Investigating the gas-to-dust ratio in the protoplanetary disk of HD 142527
Kang-Lou Soon, Munetake Momose, Takayuki Muto, Takashi Tsukagoshi, Akimasa Kataoka, Tomoyuki Hanawa, Misato Fukagawa, Kazuya Saigo, Hiroshi Shibai
aa r X i v : . [ a s t r o - ph . E P ] S e p Investigating the gas-to-dust ratio in theprotoplanetary disk of HD 142527
Kang-Lou S
OON , Munetake M OMOSE , Takayuki M UTO , TakashiT SUKAGOSHI , Akimasa K ATAOKA , Tomoyuki H ANAWA , MisatoF UKAGAWA , Kazuya S AIGO and Hiroshi S HIBAI College of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512, Japan Division of Liberal Arts, Kogakuin University, 1-24-2 Nishi-Shinjyuku, Shinjyuku-ku, Tokyo163-8677, Japan National Astronomical Observatory Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, Chiba263-8522, Japan Department of Earth and Space Science, Graduate School of Science, Osaka University,1-1, Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan ∗ E-mail: [email protected]
Received h reception date i ; Accepted h acception date i Abstract
We present ALMA observations of the . dust continuum and the CO J = 1 − and C O J = 1 − line emissions of the protoplanetary disk associated with HD 142527. The . continuum shows a strong azimuthal-asymmetric distribution similar to that of thepreviously reported
336 GHz continuum, with a peak emission in dust concentrated region inthe north. The disk is optically thin in both the . dust continuum and the C O J = 1 − emissions. We derive the distributions of gas and dust surface densities, Σ g and Σ d , and thedust spectral opacity index, β , in the disk from ALMA Band 3 and Band 7 data. In the analyses,we assume the local thermodynamic equilibrium and the disk temperature to be equal to thepeak brightness temperature of CO J = 3 − with a continuum emission. The gas-to-dustratio, G / D , varies azimuthally with a relation G / D ∝ Σ − . , and β is derived to be ≈ and ≈ . in the northern and southern regions of the disk, respectively. These results are consistent with he accumulation of larger dust grains in a higher pressure region. In addition, our results showthat the peak Σ d is located ahead of the peak Σ g . If the latter corresponds to a vortex of highgas pressure, the results indicate that the dust is trapped ahead of the vortex, as predicted bysome theoretical studies. Key words: protoplanetary disks — stars: individual (HD 142527) — stars: pre-main sequence —submillimeter: planetary systems Dust particles in protoplanetary disks are the foundations of planet formation (Armitage 2010).In the minimum-mass Solar Nebula model, gas and dust particles are distributed smoothly ina radial direction, with surface densities that follow a piecewise power law (Weidenschilling1977b; Hayashi 1981). The high angular resolution observations by the Atacama LargeMillimeter/submillimeter Array (ALMA), however, revealed complicated morphologies in pro-toplanetary disks as traced by the dust continuum and molecular line emissions, such as dust-depleted gaps, spiral-arms, and crescent-like distributions (Casassus et al. 2013; van der Marelet al. 2013; Isella et al. 2013; P´erez et al. 2014; ALMA Partnership et al. 2015; van der Marelet al. 2016; Nomura et al. 2016; Boehler et al. 2018; Andrews et al. 2018; Tsukagoshi et al.2019). These observations also show that the spatial distributions of the gas and dust are notnecessarily similar, thus resulting in a gas-to-dust ratio that spatially varies within the disks.Various mechanisms in protoplanetary disks can lead to a different evolution of thegas and dust and thus result in spatial variation of the gas-to-dust ratio. For example, dustparticles can lose their angular momentum due to gas-dust friction and radially drift towardsthe central star (Weidenschilling 1977a). The gas-dust friction may also result in the settling oflarger grains toward the disk midplane (Dominik et al. 2007; Pinte et al. 2016). Dust filtrationmay also occur at the edges of gaps in the dust that has been cleared by planets, in whichsmaller particles migrate inward to the disk inner region while larger particles are retainedat the edges (Rice et al. 2006). Large-scale high pressure gas vortices can also trap dustparticles in the azimuthal direction, which may explain the asymmetric structure observed insome protoplanetary disks (Barge & Sommeria 1995; Klahr & Henning 1997; Birnstiel et al.2013; Zhu & Baruteau 2016; Baruteau & Zhu 2016). Other mechanisms that can change the gas-to-dust ratio are the growth and fragmentation of dust particles near the snowline (Zhang et al.2015; Okuzumi et al. 2016), as well as secular gravitational instability (Takahashi & Inutsuka2014; Takahashi & Inutsuka 2016). In these cases the dust particles tend to accumulate inconcentric rings around the star. Gas may also be dispersed from the disk by photoevaporation,creating regions with a low gas-to-dust ratio within several astronomical units of the inner disk,favorable for planet formation (Gorti et al. 2015). The existence of one or several planets canalso dramatically alter the gas and dust disk structure (Dipierro et al. 2016; Kanagawa etal. 2016; Dong et al. 2017). While the dominant mechanisms that result in the distributionof the gas-to-dust ratio may differ from disk to disk, the ratio may provide clues concerningthe processes that lead to the observed disk structures and is crucial in understanding theback-reaction from dust to gas if the ratio is low (Gonzalez et al. 2017; Dipierro et al. 2018).HD 142527 is a binary system consisting of two pre-main sequence stars: the primarystar HD 142527A and the secondary star HD 142527B. The distance to HD 142527 derivedby Arun et al. (2019) based on the
Gaia observations (Gaia Collaboration et al. 2016; GaiaCollaboration et al. 2016) is 157 pc ± − F7IIIe (Malfaitet al. 1998; van den Ancker et al. 1998) star with a mass of approximately 2 . M ⊙ and age of2 .
