150 K, prompting the possibility of formingsmall icy planets there. Keywords: protoplanetary disks — planet–disk interactions — planets and satellites: formation —stars: individual (DM Tau) INTRODUCTIONPlanets are believed to form in protoplanetary disks (e.g., Hayashi et al. 1985; Pollack et al. 1996). The earlystages of planet formation can be identified by disk structures such as gaps and asymmetric structures via planet–diskinteractions (e.g., Kley & Nelson 2012). Such structures have been reported in tens of dust disks with Atacama Large(sub-)Millimeter Array (ALMA; e.g., van der Marel et al. 2018; Andrews et al. 2018; Long et al. 2018), and roughly10 disks show asymmetries (e.g., Francis & van der Marel 2020; van der Marel et al. 2020; Tsukagoshi et al. 2019;P´erez et al. 2018; Dong et al. 2018b). Particularly, asymmetric structures such as the blob and the crescent featurespossibly due to azimuthal gas pressure maxima (e.g., Raettig et al. 2015; Ragusa et al. 2017) could be on-going planetforming sites because gas pressure maxima efficiently trap dust grains, potentially leading to planetesimal formation.Two major possible origins of these asymmetries are discussed by van der Marel et al. (2020): long-lived anticyclonicvortices at gap edges possibly curved by companions (e.g., Raettig et al. 2015) and gas horseshoes due to eccentriccavities curved by massive companions (e.g., Ragusa et al. 2017). The main difference between the two is in the mass ofcompanions: a vortex can be produced at edges of gaps possibly opened by planets, whereas a horseshoe structure needsto be triggered by a much more massive companion, i.e., a brown dwarf. Therefore, in the vortex scenario, asymmetriescould be signpost of planets, while they are not in the horseshoe scenario. Though the origins of individual asymmetric
Corresponding author: Jun [email protected] a r X i v : . [ a s t r o - ph . E P ] F e b Hashimoto et al. disks have not been determined by current observations (van der Marel et al. 2020), investigating asymmetric diskscould help understanding of planet formation.DM Tau (spectral type: M1, Kenyon & Hartmann 1995; T eff : 3705 K, Andrews et al. 2011; M ∗ : 0.53 M (cid:12) , Pi´etuet al. 2007; distance: 145 pc, Gaia Collaboration et al. 2018) is a single star system (Nguyen et al. 2012; Willsonet al. 2016), and its protoplanetary disk has a weak asymmetry in the outer disk at r ∼
20 au (Kudo et al. 2018).The spectral energy distribution (SED) of DM Tau shows a deficit at λ ∼ µ m, which was interpreted as thepresence of a deep cavity at r ∼ . (cid:48)(cid:48) r =3 and 20 au and low contrast rings at r (cid:38)
60 au. The CO (2–1) gas disk around DM Tau has nocavity/ring structures (Kudo et al. 2018), possibly due to a high optical depth of CO, while other molecular speciessuch as C H show a ring structure at r ∼
80 au (Bergin et al. 2016). A candidate giant planet was reported at r ∼ M ∼ × − M (cid:12) /yr (Manara et al. 2014), is comparable with thatof typical T Tauri stars (Najita et al. 2015). As small (sub-micron size) dust grains coupled with the gas flow into thecentral star, significant infrared excess at λ ∼ µ m should appear in the SED. Hence the origin of DM Tau’s 3-aucavity with both high mass accretion rate and strongly depleted dust grains in the cavity is still under debate (e.g.,Manara et al. 2014; Kudo et al. 2018).In this paper, we report follow-up observations of DM Tau with ALMA in cycle 6. Our original aim for these newobservations was to confirm a weak asymmetry with a contrast of 20 % in the inner ring at r ∼ r ∼
20 au. We also performed SED fitting to test theexistence of dust grains inside the 3-au cavity around DM Tau. OBSERVATIONSThe ALMA observations of DM Tau summarized in Table 1 were carried out with Band 6 in the C43-9/10 con-figuration on 2019 June 5, UT under the project 2018.1.01755.S, using 44 antennas with a baseline length extendingfrom 83.1 m to 15.2 km. Since the short baseline data are available in the ALMA archive (ID: 2013.1.00498.S; PI:L. Perez), we did not request these observations. The long baseline data were taken with four spectral windows (SPWs):three with 128 channels spanning 1.875 GHz (31.25 MHz per channel) centered on 213.5, 216.3, and 228.0 GHz; andone with 3840 channels spanning 1.875 GHz (448.3 kHz per channel, 0.64 km/s velocity resolution) centered on the CO J = 2 → − λ between the two data sets and confirmed their consistency.The images of both data sets were aligned by two manners as follows . Method A —
We separately synthesized the dust continuum images of short and long baseline data by CASA withthe
CLEAN task using a multi-frequency deconvolution algorithm (Rau & Cornwell 2011). We then conducted ellipseisophoto fitting at 30 σ in the images of both data. The phase centers for both data sets were corrected to thecenters of ellipse isophoto fitting by fixvis in the CASA tools. To test whether the new phase center is the centerof the disk, we subtracted the 180 ◦ -rotated image in the visibility domain. This procedure corresponds to producing We originally attempted to align short and long baseline data by correcting the proper motion. The proper motions of both data werecalculated with the function EPOCH PROP in GAIA ADQL ( https://gea.esac.esa.int/archive/ ). The phase centers and pointing tables forboth data sets were corrected by fixvis and fixplanets, respectively, in the CASA tools. However, we found that the new phase centers ofshort and long baseline data are shifted to ∼
16 and ∼ symmetric Disk of DM Tau
3a synthesized image with only the imaginary part of the visibilities. Because the visibility is complex conjugate,the subtraction of the 180 ◦ -rotated image is mathematically equal to setting the real part as zero and doubling thevalue of the imaginary part, respectively. In other words, the real part contains information of both symmetric andasymmetric structures of objects, whereas the imaginary part contains only information of asymmetries. Therefore,by synthesizing the image with only the imaginary part, we selectively remove only symmetric structures, vice versa,only asymmetric structures can be efficiently detected . We searched the minimum r.m.s in the central region of theimages with shifting images relative to the center of ellipse isophoto fitting in the visibility domain by the phase shiftdefined as exp [2 πi ( u ∆R . A . + v ∆DEC)], where u and v are the spatial frequencies and ∆R.A. and ∆DEC are shiftvalues, respectively. Figures 7 and 8 in Appendix shows dust continuum images synthesized with only the imaginarypart, including the image with the minimum r.m.s. We found that the shift values with the minimum r.m.s are (∆RA,∆DEC) of (0 mas, 0 mas) and (+4 mas, − fixplanets in the CASA tools. The new phase centers of long and short baseline data inICRS coordinates are (4h33m48.74961s, 18d10m9.6177s) and (4h33m48.74792s, 18d10m9.6819s), respectively. Method B —
We also check the shift value with the minimum χ of the imaginary part. The value of χ is definedas (cid:80) (cid:0) W j Im V j (cid:1) , where the subscript j represents the j -th data. Im V j and W j are the visibilities in the imaginarypart and weights, respectively. We found that the shift values with the minimum χ are (∆RA, ∆DEC) of (+1 mas,+1 mas) and (+5 mas, − CLEAN task, we setthe uv -taper to obtain a nearly circular beam pattern (Table 1), and we do not use the ‘multi-scale’ option. The r.m.s.noise in the region far from the object is 8.4 µ Jy/beam with a beam size of 35.0 × ◦ .The CO J = 2 → uv plane with the uvcontsub task in the CASA tools. The combined line image cube with channel widths of0.7 km/s was produced by the CLEAN task. We also set the uv -taper to obtain the nearly circular beam pattern(Table 1). The integrated line flux map (moment 0) and the intensity-weighted velocity map (moment 1) are shownin Figure 2 while channel maps at − · km/s with a beam size of 45.6 × − ◦ while that in themoment 1 map at the 0.7 km/s bin is 589 mJy/beam. The peak SN ratio is 15.9 in the channel map of +2.5 km/s. RESULTSFigure 1 shows the dust continuum images of the DM Tau disk combining long and short baseline data at band 6.The entire disk is shown in Figure 1(a). As reported by Kudo et al. (2018), we confirmed three components in thedisk: the inner ring at r (cid:46)
10 au, the outer ring at r ∼
20 au, and the extended structure at r (cid:38)
60 au, as noted inFigure 1(d). We discovered that the extended structure consists of two faint rings at r ∼
90 and ∼
110 au with SNratios of ∼ ∼
5, respectively. This “w”-shaped double gap structure, found in a number of other disks, could beproduced by a super-Earth mass planet in a low viscosity environment (Dong et al. 2017, 2018a; P´erez et al. 2019;Facchini et al. 2020).The structure of the outer ring at an SN of ∼
70 is consistent with that in Kudo et al. (2018). In the image subtractingthe 180 ◦ -rotated image in Figure 7, we found two prominent asymmetries at PA of ∼ ◦ and ∼ ◦ (hereafter blobs Aand B) in the outer ring. These two blobs can be seen in the dust continuum image (Figure 1b) and the azimuthalprofile of the outer ring at r ∼
20 au in Figure 1(e), i.e., these two locate at the same radial location. We also synthesizedthe dust continuum images with different imaging parameters (e.g., using the multi-scale option) in the CLEAN task inAppendix B and Figure 9, and confirmed the presence of the two blobs at roughly the same location in the images withdifferent parameters. The contrasts of these two relative to the opposite side of the ring are ∼ × to ∼ × . Notethat blob A has already been reported by Kudo et al. (2018). The total flux density derived by visibility fitting in § ± This method would also serve as a diagnosis to test a misalignment between an observed disk and a modeled disk. When the modeled diskis misaligned to the observed disk, spurious asymmetries could easily generate even if both disks are symmetric. The original phase centers in long and short baseline data are (04h33m48.734901s, 18d10m09.63258s) in ICRS and (04h33m48.729253s,18d10m09.78982s) in FK5 J2000.0, respectively.
Hashimoto et al.
Table 1.
ALMA Band 6 Observations and Imaging ParametersLong Baseline Short BaselineObserving date (UT) 2019.Jun.05 2015.Aug.12Configuration C43-9/10 —Project code 2018.1.01755.S 2013.1.00498.STime on source (min) 134.3 14.2Number of antennas 44 44Baseline length 83.1 m to 15.2 km 15.1 m to 1.6 kmBaseband freq. (GHz) 213.5, 216.3, 228.0, 230.0 217.0, 218.8, 219.3, 219.7,220.2, 230.7, 231.2, 232.3Channel width (MHz) 15.63, 15.63, 15.63, 0.488 15.63, 7.813, 7.813, 0.488,0.488, 0.244, 3.906, 15.63Continuum band width (GHz) 7.5 6.56Bandpass calibrator J0423 − − − CO J = 2 → uv -taper Gaussian parameter 3.5 × λ at PA of 115 ◦ × λ at PA of 120 ◦ Beam shape 35.0 × ◦ × − ◦ r.m.s. noise ( µ Jy/beam) 8.4 2988 (moment 0)589 (moment 1 at 0.7 km/s bin) observations (109 ±
13 mJy, Beckwith et al. 1990) and previous ALMA observations (93.3 ± § ± τ ν is calculated with the relationship: I ν = B ν T mid { − exp( − τ ν ) } , (1)where I ν , B ν , and T mid are intensity, the Plunck function, and the midplane temperature, respectively. We use themidplane temperature profile with the simplified expression for a passively heated, flared disk in radiative equilibrium(e.g., Dullemond et al. 2001): T mid ( r ) = (cid:18) φL ∗ πr σ SB (cid:19) . , (2)with L ∗ the stellar luminosity (taken as 0.36 L (cid:12) from Manara et al. 2014), φ the flaring angle (taken as 0.02), and σ SB the Stefan-Boltzmann constant. At the outer ring at r =20 au, T mid is estimated to 21.6 K, and thus, the opticaldepth τ ν is calculated to 1.3 +0 . − . .Since measuring the flux density of the inner ring in the synthesized image is not straightforward, potentially dueto a contamination of the bright outer ring, we derive it in the best-fit modeled image in the visibility fitting ( § +0 . − . K and 1.74 ± M Jup assuming a distance of 145 pc, an opacity per unit dust mass κ ν =2.3 cm g − at 230 GHz (Beckwith & Sargent 1991), a temperature of 100 K, and a gas-to-dust mass ratio of100. Note that Francis & van der Marel (2020) suggested the gas-to-dust mass ratio of 10 – 10 for the inner ring ofDM Tau assuming viscosity α of 10 − , and thus, the inner ring may be two or three orders magnitude more massive. symmetric Disk of DM Tau blob Ablob B S u rf ace b r i gh t n e ss ( µ J y / b ea m ) Data3 σ noiseInner ring Outer ring Extended structure 10 100 1000 0 20 40 60 80 100 120Radius (au) 500 520 540 560 580 600 620 640 660 0 50 100 150 200 250 300 350Position angle (°)Blob ABlob BFlux density ( µ Jy/beam)
1 280 560
Flux density ( µ Jy/beam)
10 103.5 197 (e) Azimuthal profile at the outer disk(d) Averaged radial profile (c) 0.1 ″ (14.5 au)(b)(a) 0.2 ″ (29 au) NE1 ″ (145 au) NE Figure 1.
Synthesized images of the dust continuum of the DM Tau disk obtained with ALMA cycle 6 at band 6. (a): Entireimage. (b): Central magnified image of panel (a). (c): Central magnified image of panel (b). The regions of panel (b) and(c) are indicated by the white and black dotted square in panel (a) and (b), respectively. The r.m.s. noise measured in theregion far from the object is 8.4 µ Jy/beam with a beam size of 35.0 × ◦ . The black star in panel (c)indicates the center of ellipse isophoto fitting. (d): Azimuthally averaged radial profile in panel (a). The synthesized image wasdeprojected with PA of 156.3 ◦ and i of 36.1 ◦ , derived in our visibility analyses in § µ Jy/beam. (e): Azimuthal profile in the outer ring at r ∼
20 au in the deprojected image. Two prominent asymmetriesat PA of ∼ ◦ and ∼ ◦ in Figure 7 are labeled as blobs A and B. Kudo et al. (2018) reported a possible asymmetry in the inner ring, i.e., 20 % brighter emission in the northwest.The inner ring in our new data shows that the southeast region is ∼
20 % ( ∼ σ ) brighter than the northwest region(Figure 1b). However, no such asymmetries in the inner ring can be seen in the image subtracting the 180 ◦ -rotatedimage in Figure 7 where only asymmetric signals are contained (see explanations of method A in § . Therefore, asthese asymmetries could be the result of image reconstruction artifacts, more data are necessary to confirm both theasymmetries and morphological variability in the inner ring. A demerit of this method is the fact that the noise level is ∼√ × higher than the normal dust continuum image because of imaging withonly the imaginary part. Therefore, asymmetries with a small contrast can be elusive. Hashimoto et al. ″ (14.5 au) NE 0.1 ″ (14.5 au) NE I n t e g r a t e d li n e i n t e n s it y ( m J y / b ea m k m / s ) . . . V e l o c it y ( k m / s ) − . . . (a) (b) Figure 2.