96 Myr (Fukagawa et al. 2013; Arun et al. 2019). The secondary star is a M dwarf with a massof 0 . M ⊙ , which orbits around the primary star at an angular distance of approximately 0 . ′′ + hint at the existence of gas filaments across this gap, through which the materialis funneled from the outer disk to the inner disk (Casassus et al. 2013). The accretion rateis estimated to be 10 − M ⊙ yr − (Mendigut´ıa et al. 2014). Near infrared images show thatthere are at least six spiral arms in the outer disk (Avenhaus et al. 2014). From the differentspatial distribution of emission seen at the near- and mid-infrared wavelengths, the outer diskis thought to be inclined to the line-of-sight, with the northeastern half appearing to be thefurthest and the southwestern half the nearest (Fukagawa et al. 2006; Fujiwara et al. 2006).The inclination angle of the outer disk and the position angle of the disk major axis have beenderived as 27 ◦ and 161 ◦ , respectively, from the kinematics traced by the CO J = 3 − ◦ relative to the outer disk (Marino et al. 2015). The inner disk shadows the northern andsouthern regions of the outer disk from stellar irradiation causing a drastic drop in the intensityof infrared wavelengths in the two regions (Avenhaus et al. 2014). At the submillimeter and3onger wavelengths, the dust continuum emission of the outer disk shows a crescent structurein which the northern region is significantly brighter than the southern region (Fukagawa et al.2013; Casassus et al. 2015). Simulations by Price et al. (2018) show that the observed featuresof the disk (e.g., spiral arms, cavity, HCO + streamers) may be explained by just consideringthe interaction between the disk and the binary system. Their results also predict that thedisk-binary interaction can create the asymmetric dust disk without invoking a gas vortex inthe disk northern region (see also Ragusa et al. 2017).In previous research, Muto et al. (2015) and Boehler et al. (2017) derived the gas anddust surface densities and the gas-to-dust ratio of the outer disk of HD 142527 by modelingALMA observations at Band 7. This research focused on the northern and southern regions ofthe outer disk, which correspond to the sectors where the dust continuum emission is brightestand faintest at Band 7, respectively. The gas-to-dust ratio was derived to be ∼ ∼
30 in thenorthern and southern regions, respectively, and the results indicate that dust is concentrated inthe northern region. However, discussions concerning the detailed spatial variations in the gas-to-dust ratio were beyond the scope of these papers as only two regions were studied. Herein,we extend on previous studies by deriving the spatial distribution of the gas-to-dust ratio acrossthe outer disk of HD 142527. We assume the local thermal equilibrium and derive the gas anddust surface densities by using ALMA observations of the CO and C O molecular line anddust continuum emissions, at both Band 3 ( ν ≈
100 GHz) and Band 7 ( ν ≈
330 GHz).This paper is organized as follows. In Section 2 we introduce the ALMA Band 3 dataas well as the previously published ALMA Band 7 data for the HD 142527 system. In Section3, we present the calibrated images of the ALMA Band 3 data and compare them to that fromBand 7. We describe the methods used to derive the gas and dust surface densities in Section4 and discuss the results in Section 5. Section 6 provides a summary of our research.
We used the ALMA Cycle 2 Band 3 and Cycle 0 Band 7 observational data of HD 142527 toinvestigate the distribution of the gas-to-dust ratio in the disk. The observational details aredescribed in the following subsections. Project code: ADS/JAO.ALMA Project code: ADS/JAO.ALMA .1 ALMA band 3 data Band 3 data were taken at seven execution blocks carried out on the nights of the 4th, 5th,and 15th July 2015. Depending on the block, the bandpass calibrator used was either theJ1427 − − − . The flux of the quasar J1427 − . ≈
20 days from the late June to the early August in 2015, and judging from these results, theflux variation during the observation period should be less than 10%. For all the executionblocks J1604 − .
94 hours and the number of 12 m antennas involved were 37to 40, thereby forming a range of baselines between 25 .
05 m and 1566 .
19 m.The ALMA correlator was configured to store linear XX and YY polarizations in fourseparate spectral windows. Two spectral windows were optimally configured for the continuumobservation with frequencies centered at 97 .