Integrated line flux map (a: moment 0) and intensity-weighted velocity map (b: moment 1) of CO J = 2 → · km/s with a beam size (white ellipse in the lower left corner) of45.6 × − ◦ . Black dotted line represents the 15 σ contour of the inner ring in the dust continuum image(1 σ of 8.4 µ Jy/beam; Figure 1), and its beam size of 35.0 × ◦ is shown as block ellipse in the lowerleft corner. The positional error in the peak position is assumed to be the values of the beam size divided by the SN ratio, i.e., ∼ The inner ring shown in Figure 1(c) is likely to have a different PA than that of 157.8 ◦ in the DM Tau system (Kudoet al. 2018). The bright part in the south region in the inner ring is located at a PA of ∼ ◦ . Since the beam shapeis close to circular, the shape of the inner ring is unlikely to be affected by the beam elongation. We performed ellipseisophoto fitting of the inner ring at 8 σ level, and found that the PA of the inner ring is 172.1 ◦ ± ◦ . The differenceis significant at 3.5 σ . Furthermore, Francis & van der Marel (2020) found that the PA of the inner ring in Kudoet al. (2018) is 141 ◦ ± ◦ by Gaussian fitting in the image domain, which suggests that the PA of the inner ring in ournew data varies comparing with previous observations in Kudo et al. (2018). These results motivated us to performvisibility analyses to test whether or not the PA of the inner ring is different from that of the system and previousobservations, because there is a possibility of image reconstruction artifacts in the inner ring (see § CO J = 2 → · km/s at 13 σ , while Kudo et al. (2018) noted that the peak emission at 9 σ is shifted with ∼
20 mas towards north . Assuming the positional errors are the values of the beam size divided by the SN ratio, thepositional error of the peak CO emissions in Kudo et al. (2018) is ∼ ∼ σ deviation. These positionalshifts between two epochs could also be artifacts. More data are needed to confirm or reject the time variability inthe inner ring. The intensity-weighted velocity map is also shown in Figure 2(b) and is consistent with that in Kudoet al. (2018). MODELING4.1.
Visibility fitting
As the spatial scale of the inner ring is a few times the beam size, the structure in the inner ring corresponds tohigh spatial frequency components in the visibilities. In general, visibility data at a high spatial frequency is moresparse even in ALMA observations, potentially resulting in image reconstruction artifacts. To confirm the differentPAs between the inner and outer rings inferred in §
3, we performed forward modelling in which observed visibilitiesare reproduced with a parametric model of the disk by utilizing all spatial frequency information. We found that errors in the CO moment 0 map estimated in Kudo et al. (2018) are updated from 3.5 to 6.0 mJy/beam · km/s. symmetric Disk of DM Tau r =20 au around DM Tau shows anexponential profile (Figure 1d), we describe the surface brightness distributions of the disk in our model with a simplepower-law radial profile with an exponential taper at the outside: I ( r ) ∝ (cid:88) i =1 α i (cid:18) rr c i (cid:19) − γ p , i exp (cid:20) − (cid:18) rr c i (cid:19) γ e , i (cid:21) , (3)where α i , r c i , γ p , i , and γ e , i are a scaling factor, a characteristic scaling radius, and exponents of the power-lawand the exponential taper, respectively. We divided the disk into two global components ( i , Figure 3a) because theinner and outer rings (component 1) are roughly one order of magnitude brighter than the extended outer structure(component 2). In the radial direction, we have the following scaling factors: α (component 1) = δ for r cav < r < r gap r gap < r < r gap r gap < rα (component 2) = r < r gap r gap < r < r gap δ for r gap < r < r gap δ for r gap < r. At r < r cav , we set a constant value with a depletion factor ( δ ) relative to the brightness at r = r cav . We note thatsince the radial profile at ∼
60 au < r < ∼
80 au is likely to be flat (Figure 1d), we added a pseudo ring in this region(i.e., at r gap < r < r gap in Figure 3a) to reproduce the nearly flat radial profile. Two components are normalized at r = r gap (Figure 3a). The total flux density ( F total ) is also set as a free parameter. The disk inclination ( i ) and PA inthe inner ring and the system (meaning the outer ring + the extended structure hereafter) are set as free parameters,i.e., i inner ring , PA inner ring , i system , and PA system . We fix the phase center.In addition to the above disk, we also add the model of blob A at PA of ∼ ◦ (Figure 7) defined as the ellipticalgaussian function in the polar coordinate as follows:A = cos PA blob σ θ + sin PA blob σ r , B = 2 (cid:18) σ θ − σ r (cid:19) sin PA blob cos PA blob , C = sin PA blob σ θ + cos PA blob σ r , Z = A( θ − θ blob ) + B( θ − θ blob )( r − r blob ) + C( r − r blob ) ,I blob ( r, θ ) ∝ exp (cid:18) −
12 Z (cid:19) , (4)where PA blob is PA of the major axis of the elliptical gaussian function in the polar coordinate, r blob and θ blob arethe radial and the azimuthal distances of blob A in the polar coordinate, and σ θ and σ r are standard deviationsalong the azimuthal and radial directions in the elliptical gaussian function, respcetively. The value of PA blob is setto zero. The model image is finally rotated and magnified with PA system and i system , respectively. The total flux ofblob A is normalized to F blob . Note that the values of FWHM r , blob and FWHM θ, blob are equal to 2 . σ r and 2 . σ θ ,respectively. Figure 11 shows the model image of blob A. Note that since blob B has lower brightness, we do notinclude blob B in our model. In total, there are 25 free parameters in our model ( F total , F blob , r cav , r gap , r gap , r gap , r gap , δ , δ , δ , δ , γ p , , γ e , , γ p , , γ e , , r c , r c , i inner ring , PA inner ring , i system , PA system , r blob , θ blob , FWHM r , blob ,FWHM θ, blob ). Hashimoto et al.
The modeled disk image was converted to complex visibilities with the public python code vis_sample (Loomiset al. 2017), in which modeled visibilities are samples with the same ( u , v ) grid points with observations. The modeledvisibilities are deprojected with the system PA and i as free parameters. The fitting is performed with a Markovchain Monte Carlo (MCMC) method in the emcee package (Foreman-Mackey et al. 2013). The log-likelihood functionln L in MCMC fitting isln L = − . (cid:88) (cid:2) f W j { (Re V obs j − Re V model j ) + (Im V obs j − Im V model j ) } (cid:3) , where the subscript j represents the j -th data. V obs j , V model j , and W j are observed and modeled visibilities, and weights,respectively. The value of f is a factor between weights and standard deviations in the visibilities. To estimate the valueof f , we calculate the standard deviations of the real and imaginary parts in 3 k λ bin along the azimuthal direction inthe visibility domain. The visibilities were deprojected with i system =36.1 ◦ and PA system =156.3 ◦ . Figure 12 shows thecomparison between weights and standard deviations, and we found that the typical value of f is 0.24. The weightsare overestimated, or the noise is underestimated, vice versa. Our calculations used flat priors with the parameterranges summarized in Table 2. We ran 5000 steps with 100 walkers, and discarded the initial 500 steps as the burn-inphase based on the trace plot in Figure 13.The fitting results with errors computed from the 16th and 84th percentiles, the radial profile of best-fit surfacebrightness, the best-fit modeled image, and the probability distributions for the MCMC posteriors are shown in Table 2,Figure 3(a), Figure 3(d), and Figure 14 in the Appendix, respectively. Though some parameters such as r blob showdouble peaks in the probability distributions (Figure 14 in the Appendix), since the differences of double peaks aresmall, we only show the results for the best-fit model in Figure 3. We subtracted modeled visibilities from observedones, and made a CLEANed image (Figure 3e and f). The reduced- χ is 1.7. We confirmed that the size of the innercavity is 3 au in radius, which is consistent with the result in Kudo et al. (2018). Though Figure 1(c) imply that theinner ring is misaligned to the outer ring, the values of PA and i in the inner ring and the system are statistically samewithin 3 σ in our visibility analyses.In the residual image in Figure 3(f), we found additional two significant residual signals as labeling blob C andD. Figure 4(a) shows the dust continuum image with subtracting the 180 ◦ -rotated image, overlaying the contours ofblob B to D in Figure 3(f). Though the counterparts of blob B and C can be seen in Figure 4(a), blob C disappearsin the image with different image shifts in Figure 7, e.g., the image with ∆R.A.=1 mas and ∆DEC=1 mas. Hence weconsider that blob B is a real structure while blob C might be an artifact. Furthermore blob D has no counterpartin Figure 4(a), and thus, we also consider that blob D is an artifact. By ellipse gaussian fitting in the image domain,blob B is spatially resolved with the size of 119 ×
78 mas (17.3 × uv -distanceof less than ∼
500 k λ (corresponding to the scale of ∼ . (cid:48)(cid:48) ◦ -rotated image (Figure 4a) inFigure 15 in Appendix. We found that both images in Figure 15 show the large scale asymmetry in the east part ofthe disk. Such large scale asymmetries have been reported in other disk systems potentially due to the shadow effect(e.g., Figure 4 in Facchini et al. 2020). The large scale asymmetry around DM Tau (Figure 3e; to be investigatedelsewhere) has clumpy structures at ∼ σ level, and could potentially induce artificial clumps in the ring of blobs Aand B. The spatial distribution of low SNR clumps caused by thermal noises is expected to be random. If blobs Aand B are indeed such artificial clumps, it is unlikely for them to reoccur in different observations. We re-imaged dustcontinuum data in cycle 5 (Kudo et al. 2018) and found that both blobs can be seen at roughly the same locations(Figure 9; Appendix B). This suggests that blobs A and B are unlikely artificial clumps caused by noises.We also found that the central region at r (cid:46) δ =0.24 +0 . − . is not zero at4.8 σ . The total flux at r (cid:46) µ Jy. This result indicates the existence of unresolved ring structure at r (cid:46) SED fitting
The visibility analyses in § ∼ µ Jy) in the central disk regionwithin r (cid:46) Visibilities are deprojected in the uv -plane with the following equations (e.g., Zhang et al. 2016): u (cid:48) = ( u cos PA system − v sin PA system ) × cos i system , v (cid:48) = ( u sin PA system − v cos PA system ) , where i system and PA system are free parameters in our visibility analyses in § symmetric Disk of DM Tau −1σ−2σ1σ3σ2σ4σ6σ5σ0 ″ (145 au) NE D a r k B r i gh t ″ (29 au) NE (f)(e)(d) ″ (29 au)0.2 ″ (29 au) V i s i b ilit y R ea l ( m J y ) V i s i b ilit y I m a g i n a r y ( m J y ) R e s i du a l ( m J y ) R e s i du a l ( m J y ) uv distance (k λ )uv distance (k λ ) -3-2-1 0 1 2 3-3-2-1 0 1 2 3 0 2000 4000 6000 8000 0 20 40 60 80 100-3-2-1 0 1 2 3 0 2000 4000 6000 8000 Model diskObservation (a)
Model diskObservation (c)(b) r gap r gap r gap r gap r cav Component2Component1 N o r m a li ze d s u rf ace b r i gh t n e ss Radius (au) δ3 δ4δ2δ1
BDC
Large scale asymmetry
Figure 3. (a) Surface brightness profile for the best-fit model with notes regarding our visibility analyses. We divided the modelsurface brightness profile into two components: component 1 (red) for the inner and outer rings at r (cid:46)
60 au and component 2(blue) for the extended structure at r (cid:38)
60 au. The gap structures are created by scaling down/up the surface brightness by afactor δ . These two components are normalized at r = r gap1 as shown by the black dotted line. To reproduce the nearly flatradial profile at ∼
60 au < r < ∼
80 au in Figure 1(d), we added a pseudo ring in this region (i.e., at r gap < r < r gap . (b and c)Real and imaginary parts of the visibilities for the observations (red dots) and the best-fit model (black line) in the top panel.The bottom panel shows residual visibilities between observations and the best-fit model. (d) Magnified image (0 . (cid:48)(cid:48) × . (cid:48)(cid:48)
6) ofthe best-fit model. (e and f) Residual image (3 (cid:48)(cid:48) × (cid:48)(cid:48) ) and its magnified image (0 . (cid:48)(cid:48) × . (cid:48)(cid:48) that the dust grains inside the cavity are heavily depleted. The NIR excess mainly comes from small (sub-micronsize) dust grains. To test the contributions of large (millimeter) dust grains in both the NIR excess in SED andthe millimeter flux ( ∼ µ Jy) of the central emission, we conducted radiative transfer modeling using a Monte Carloradiative transfer (MCRT) code (
HO-CHUNK3D ; Whitney et al. 2013). For this purpose, we put additional large andsmall dust grains inside the inner cavity at r = 3 au. The new cavity radius at r < r newcav hereafter. The fiducial surface density model and other models shown in Figure 5(a).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 mid-plane (e.g., D’Alessio et al. 2006). Themodeled disk structure and dust properties in the MCRT code is described in our previous studies (Hashimoto et al.2015): small dust grains from the standard interstellar-medium dust model (a composition of silicates and graphites;a size distribution of n ( s ) ∝ s − . from s min = 0 . µ m to s max = 0 . µ m) in Kim et al. (1994) and large dust grains(a composition of carbons and silicates; a size distribution of n ( s ) ∝ s − . from s min = 0 . µ m to s max = 1000 µ m)from Model 2 in Wood et al. (2002). The radial surface density is assumed to be a simple power-law radial profilesimilar to eq. (3):0 Hashimoto et al.
Table 2.