50 GHz and 99 .
50 GHz, and both had an effectivebandwidth of 1 .
875 GHz. The other two windows, each having 3840 channels, were centeredat 109 .
78 GHz and 110 .
19 GHz to target the J = 1 − O and CO with aspectral resolution of 15 .
259 kHz (∆ v ≈ .
04 km s − ).We used CASA version 5.1.0 to image the calibrated visibility and combined the twowide band spectral windows to obtain a continuum centered at 98 . .
5) and deconvolution scale parameters of 0 (corresponding to a point source), 1,and 2 times the average beam size. These parameters are constant throughout the imagingprocess. In order to improve the signal-to-noise ratio, we performed self-calibration to thecontinuum image as follows. First, we solved the gain phase of the initial CLEAN modelfor the continuum image starting from a time interval equal to the total time duration ofeach scan (which is between 2 minutes and 7 minutes) of the target, followed by shorter timeintervals in the order of 240 s, 120 s, and 60 s. After every phase calibration, we performedCLEAN to the continuum image to obtain a new model that could be used in the succeedingphase calibration. Once the phase calibration was completed, we solved the gain amplitudeof the last phase-calibrated model at a time interval equal to the time duration of each scan.Lastly, we applied the phase-calibrated and gain-calibrated models to the visibility data of The source name for J1427 − −
421 by mistake in the execution block of ADS/JAO.ALMA . σ = 9 . µ Jy beam − is reached. Thesynthesized beam in full width at half maximum (FWHM) of the final image is 0 . ′′ × . ′′ . A . = 78 . ◦ .Before imaging the J = 1 − CO and C O, we applied the phaseand amplitude solutions that were derived from the self-calibration to the visibility data of thecontinuum to these CO visibility data. We used Briggs weighting and multiscale deconvolution,similar to the continuum imaging. We then smoothed the frequency channels to an equivalentvelocity resolution of 0 .
30 km s − . The velocity resolution is set at a slightly smaller value thanthe observed velocity dispersion, which is approximately 0 . − as shown in figures 3 and4 of Muto et al. (2015) as well as in figure 3(d) in this paper, to reveal the emission with thebest sensitivity. Finally, we applied a CASA task imsmooth to smooth the image cubes of COand C O so that they had the same angular resolution in the 98 . . ′′ × . ′′
44 (P . A . = 78 . ◦ ). The noise level is σ = 2 . − .We also created a spectral cube of ∆ v = 0 .
12 km s − for both the CO and C O lineemissions to derive their peak brightness temperature. The beam size was also smoothed tomatch that of the 98 . σ = 2 . − . The observational setup and calibration process of the Band 7 data are described in detail byFukagawa et al. (2013) and Muto et al. (2015). In this study, we use the calibrated imagesof the 336 GHz continuum and the CO J = 3 − O J = 3 − .
12 km s − . The synthesizedbeams of the Band 7 images are smaller than that from Band 3, so we applied imsmooth tothe Band 7 images to obtain a spatial resolution identical to that of the Band 3 images, i.e., asynthesized beam of 0 . ′′ × . ′′
44 (P . A . = 78 . ◦ ) The resultant noise rms was 150 µ Jy beam − for the continuum, and 5 . − and 7 . − for the CO and C O imagecubes, respectively. 6 − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) . − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b)
336 GHz continuum (mJy beam − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectral index α − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (d) . . . . . . . . . . . . . . − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (e) . . . . . . . . . . . .
336 GHz continuum (K)
Fig. 1: Images of the 98 . − , while panels (d) and(e) in units of Kelvin. North is up and east is to the right. The white contours denote the 5 σ level, which is 48 µ Jy beam − or 0 .
91 K for the 98 . µ Jy beam − or 2 .
63 Kfor the 336 GHz images. The spectral index α derived from these dust continuum emission isshown in panel (c). The white ellipse at the bottom left corner indicates the synthesized beam(0 . ′′ × . ′′
44, P . A . = 78 . ◦ ). . continuum emission The dust continuum emissions of the disk surrounding HD 142527 at 98 . λ = 3 . λ = 0 .
89 mm) are shown in figure 1. The bottom panels in figure 1 present thedust continuum emission in terms of brightness temperature T B (in units of Kelvin), which wasconverted from the flux density F d (in units of mJy beam − ) using the inverse of the Planckfunction 7 − − − − − . A . ( ◦ )05 (4 . (7 . (10 . I d , . ( m J y b e a m − ) . (10 . (15 . (20 . (25 . I d , ( m J y b e a m − ) . Fig. 2: Dust continuum emission at 98 . . A . . The values in the parentheses denote theequivalent brightness temperature derived from the beam size of 0 . ′′ × . ′′