Results of MCMC fitting and its parameter ranges r cav r gap r gap r gap r gap δ δ δ δ (au) (au) (au) (au) (au)(1) (2) (3) (4) (5) (6) (7) (8) (9)3.22 +0 . − . +0 . − . +0 . − . +0 . − . +1 . − . +0 . − . +0 . − . +0 . − . +0 . − . { } { } { } { } { } { } { } { } { } γ p , γ e , γ p , γ e , r c1 r c2 i inner ring PA innner ring i system PA system (au) (au) ( ◦ ) ( ◦ ) ( ◦ ) ( ◦ )(10) (11) (12) (13) (14) (15) (16) (17) (18) (19)1.87 +0 . − . +0 . − . +0 . − . +0 . − . +4 . − . +7 . − . +7 . − . +3 . − . +0 . − . +0 . − . { -1 .. 3 } { -1 .. 3 } { } { } { } { } { } { } { } { } Flux total
Flux blob r blob θ blob FWHM r , blob FWHM θ, blob (mJy) ( µ Jy) (au) ( ◦ ) (au) ( ◦ )(20) (21) (22) (23) (24) (25)94.74 +0 . − . +28 . − . +0 . − . +0 . − . +1 . − . +3 . − . { } { } { } { } { } { } Note — Parentheses describe parameter ranges in our MCMC calculations. (14.5 au) NE −7σ7σ0 F l ux d e n s it y ( µ J y / b ea m ) R e s i du a l Blob ABlob BBlob C(Artifact ?)Blob D(Artifact ?) (b) Image with real and imaginary parts(b) Image with real and imaginary parts(a) Image with only imaginary part(a) Image with only imaginary part
Figure 4.
Left: The synthesized dust continuum image of short and long baseline data made with the only imaginary part(i.e., the image subtracting 180 ◦ -rotated image). Right: Normal dust continuum image. Black and white lines are 5 σ contoursin Figure 3(f). Σ( r ) = α Σ (cid:18) rr c (cid:19) − q exp (cid:34) − (cid:18) rr c (cid:19) − q (cid:35) , symmetric Disk of DM Tau α = r < r newcav δ for r newcav < r < < r <
20 auwhere Σ is the normalized surface density determined from the total (gas + dust) disk mass ( M disk ) assuming agas-to-dust mass ratio of 100, r c is the characteristic radius of 50 au, q is the radial gradient parameter, and α is thescaling factor for the surface density. As the main purpose of our MCRT modeling effort is to reproduce the DM TauSED at λ (cid:46) µ m, we set a grid size of r = 20 au in the code, i.e., inside the 20 au cavity. We set M disk = 0.1 M Jup to reproduce a flux of 1.74 mJy inside the 20-au cavity at 1.3 mm, and fix q = 1. The scale heights ( h ) of large andsmall grains are assumed to vary as a power law with a radius, i.e., h ∝ r p . To simplify, we assume p = 1.25 witha typical midplane temperature profile of T ∝ r − . . We fix the scale heights of 1 and 4 au at r = 100 au for large( h large r =100au ) and small ( h small r =100au ) dust disks, respectively, taken from Andrews et al. (2011) for the small dust disk. Themass fraction ( f ) of large dust grains in the total mass of dust grains is set to 0.9. The disk inclination is set to 30 ◦ .The HO-CHUNK3D code calculates the accretion luminosity at the star based on the mass accretion rate. Half of the fluxis emitted as X-rays (which heat the disk) and half as stellar flux at a higher temperature. We set a mass accretionrate of ˙ M = 6 × − M (cid:12) /yr (Manara et al. 2014). In the code, we vary three parameters: r newcav (same values forlarge and small dust disks), δ large , and δ small (where the superscript represents large or small dust grains) as shown inTable 3. − − − − 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 ] − Wavelength ( µ m) λ F [ e r g s c m ] − − λ - - - (a) Large dust grains (c) SED(b) Small dust grains r r Fiducial model C model Dmodel Amodel B
Fiducial model Cmodel Dmodel Amodel B
Fiducial model C PhotosphereSpitzer/IRS
Figure 5.
Results of MCRT modeling. We set r newcav = 0.1 or 1.0 au while r = 3 au is derived from the visibility analysesin § r < δ . As DM Tau SED has no NIR excess, we set no surface brightness at r < r newcav . (c)SEDs for our modeling. The black dots are DM Tau spectra obtained with the Spitzer Space Telescope. Figure 5(c) shows the SEDs for each model. Our fitting procedure includes three steps, as follows.1. We first set r newcav = 1 au with varying values of the depletion factor δ with the same values in large and smalldust disks to reproduce the flux of the central unresolved ring structure ( ∼ µ Jy) at band 6, and found that δ = 3 × − is a reasonable parameter (model A).2. As the SED for model A largely emits at ∼ µ m (Figure 5c), we only vary δ of small dust grains at 10 − to10 − (models B and C and fiducial model). We found that the fiducial model well reproduces the DM Tau SEDat λ (cid:46) µ m.3. We also set r newcav = 0.1 au (model D). However, even for δ = 0 for small dust grains, this model largely emitsin the NIR wavelengths.In summary, the fiducial model could reasonably account for both the DM Tau SED and the flux of the centralunresolved ring structure. This could be because the midplane temperature at r > Hashimoto et al.
Table 3.
Parameters in our MCRT modelingModel R newcav δ large δ small r c p q h large r =100 au h small r =100 au M disk ˙ M (au) (au) (au) (au) ( M Jup ) ( M (cid:12) yr − )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)fiducial 1.0 3 × − × −
50 1.25 1 1 4 0.1 6 × − A 1.0 3 × − × −
50 1.25 1 1 4 0.1 6 × − B 1.0 3 × − × −
50 1.25 1 1 4 0.1 6 × − C 1.0 3 × − × −
50 1.25 1 1 4 0.1 6 × − D 0.1 3 × − × − shown in Figure 16 in the Appendix. Our modeling suggests that small dust grains inside the 3-au cavity are depletedwhile large ones remain present.In our two modeling efforts for visibility analyses ( § § r <
20 au in Figure 17in the Appendix. We confirm that the two radial profiles in our modeling efforts are consistent with each other. DISCUSSIONS5.1.
Multiple blobs
Asymmetric structures referred to as blobs in this paper are interpreted as dust trapped in gas vortices (e.g., Raettiget al. 2015) or gas horseshoes (e.g., Ragusa et al. 2017). For the latter, only one blob is expected at the edge of acavity, and thus, DM Tau’s multiple blobs would not be this case. Furthermore, a gas horseshoe is expected at theedge of a cavity opened by massive companions (i.e., brown dwarfs). Previous near-infrared sparse aperture maskinginterferometry (Willson et al. 2016) and radial-velocity measurement (Nguyen et al. 2012) have ruled out the presenceof such companions in the cavity, disfavoring the gas horseshoe origin of DM Tau’s blobs. Note that though van derMarel et al. (2020) mentioned the spiral structures as a third origin of asymmetries, since scattered light images ofDM Tau is not available, it is unclear whether the spiral structures are responsible for DM Tau’s blobs.Theoretical works of vortices (e.g., Ono et al. 2018) predict that multiple small vortices at similar radial locationstend to merge into one large vortex within hundreds of orbits. The existence of multiple blobs would therefore indicatethe youth of vortices. Another interpretation of multiple blobs is a destruction of a large-scale vortex due to theheavy-core instability (Chang & Oishi 2010), triggered by a close to unity dust-to-gas mass ratio in the core of avortex. Recent numerical simulations by Li et al. (2020) show multiple small blobs in the ring after the destructionof a large vortex. As the orbital number (system age divided by Keplerian orbital period at the radial location of theblob) of DM Tau’s blob A is more than 10 , DM Tau’s blobs may be the outcome of vortex destruction. In this case,the dust-to-gas mass ratio is expected to be close to unity. For DM Tau however, the azimuthally-averaged dust-to-gasmass ratio is estimated to be ∼ r ∼
20 au (Francis et al. in perp.), disfavoring the scenario.A third possibility is that the azimuthal position of trapped dust depend on the dust size (Baruteau & Zhu 2016):centimeter-sized dust grains are trapped ahead of the gas vortex center in the azimuthal direction while millimeter-sizedust grains concentrate closer to the vortex center. To examine this possibility, multiple wavelength observations tomeasure the spectral index sensitive to the grain size are necessary.We also compare the shape of DM Tau’s blob A with other asymmetries. Asymmetric structures have been reportedin roughly 10 protoplanetary disks (e.g., Francis & van der Marel 2020; van der Marel et al. 2020; Tsukagoshi et al.2019; P´erez et al. 2018; Kraus et al. 2017). Table 4 summarizes the physical quantities of blobs, mainly relevant to theirmorphology . We found that DM Tau’s blob A is located at the smallest radial location in the sample. Furthermore, V1247 Ori shows the crescent structure (Kraus et al. 2017). However, we do not include V1247 Ori because the structure was notcharacterized with the Gaussian profile (Kraus et al. 2017). TW Hya also shows the asymmetry (Tsukagoshi et al. 2019). Though allasymmetries in Table 4 are located at the inner/outer edges of the ring, TW Hya’s blob is not the case. TW Hya’s blob may be createdby different mechanisms, and thus, we do not include TW Hya’s blob in Table 4. symmetric Disk of DM Tau Table 4.
Physical quantities of blobs and other propertiesObject Radial location Radial width Azimuthal width Aspect ratio Refs(au) (au) (deg; au)(1) (2) (3) (4) (5) (6)DM Tau 24 1.7 45; 18.7 11 1AB Aur 170 96 122; 361.8 3.8 2CQ Tau 50 19 59; 51.5 2.7 250 19 59; 51.5 2.7 2HD 34282 137 110 52; 124.3 1.1 3HD 34700 155 72 64; 173 2.4 4HD 142527 180 81 155; 486.7 6.0 2HD 143006 74.2 11 38.4; 49.7 4.5 5IRS 48 70 29 58; 70.8 2.4 2MWC 758 50 7.5 49; 42.7 5.7 290 15 47; 73.8 4.9 2SAO 206462 79 20 96; 132.3 6.6 2SR 21 55 19 82; 78.7 4.1 258 19 165; 166.9 8.8 2
Note — Radial width of IRS 48 is calculated with 2.17 σ r because the radial profile ofIRS 48 was found to be best fit with a 4th power in 2D Gaussian in van der Marel et al.(2020). The aspect ratio is defined as the azimuthal width divided by the radial width.References for blob information of radial locations and shapes: 1) this work, 2) van derMarel et al. (2020), 3) van der Plas et al. (2017), 4) Benac et al. (2020), 5) P´erez et al.(2018). its aspect ratio (the azimuthal width divided by radial width) is the largest. Figure 6 shows these observational results,which places DM Tau’s blob A in a novel parameter space of asymmetries.5.2. Central emission
Our visibility analyses in § σ ) within the 3 au cavity. Central point sources inthe cavity of the disk can been seen in roughly half of the samples (see Figure 1 in Francis & van der Marel 2020). Forthese point sources, it has been shown that their total mm-dust mass is not correlated with the NIR excess, generallyassociated with small grains at the inner dust rim (Francis & van der Marel 2020). Our modeling in § (cid:46) § r = 1 au while centimeter dust grainsmay efficiently drift there, as shown in Brauer et al. (2008).4 Hashimoto et al. R a d i a l F W H M ( a u ) Radial location (au) 10 100 A s p ec t r a ti o Radial location (au) 0 2 4 6 8 10 12
Figure 6.
Comparison of the shape of DM Tau’s blob A with other asymmetries. The aspect ratio is defined as the azimuthalwidth divided by the radial width. Red circle represent DM Tau. Physical quantities are summarized in Table 4.
The water snowline around typical T Tauri stars is expected to be located at a few au from the central star (Notsuet al. 2016). Inside the snowline, the temperature exceeds the sublimation temperature ( T ∼
150 K; Notsu et al. 2016)and the water is released into the gas phase. Thus, dust grains inside the snowline contain rock and iron without waterice, and are believed to grow to form rocky planets. However, it has been believed that collisional fragmentationsare dominant inside the water snowline due to a lack of water ice in the dust grains (e.g., Blum & Wurm 2008). Onthe other hand, recent laboratory experiments by Steinpilz et al. (2019) show that silicate dust grains without waterare an order of magnitude stickier than those with water. These results might invoke the possibility of the formationof rocky planetesimals. In the case of DM Tau, the disk midplane temperature is below 150 K except at the wall ofthe 1-au cavity (Figure 16 in Appendix), and thus, dust grains would contain water ice. This could be because thelarge depletion factor of 0.4 in the large dust grains in the 1-au ring results in a large optical depth, and the midplanetemperature is under the conditions of radiative equilibrium. The flux of 50 µ Jy in the 1-au ring translates to a totalmass (gas + dust) of 0.4 M Earth (a dust mass of 0.3 M Moon ) assuming a distance of 145 pc, an opacity per unit dustmass κ ν = 2.3 cm g − at 230 GHz (Beckwith & Sargent 1991), a temperature of 100 K, and a gas-to-dust massratio of 100. We note that since dust grains in the 1-au ring might grow more than those in the outer disk region, asdiscussed in the previous paragraph, the dust opacity could be smaller than 2.3 cm g − . Therefore, the derived dustmass of 0.3 M Moon is probably a lower limit. These results suggest that small icy planets, i.e., mini Neptunes, mayform in the 1-au ring around DM Tau. CONCLUSIONWe present new ALMA observations of DM Tau including dust continuum images at 1.3 mm and CO J = 2 → r = 3, 20, 90, and 110 au, and (b) two blobs at PA of ∼ ◦ and ∼ ◦ in the outerring at r ∼
20 au. To characterize the inner ring regions at r (cid:46)
10 au, we analyze the dust continuum emissions in thevisibility domain and conduct modeling efforts using the MCRT code (Whitney et al. 2013). Consequently, we foundthe unresolved 1-au ring inside the 3-au inner ring. Furthermore, model disks with different disk inclinations and PAsbetween the inner ring at r ∼ σ . symmetric Disk of DM Tau ∼ × to ∼ × relative to the outer ring. These two blobs are locatedat the smallest radial location among 11 asymmetric disks. Furthermore, the aspect ratio of blob A is the largest.These observational results, which places DM Tau’s blob A in a novel parameter space of asymmetries. The originof two blobs is not determined by our observations. The early phase of the vortex formation (e.g., Ono et al. 2018),the destruction of the large scale vortex (e.g., Li et al. 2020), or double continuum emission peaks with different dustsizes (Baruteau & Zhu 2016) could account for the multiple blobs. Future high spatial resolution observations in themultiple wavelengths with ALMA and JVLA would help identify the origin.We also found the significant emissions with a lower limit mass of 0.4 M Earth inside the 3 au cavity. As the DM TauSED shows negligible NIR excess, the inside of the 3-au cavity around DM Tau has been believed to be a dust-freeregion. By fitting both the DM Tau SED and the flux of the central emissions using the MCRT