44. The error barsdenote the standard deviation of the averaged intensity.
Table 1: Maximum and minimum of the 98 . . r, P . A . ) † (1 . ′′ , ◦ ) (1 . ′′ , ◦ ) (1 . ′′ , ◦ ) (1 . ′′ , ◦ ) F d (mJy beam − ) ‡ . ×
10 1 . × − . × . × T B (K) ‡ . . . . ≡ Max / Min 58 . . † The coordinates ( r, P . A . ) indicate the center of an area of radial size 0 . ′′ ◦ . ‡ The standard deviations (not shown) of flux density F d and brightness temperature T B inthe area centered at ( r, P . A . ) are less than 1% of their mean values. T B = hνk " ln hν c F d / Ω + 1 ! − , (1)where c , h , and k denote the speed of light, the Planck constant, and the Boltzmann constant,respectively. The solid beam angle Ω is defined asΩ = πθ maj θ min , (2)where θ maj and θ min are the FHWM of the beam major and minor axes, respectively. Thesignal-to-noise ratio of the peak continuum flux at 98 . . σ level, is 72 . . .
476 mm) obtained with the Australia8elescope Compact Array (ATCA) at a coarser beam of 16 . ′′ × . ′′ . ± . µ m and 3 .
476 mm is derived to be ≈ . . . . ≈
76 au) marginallyresolves the disk in the radial direction. The 98 . σ level, and it shares a similar distribution withthat observed at 336 GHz, i.e., the outer disk exhibits a crescent-like structure as a result of theconcentration of dust in the northern region. Hereafter, we use the word ridge to refer to theline that connects the radial peak of a physical quantity in every P . A . direction (as seen fromthe central star) on the outer disk. To search for the maximum and minimum values along theridge, the averaged values from an area of radial size 0 . ′′ ◦ with coordinatesindicated by ( r, P . A . ) will be used. The maximum and minimum values of the continuumemission along the ridge are listed in Table 1. The contrast of the 98 . . > ∼
1, hence its emission is saturated (Casassuset al. 2015). The lower optical depth at 98 . T B , i.e.,8 . . α is defined as α ≡ log " F d , F d , . log (cid:20)
336 GHz98 . (cid:21) , (3)and is shown in figure 1(c). The index varies smoothly in the azimuthal direction; in thenorthern region α ≈ .
8, while in the southern region α ≈ .
4. When the Rayleigh-Jeansapproximation is valid, the flux density is proportional to ν β , where β is the dust opacityspectral index. The smaller value of α might indicate a smaller β (Beckwith et al. 1990;Beckwith & Sargent 1991; Miyake & Nakagawa 1993), but the spectral slope also gets flatteras the optical depth at 336 GHz gets higher. We will derive β and optical depth from the dustcontinuum images at 98 GHz and 336 GHz in Section 4.1.Figure 2 shows the flux density of the continuum emission on the ridge as a function ofP . A . . A dip in intensity at P . A . ∼ ◦ is seen at 336 GHz, rendering the emission morphology tobe a double-peaked structure; however, there is no dip at the same P . A . direction at 98 . . A . ∼ ◦ (as well as at P . A . ∼ ◦ , see Avenhaus et al. 2014) and is thought to be the result of a shadowfrom a warped inner disk (Marino et al. 2015). On the other hand, the 98 . CO J = 1 − line emission Figure 3 displays the moment maps of the CO J = 1 − . CO 0th-moment is observed tohave a wider radial extent of approximately 3 arcsec and is more axisymmetric. The contrastbetween the north and the south is approximately 1 .
4; the ridge in the 0th-moment map hasa maximum at (0 . ′′ , ◦ ) where the integrated intensity is F int = 71 . − km s − anda minimum at (1 . ′′ , ◦ ) where F int = 49 . − km s − . In the northern region, theridge of the 0th-moment is located inwards of that associated with the continuum emission,which is owing to the higher optical depth of the CO line.Figures 4(a) and (c) show the peak T B of the CO J = 1 − .
12 km s − . Figure 4(a) shows the peak T B of the line emission after subtracting the contin-uum level; the continuum level is estimated from the line free channels of the spectral windowcontaining the CO line emission, which is centered at 110 . T B of CO including the 110 . T B in figure 4(a) shows a dip in the northern region where the dustcontinuum emission is brightest. This is similar to the J = 3 − CO, CO(figure 4b), and C O (figure 6b) (Fukagawa et al. 2013; Perez et al. 2015; Boehler et al. 2017),as well as that of HCN J = 4 − J = 7 − T B of CO with the continuum emission included, shown in figure4(d), has a higher brightness temperature in the north and there is no dip observed at the peak10 − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) - moment (mJy beam − · km s − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b) . . . . . . . - moment (mJy beam − · km s − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (c) . . . . . . . . . . . . . . . . . . . . . . . - moment (km s − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - moment (km s − ) Fig. 3: Moment maps of the CO J = 1 − v = 0 .