code, our modelingshows that inside the 3-au cavity, there is an additional 1-au dust ring where large (millimeter size) dust grains areless depleted than small (sub-micron size) dust grains. This would be due to efficient grain growth in the 1-au dustring. Furthermore, our modeling indicates that the disk midplane temperature in the 1-au ring is less than the typicalwater sublimation temperature of 150 K (e.g., Notsu et al. 2016), which suggests that only small icy planets (i.e., miniNeptunes) could form even in the terrestrial planet formation regions around DM Tau.ACKNOWLEDGMENTSWe thanks the 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) APPENDIX A. DUST CONTINUUM IMAGES SYNTHESIZED WITH ONLY THE IMAGINARY PARTFigure 7 and 8 show the dust continuum images synthesized with only the imaginary part of long and short baselinedata, respectively, by shifting 1 mas in R.A. and DEC directions. The image is shifted relative to the center of ellipseisophoto fitting (see §
2) in the visibility domain by the phase shift defined as exp [2 π ( u ∆R . A . + v ∆DEC)], where u and v are the spatial frequencies and ∆R.A. and ∆DEC are shift values, respectively. The r.m.s values are measuredinside the black dotted circles with radii of 0 . (cid:48)(cid:48) . (cid:48)(cid:48) σ noises in Figure 7and 8 are 11.6 µ Jy/beam and 89.0 µ Jy/beam, respectively, measured in the region far from the object. B. DUST CONTINUUM IMAGES WITH DIFFERENT IMAGING PARAMETERSWe synthesized dust continuum images with different imaging parameters in the CLEAN task to examine therobustness of blobs A and B. We also re-imaged the dust continuum data obtained in cycle 5 (Kudo et al. 2018) tocheck whether the two blobs are present in different datasets. To minimize the effect of the beam elongation, weadjusted the uv -taper parameters to obtain a nearly circular beam. Figure 9(a) shows the dust continuum image usingthe same parameters with Figure 1, but using the multi-scale option with scales of [0, 5, 10, 15, 25] in the CLEANtask. We confirmed that the image is consistent with Figure 1. Figure 9(b) and (c) are the same with Figure 9(a), butwith robust=2.0 and − Hashimoto et al. ∆ R.A. = -1 mas, ∆ DEC = -1 mas,r.m.s = 22.4 µ Jy/beam ∆ R.A. = -1 mas, ∆ DEC = 0 mas,r.m.s = 20.8 µ Jy/beam ∆ R.A. = -1 mas, ∆ DEC = 1 mas,r.m.s = 21.3 µ Jy/beam ∆ R.A. = 0 mas, ∆ DEC = -1 mas,r.m.s = 21.3 µ Jy/beam ∆ R.A. = 0 mas, ∆ DEC = 0 mas,r.m.s = 19.8 µ Jy/beam ∆ R.A. = 0 mas, ∆ DEC = 1 mas,r.m.s = 20.4 µ Jy/beam ∆ R.A. = 1 mas, ∆ DEC = -1 mas,r.m.s = 22.8 µ Jy/beam ∆ R.A. = 1 mas, ∆ DEC = 0 mas,r.m.s = 21.7 µ Jy/beam ∆ R.A. = 1 mas, ∆ DEC = 1 mas,r.m.s = 22.6 µ Jy/beam (72.5 au) NE (72.5 au) NE (72.5 au) NE (72.5 au) NE (72.5 au) NE (72.5 au) NE (72.5 au) NE (72.5 au) NE (72.5 au) NE −9σ9σ0
Blob ABlob B
Figure 7.
The dust continuum images synthesized with only the imaginary part of long baseline data by shifting 1 mas inR.A. and DEC directions. The r.m.s value is measured inside the black dotted circle with a radius of 0 . (cid:48)(cid:48)
3. The 1 σ noise is11.6 µ Jy/beam measured in the region far from the object. the multi-scale option was not used in Figure 9(b to d). We confirmed the presence of blobs A and B at roughly thesame locations in all cases. C. CO J = 2 → CO J = 2 → − D. BLOB STRUCTUREFigure 11 shows the model image of blob A used in MCMC calculations in § symmetric Disk of DM Tau ∆ R.A. = 3 mas, ∆ DEC = -3 mas,r.m.s = 114.0 µ Jy/beam ∆ R.A. = 3 mas, ∆ DEC = -2 mas,r.m.s = 109.7 µ Jy/beam ∆ R.A. = 3 mas, ∆ DEC = -1 mas,r.m.s = 111.6 µ Jy/beam ∆ R.A. = 4 mas, ∆ DEC = -3 mas,r.m.s = 110.0 µ Jy/beam ∆ R.A. = 4 mas, ∆ DEC = -2 mas,r.m.s = 106.6 µ Jy/beam ∆ R.A. = 4 mas, ∆ DEC = -1 mas,r.m.s = 109.6 µ Jy/beam ∆ R.A. = 5 mas, ∆ DEC = -3 mas,r.m.s = 111.4 µ Jy/beam ∆ R.A. = 5 mas, ∆ DEC = -2 mas,r.m.s = 111.9 µ Jy/beam ∆ R.A. = 5 mas, ∆ DEC = -1 mas,r.m.s = 118.6 µ Jy/beam ∆ R.A. = 3 mas, ∆ DEC = -3 mas,r.m.s = 114.0 µ Jy/beam ∆ R.A. = 3 mas, ∆ DEC = -2 mas,r.m.s = 109.7 µ Jy/beam ∆ R.A. = 3 mas, ∆ DEC = -1 mas,r.m.s = 111.6 µ Jy/beam ∆ R.A. = 4 mas, ∆ DEC = -3 mas,r.m.s = 110.0 µ Jy/beam ∆ R.A. = 4 mas, ∆ DEC = -2 mas,r.m.s = 106.6 µ Jy/beam ∆ R.A. = 4 mas, ∆ DEC = -1 mas,r.m.s = 109.6 µ Jy/beam ∆ R.A. = 5 mas, ∆ DEC = -3 mas,r.m.s = 111.4 µ Jy/beam ∆ R.A. = 5 mas, ∆ DEC = -2 mas,r.m.s = 111.9 µ Jy/beam ∆ R.A. = 5 mas, ∆ DEC = -1 mas,r.m.s = 118.6 µ Jy/beam (145 au) NE (145 au) NE (145 au) NE (145 au) NE (145 au) NE (145 au) NE (145 au) NE (145 au) NE (145 au) NE −4σ4σ0
Figure 8.
Same with Figure 7, but short baseline data. The r.m.s value is measured inside the black dotted circle with a radiusof 0 . (cid:48)(cid:48)
5. The 1 σ noise is 89.0 µ Jy/beam measured in the region far from the object.E.
WEIGHT VALUES AND THE STANDARD DEVIATIONS IN REAL AND IMAGINARY PARTSFigure 12 shows the comparison of the values of weight and the standard deviations in real and imaginary parts.The standard deviations (stddev) are calculated in each 3 k λ bin in the deprojected visibilities of real and imaginaryparts with i of 36 ◦ and PA of 156 ◦ . We found that the values of weight are typically 3.85 × higher than 1/stddev ofreal and imaginary parts. F. TRACE PLOT IN MCMC CALCULATIONSFigure 13 shows the trace plot of 100 walkers of the parameter r gap1 in our MCMC calculations ( § Hashimoto et al. F l ux d e n s it y ( µ J y / b ea m ) F l ux d e n s it y ( µ J y / b ea m ) . F l ux d e n s it y ( µ J y / b ea m ) F l ux d e n s it y ( µ J y / b ea m ) (a) Multi-scale CLEAN (cycle 6 data) (b) Robust = 2.0 (cycle 6 data)B A ″ (29 au) NE 0.2 ″ (29 au) NE0.2 ″ (29 au) NE (c) Robust = − Figure 9.
The dust continuum images with different imaging parameters of cycle 6 data in panels (a) to (c) and cycle 5 datataken from Kudo et al. (2018) in panel (d). (a) The dust continuum image synthesized with the multi-scale option and otherparameters fixed as in Figure 1. The image is consistent with Figure 1. The noise level is 8.4 µ Jy/beam with the beam shapeof 35 ×
34 mas at PA of 67.5 ◦ . (b and c) Same with panel (a), but with robust=2.0 and − µ Jy/beam with the beam of 42 ×
40 mas at PA of46.8 ◦ and 15.8 µ Jy/beam with the beam of 24 ×
23 mas at PA of − ◦ , respectively. (d) Same with panel (b), but cycle 5data (Kudo et al. 2018). The noise level is 11.8 µ Jy/beam with the beam shape of 38 ×
37 mas at PA of 27.6 ◦ . The blackdotted lines in all panels represent the 60 σ contours in the dust continuum image in Figure 1.G. HISTOGRAMS OF THE MARGINAL DISTRIBUTIONS OF THE MCMC POSTERIORSFigure 14 shows histograms of the marginal distributions of the MCMC posteriors for 25 free parameters calculatedin our modeling in § symmetric Disk of DM Tau (mJy/beam)Linear scaled flux density −3 7 17−1.8 4.2 10.2 ( σ ) + + + + + + + + + + + + + + + + + + − − ″ (145 au) NE Figure 10.
Channel maps for CO J = 2 →
1. The r.m.s. noise for the 0.7-km/s bin is 0.589 mJy/beam with a beam size of45.6 × − ◦ H. A POSSIBLE LARGE SCALE ASYMMETRYFigure 3(e) in our visibility analyses in § ◦ -rotatedimage in Figure 15. Both images show that the east part of the disk is brighter. Thus, DM Tau could have the diskwith large scale asymmetry.0 Hashimoto et al. PA system + 90° (i.e., 246.3°) θ blob r blob Best-fit image of blob A20 au PA system =156.3° Figure 11.
The best-fit model image of bolb A derived by MCMC calculations in § i system =36.1 ◦ .I. MIDPLANE TEMPERATURE CALCULATED BY THE MCRT MODELINGFigure 16 shows a profile of the midplane temperature of large and small dust grains in the fiducial model calculatedin the MCRT modeling in § symmetric Disk of DM Tau Real partImaginary partWeight uv distance (k λ ) W e i gh t o r s t dd e v ( J y ) - - Figure 12.
Comparison of the values of weight and the standard deviations (stddev) in real and imaginary parts. The valuesof weight are typically 3.85 × higher than 1/stddev of real and imaginary parts.J. THE AZIMUTHALLY AVERAGED RADIAL PROFILES GENERATED BY THE MCMC MODEL FITTINGAND MCRT MODELINGFigure 17 shows the azimuthally averaged radial profile at r <
20 au generated by the MCMC model fitting andMCRT modeling in § § Andrews, S. M., Wilner, D. J., Espaillat, C., et al. 2011,ApJ, 732, 42, doi: 10.1088/0004-637X/732/1/42Andrews, S. M., Huang, J., P´erez, L. M., et al. 2018, ApJL,869, L41, doi: 10.3847/2041-8213/aaf741Baruteau, C., & Zhu, Z. 2016, MNRAS, 458, 3927,doi: 10.1093/mnras/stv2527Beckwith, S. V. W., & Sargent, A. I. 1991, ApJ, 381, 250,doi: 10.1086/170646 Beckwith, S. V. W., Sargent, A. I., Chini, R. S., & Guesten,R. 1990, AJ, 99, 924, doi: 10.1086/115385Benac, P., Matra, L., Wilner, D. J., et al. 2020, arXive-prints, arXiv:2011.03489.https://arxiv.org/abs/2011.03489Bergin, E. A., Du, F., Cleeves, L. I., et al. 2016, ApJ, 831,101, doi: 10.3847/0004-637X/831/1/101Blum, J., & Wurm, G. 2008, ARA&A, 46, 21,doi: 10.1146/annurev.astro.46.060407.145152 Hashimoto et al.
16 18 20 22 24 26 28 1 10 100 1000 10000 r g a p1 ( a u ) Step Number
Figure 13.
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92 96 100 104 108 0.6 1.2 1.8 2.4 0.6 1.2 1.8 2.4-0.8 0.0 0.8 1.6 2.4-0.8 0.0 0.8 1.6 2.4 60.9 63.8 66.7 69.617.4 20.3 23.2 26.11.16 2.32 3.48 4.64 29 58 87 11629 58 87 1162.0 4.0 6.0 8.02.0 4.0 6.0 8.00.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 100.1 104.4 108.8 113.174.0 78.3 82.7 87.032 34 36 3830 40 50 60 70144 152 160 168 176144 152 160 168 176
FWHM θ ,blob = 45.38 −2.81+3.23 FWHM r ,blob = 1.71 −0.49+1.03 i inner disk = 26.67 −1.41+7.62 i system = 36.11 −0.23+0.44 r blob = 23.65 −1.64+0.83 −0.45+0.51 θ blob = 9.37 PA inner disk = 157.26 −2.60+3.53 δ1 = 0.24 −0.05+0.03 δ2 = 0.012 −0.000+0.000 r gap3 = 83.07 −0.45+0.51 r gap4 = 111.51 −1.40+1.76
20 40 60 80 160 240 320 400 4801.16 2.32 3.48 4.643 6 9 1217.4 20.3 23.2 26.1 F blob = 220.0 −10.6+28.4 γ p,2 = 2.30 −0.11+0.07 γ p,1 = 1.87 −0.11+0.12 γ e,1 = 1.63 −0.19+0.13 γ e,2 = 1.04 −0.03+0.03 r c −5.65+4.62 r c2 = 118.72 −21.26+7.23 r cav = 3.22 −0.12+0.31 −0.03+0.09 r gap1 = 21.25 r gap2 = 69.24 −1.42+0.71 δ4 = 3.40 −0.23+0.28 δ3 = 2.08 −0.13+0.16 F total = 94.74 −1.74+0.82 PA system = 156.31 −0.48+0.32 Figure 14.
Histograms showing marginal distributions of the MCMC posteriors for 25 free parameters calculated in ourmodeling in § Hashimoto et al.
Negative Positive (b) Image with subtracting modeled disk(a) Image with subtracting 180°-rotated disk ″ (145 au) NE1 ″ (145 au) NE Figure 15.
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Figure 16.
Midplane temperature of large and small dust grains in the fiducial model calculated in the MCRT modeling in § Hashimoto et al. S u rf ace b r i gh t n e ss ( m J y / a r c s ec ) Radius (au)MCRT modeling MCMC model fitting Figure 17.
Radial profiles of modeled dust continuum images generated by MCMC model fitting and MCRT modeling. Theprofile in the MCMC model fitting at 3 au < r <
20 au is described as I ( r ) ∝ (cid:0) r .
88 au (cid:1) − . exp (cid:104) − (cid:0) r .
88 au (cid:1) . (cid:105) in §§