30 km s − . The white ellipse in the left bottom corner indicates thesynthesized beam, which is identical to that of the 98 . . ′′ × . ′′ . A . = 78 . ◦ ). The moment maps are created from velocity channels in the range of v lsr =1 . − − . − (see Appendix 1) after applying a Keplerian mask in the channels andthen clipping emissions lower than 3 . σ ( σ = 2 . − ). In panel (b), the 98 . − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) . . . . . . . . . . CO J = 1 − T B (K) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b) . . . . . . . . . . . . . CO J = 3 − T B (K) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (c) . . . . . . . . . . . . . . CO J = 1 − T B with continuum (K) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (d) . . . . . . . . . . . . CO J = 3 − T B with continuum (K) Fig. 4: Peak surface brightness of CO; the left and right panels show the peak T B of the J = 1 − J = 3 − T B aftersubtracting the continuum. The black contours in panel (a) denote the narrow-band continuumemission (see text for details), while those in panel (b) denote the 336 GHz continuum emissionas shown in figure 1(d). The maps in the bottom row are the peak T B with the continuumemission. In panels (a) and (c), the white contours denote the 3 . σ level, which are 6 .
56 K and6 .
74 K, respectively. In panels (b) and (d), the white contours denote the 5 σ level, which are6 .
91 K and 6 .
97 K, respectively.of the continuum emission. In each P . A . direction, the peak T B of CO J = 1 − T B = (26 −
40) K; it is similar to that of the CO J = 3 − . A . = 200 ◦ − ◦ where the peak T B of CO J = 1 − T B ≈
26 K, compared to that of CO J = 3 −
2, which is12 − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) - moment (mJy beam − · km s − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b) . . . . . . . - moment (mJy beam − · km s − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . - moment (km s − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - moment (km s − ) Fig. 5: Similar to figure 3, for the C O J = 1 − v = 0 .
30 km s − . The synthesized beam has the same size and shape as that of the 98 . . ′′ × . ′′
44, P . A . = 78 . ◦ ) The moment maps are created from velocitychannels in the range of v lsr = (1 . − .
7) km s − (see Appendix 1), after applying a Keplerianmask in the channels and then clipping emissions lower than 3 . σ ( σ = 2 . − ). T B ≈
36 K, suggesting that the J = 1 − O J = 1 − line emission Figure 5 displays the moment maps of the C O J = 1 − CO J = 1 − CO, the C O is confined in a narrower radial extent of r ≈ . ′′ − . ′′
0. This is becauseof the weaker emission of C O J = 1 −
0. In the southwestern region of P . A . = 180 ◦ − ◦ ,the emission is much weaker and is below 10 σ .13 − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) . . . . . . . . . . C O J = 1 − T B (K) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b) . . . . . . . . . . . . . C O J = 3 − T B (K) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (c) . . . . . . . C O J = 1 − T B with continuum (K) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (d) . . . . . . . . . . CO J = 3 − T B with continuum (K) Fig. 6: Similar to figure 4, for the C O J = 1 − J = 3 − J = 1 − . σ level, which are 6 .
53 K and 6 .
70 K, respectively.In panels (b) and (d), the white contours denote the 5 σ level, which are 6 .
32 K and 6 .
38 K,respectively.The peak of the 0th-moment in figure 5(a) is located at (0 . ′′ , ◦ ), close to the continuumpeak with F int = 28 . − km s − . The ridge of 0th-moment is lowest at (0 . ′′ , ◦ )where F int = 6 .
95 mJy beam − km s − . The contrast of the ridge is thus 4 . O J = 1 −
0, while figure 6(c)shows the peak T B with the continuum emission. The continuum emission in figure 6(a) iscentered at 109 . O J = 1 − CO J = 1 − J = 3 −
2, as well as that of the C O J = 3 − O J = 1 − T B is ≈
25 K in the north while it is ≈
10 K in the south, and its distribution issimilar to that of the continuum emission.
In this section, we derived the gas and dust surface density for the disk of HD 142527 under theassumptions of local thermodynamic equilibrium (LTE). We do not consider dust sedimentationat the midplane and assume that the gas and dust are well-mixed in the disk. We assume thephysical temperatures of the gas and dust, T d and T g , to be identical. These temperaturesare taken from the peak T B of CO J = 3 − CO J = 3 − . A . = 161 ◦ − ◦ ) is closest to us while the eastern region is the furthest from us.The disk temperature at the far side is higher by about 3 K, since the surface of the disk thatis irradiated by the central star is exposed to us. The disk is assumed to be isothermal in avertical direction. A model where T d is assumed to be 80% of T g is discussed in Appendix 2. The dust surface density is derived from Σ d = τ d /κ d , where τ d is the optical depth of the dustcontinuum emission and κ d is the dust opacity. We first calculate τ d at 98 . I d = [ B ν ( T d ) − B ν ( T bg )] [1 − exp( − τ d )] , (4)where I d denotes the intensity of the continuum emission, B ν is the Planck function, T bg = 2 . τ d at 98 . .
24 and is co-spatial to its peak continuum emission. On theother hand, peak τ d at 336 GHz is 0 .
82, and is located at the western component of the double-peaked structure seen at the 336 GHz emission; this is due to the lower disk temperature atthe near side. The dust opacity is highly uncertain and depends on the particle compositions,15tructures, as well as size distributions (Miyake & Nakagawa 1993; Draine 2006; Kataoka etal. 2014; Birnstiel et al. 2018); in the analyses, we adopt the canonical dust opacity (per dustmass) κ d described by Beckwith et al. (1990), κ d = 10 (cid:18) ν Hz (cid:19) β cm g − , (5)where β is the dust opacity spectral index and is calculated from the τ d distributions via β = log " τ d , τ d , . log (cid:20)
336 GHz98 . (cid:21) (6)and shown in figure 7(c). The opacity index varies throughout the disk; in the southern region, β is close to the interstellar value of 1 . ≈
1. The β in the north can be interpreted as the consequence of the growthof dust grains and is qualitatively consistent with the modeling results based on polarizationobservations (Ohashi et al. 2018). Dust scattering can strongly depend on the dust compositionsand structures (Tazaki et al. 2016; Tazaki & Tanaka 2018), but we have ignored it in thisstudy. This is because the observed intensity does not depend strongly on the dust scatteringif the scattering opacity is comparable to the absorption opacity, and the modeling of the dustcontinuum map shows that this is the case in the lopsided disk around HD 142527 (Soon et al.2017; Boehler et al. 2017).Figure 8(a) shows the derived dust surface density Σ d . Along the ridge of Σ d , themaximum is located at (1 . ′′ , ◦ ) where Σ d = 3 . × − g cm − and the minimum is locatedat (1 . ′′ , ◦ ) where Σ d = 9 . × − g cm − . The derived spatial location of the peak Σ d doesnot correspond to that of the peak continuum emission at 98 . β distribution.Similarly, because of the temperature and β distributions, the derived Σ d ridge contrast of 33is lower than that of the 98 . . A . = 16 ◦ − ◦ (north P . A . sector) and P . A . = 216 ◦ − ◦ (south P . A . sector) using adisk model, in which the peak dust surface densities are 0 .
65 g cm − in the north sector and0 .
012 g cm − in the south sector (see Figure 13 and Table 1 of their paper). Their modeling isbased on the ALMA observations with a beam of 0 . ′′ × . ′′
21. By convolving the models of dustsurface density derived by Boehler et al. (2017) with the beam size of our ALMA observations(i.e., 0 . ′′ × . ′′
44, P . A . = 78 . ◦ ), the peak dust surface densities in the north and south P . A . sectors are derived to be ≈ . − and ≈ .
006 g cm − , respectively. After correcting for16 − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) . . . . .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 . τ d at 98 . − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b) . . . . .
00 0 .
20 0 .
40 0 .
60 0 .
80 1 . τ d at 336 GHz − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Opacity index β Fig. 7: Optical depth τ d of the (a) 98 . β derived from Equation (6) is shown in panel (c).the difference in dust opacity , these correspond to ≈ . − and ≈ .
009 g cm − . Whileour results in the south P . A . sector agrees with Boehler et al. (2017), our results for the northP . A . sector, i.e., Σ d ≈ . − , is approximately 70% of that derived by Boehler et al. (2017).This inconsistency may be due to the high optical depth of the dust continuum in the northernregions; the inherent uncertainty in the estimate on Σ d is large (Soon et al. 2017). Furthermore,omitting the dust scattering may underestimate Σ d , and hence the Σ d ridge contrast (Soon etal. 2017; Birnstiel et al. 2018). We derived the disk H gas surface density Σ g from the J = 1 − J = 3 − O by assuming the interstellar abundance χ (C O / H ) = 1 . × − (Wilson 1999); thevalidity of the abundance is discussed in Section 5.3. The J = 3 − g in the region of P . A . = 180 ◦ − ◦ , where the J = 1 − τ g in the velocity channels is calculated from theradiative transfer equation, which is similar to Equation (4) but takes the form I g = [ B ν ( T g ) − B ν ( T bg )] [1 − exp( − τ g )] exp( − τ d ) , (7)i.e., the factor exp( − τ d ) is included to account for the line emission absorbed by the dust. Here, τ d is the optical depth of the narrow-band continuum emission at 109 . O J = 1 − Boehler et al. (2017) use a constant dust absorption opacity of . − . The dust opacity κ d used in this study are ≈ . − and ≈ . − in the north and south P . A . sectors, respectively. − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) . . . . . . .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 .
30 0 . Σ d (g cm − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b) . . . . . . . . . . . Σ g (g cm − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (c) G / D ≡ Σ g / Σ d − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (d) . . . . . G / D ≡ Σ g / Σ d Fig. 8: Derived results of (a) dust surface density Σ d , (b) gas surface density Σ g , and (c)gas-to-dust ratio G / D ≡ Σ g / Σ d . In panel (d) the contours of Σ d in panel (a) are superimposedon the G / D image.equation is applied to the C O J = 3 − τ d refers to the336 GHz continuum emission, i.e., the continuum image in figure 1(b). The optical depth τ g isrelated to the total (particle number) column density N tot of the CO isotopologue by N tot = 3 h π µ J u kT ex hB + 13 ! exp (cid:18) E J u kT ex (cid:19) × " exp hνkT ex ! − − X [ τ g ( v )∆ v ] cm − , (8)where µ , J u , and B , are the dipole moment, the rotational quantum number of the linetransition upper level, and the rigid rotor rotational constant, respectively (Mangum & Shirley2015). The excitation temperature T ex is equal to T g in the LTE analysis. The gas surfacedensity is then calculated by Σ g = m H N tot /χ , where m H is the molecular mass of H .Figure 8(b) shows the derived results of Σ g . At P . A . = 180 ◦ and P . A . = 240 ◦ , the surface18ensity derived from the C O J = 1 − O J = 3 − g derived from the two lines. Along the ridge of Σ g , themaximum is located at (1 . ′′ , ◦ ) where Σ g = 9 . × − g cm − , while the minimum is locatedat (1 . ′′ , ◦ ) where Σ g = 1 . × − g cm − . The contrast between the two directions isapproximately 5, similar to the contrast of the C O J = 1 − .
125 g cm − and 0 . − in the northand south P . A . sectors, respectively. Similar to the beam convolution performed to the modeldust surface density in discussed in Section 4.1, after convolving the model gas surface densityderived by Boehler et al. (2017) with our observations beam size the peaks are derived to be ≈ . − and ≈ . − . Our results are thus consistent with those derived by Boehleret al. (2017).Along the ridge of CO J = 1 − . A . = 200 ◦ − ◦ , τ g can also be solvedfrom Equation (7). Within this P . A . and the radial range r = 0 . ′′ − . ′′
6, the column densityderived from the CO J = 1 − O J = 3 − N tot ( CO) = (1 . ± . × cm − and N tot (C O) = (1 . ± . × cm − , respectively; the uncertaintiesonly include the propagation of 1 σ noise level. The ratio N tot ( CO) /N tot (C O) is derived tobe 9 . ± .
67, and it agrees with the value of the local interstellar medium (8 . ± .
1) withinthe uncertainty (Wilson 1999).
Figure 8(c) shows the G/D, defined as the ratio of Σ g to Σ d ; figure 10(c) shows the sameresults in polar coordinates. The estimated G / D is ∼ ∼
20 in the northern and southernregions, respectively, and G / D gradually varies along the azimuthal direction. Our resultsare consistent with the modeling results by Muto et al. (2015) and Boehler et al. (2017), butthey only focused on two sectors centered at P . A . = 21 ◦ and P . A . = 221 ◦ . We successfullyderived the projected G / D distribution across the disk and found that G / D in the outer diskvaries along the azimuthal direction. The low G / D in the northern region may be importantin the formation of planetesimals (Lambrechts & Johansen 2012; Raettig et al. 2015). Two-dimensional simulations predicted that a vortex would be destroyed by the dust back reactionwhen G / D got low (Fu et al. 2014), but succeeding three-dimensional simulations have shownthat this effect disappears (Lyra et al. 2018).Figure 9(a) shows the relation between Σ g and Σ d on the dust ridge, where the peak T B − − − Σ d (g cm − )10 − Σ g ( g c m − ) (a) Σ g = (1 . ± . (cid:18) Σ d .
10 g cm − (cid:19) . ± . G / D = G / D = G / D = P . A . sector (000 ◦ , ◦ )(060 ◦ , ◦ )(120 ◦ , ◦ ) (180 ◦ , ◦ )(240 ◦ , ◦ )(300 ◦ , ◦ ) − − − τ d − Σ g ( g c m − ) (b) Σ g = (1 . ± . (cid:18) τ d . (cid:19) . ± . P . A . sector (000 ◦ , ◦ )(060 ◦ , ◦ )(120 ◦ , ◦ ) (180 ◦ , ◦ )(240 ◦ , ◦ )(300 ◦ , ◦ ) Fig. 9: Panel (a) shows the correlation between the gas surface density Σ g and the dust surfacedensity Σ d ; the gray lines indicate the gas-to-dust ratio of G / D = 1 , , g and the dust optical depth at 98 . τ d . The best-fit powerlaw of exponent p is drawn as red dashed line. In both panels, the data points are averagedvalues in a bin of angular size 20 ◦ and radial size 0 . ′′
5, and the error bars indicate the standarddeviation of the values in the bin. The colors of the data points denote the P . A . of the points.of CO J = 3 − p (indicated in the top left corner of theplots) is p = 0 .
47. The relation Σ g ∝ Σ p d corresponds to G / D ∝ Σ p − , and therefore figure 9(a)suggests that G / D varies approximately with ∝ Σ − . . This relation may be a critical test forfuture theoretical studies to understand the trapping efficiency of dust grains and the origin ofthe asymmetric disk structure around HD 142527.Figure 9(b) is similar to figure 9(a), but with the horizontal axis replaced by the dustoptical depth at 98 . p = 0 . β (or κ d ) as shown in figure 7(c). Figure 10 compares the spatial distributions of Σ g and Σ d in the polar coordinates. From figures3(c), 5(c), and the infrared images (Fujiwara et al. 2006), the disk is thought to be rotating ina clockwise rotation. Comparing figures 10(a) and 10(b), we see that the peak Σ d is located atP . A . ≈ ◦ , which is downstream of the peak Σ g located at P . A . ≈ ◦ . If the northern regionof high Σ g corresponds to a vortex with higher pressure, then the dust will accumulate at aregion shifted ahead of the vortex. This picture is consistent with the theoretical prediction byBaruteau & Zhu (2016) if the Stokes number, St, of the dust particles is > ∼
1; we estimate the20 a) . . . . . (b) . . . . . . . . (c) (d) . . . . . − − − − − − . A . ( ◦ )0 . . . . . . r ( ′′ ) (e) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Σ g ( g c m − ) . . . . . . . . Σ d ( g c m − ) G / D ≡ Σ g / Σ d . . . . . . . τ d a t . G H z . . . . . . . β Fig. 10: Derived results of (a) gas surface density Σ g , (b) dust surface density Σ d , (c) gas-to-dust ratio G / D, (d) dust optical depth at 98 . β plotted in polar coordinates. The purple dashed line and the gray dotted line in panels (a) and(b) denote the Σ g and Σ d ridges, which are also superimposed on the G / D map in panel (c).21hysical radius of the dust particle s by using equation (1) in the paper by the same authors,i.e., s ≈ . × (cid:18) St1 (cid:19) ρ pc − ! − Σ g . − ! mm , (9)where ρ pc is the internal mass density of the particles. The gas surface density is Σ g ≈ . − where Σ d peaks, and by assuming that ρ pc = 1 g cm − , s > ∼ > ∼ β in the north indicates a particle growth, β ≈ ≈ −
10 mm, and it agrees with the above size estimation. In addition, the estimated sizeis also consistent with the continuum observations at 34 GHz which should be dominated bythermal emission from particles of size ∼ . A . ≈ ◦ (the other is at P . A . ≈ ◦ , Casassus et al. 2015). On theother hand, the dust size estimated here is larger than the estimated size of 150 µ m basedon polarization modeling (Ohashi et al. 2018). One possible explanation to the discrepancyis a segregation of dust size in the disk vertical direction, such that smaller particles (efficientscatterers) float at the upper atmosphere while larger particles (efficient emitters) sediment atthe midplane.Figure 10(d) shows the dust optical depth at 98 . τ d , at polar coordinates.Comparing figures 10(a) and 10(d), we see that the peaks of τ d and Σ g share a similar spatiallocation in the north, which is contrary to the relative distributions of the peaks of Σ d and Σ g .We caution that the derivation of Σ d is highly dependent on κ d , and in this paper we derived Σ d using a κ d whose spatial variation is determined by the β distribution. As shown in Appendix3, our derived parameters of the dust disk can also reproduce the intensity distributions of thecontinuum emission at 700 GHz reported by Casassus et al. (2015). To better disentangle κ d and Σ d , however, radiative transfer modeling of a wider frequency range may be required, andthis is beyond the scope of this study.The observations of asymmetric protoplanetary disk around HD 135444B reveal a fre-quency dependent azimuthal shift in the peak continuum position, which can be interpreted asa consequence of size segregation of dust grains trapped by a vortex (Cazzoletti et al. 2018).Comparing figure 1(a) and (b) (see also Table 1), there is also an azimuthal offset between the98 . β distribution in the outer disk shown in figure 10(e) is nearly mirror symmetric withrespect to P . A . = 0 ◦ , and there is no gradient along the azimuthal direction from upstream todownstream indicative of dust size segregation. The dynamic range of the observed frequencies22n this study may be insufficient to discuss size segregation in the disk (cf. Casassus et al.2015). In a protoplanetary disk, the abundance of CO as relative to H can be lower than that in theinterstellar medium if CO is depleted due to freeze-out onto dust grains. In addition, CO canalso be depleted by photodissociation in the disk upper layer by UV radiation (Miotello et al.2014; Miotello et al. 2016; Miotello et al. 2017). In fact, the gas masses of several T Tauri disksderived from the HD J = 1 − CO, and C O are thus expected to be varying spatially(Shimajiri et al. 2014). In Section 4.2 we derived N tot ( CO) /N tot (C O) to be similar tothe CO to C O ratio in the local interstellar medium; these results might suggest thatisotope-selective photodissociation is insignificant in the case of HD 142527. The abundancesof these isotopologues relative to CO, however, are still currently unknown and therefore furtherinvestigation is required to confirm the photodissociation of CO.Even if the effects of freeze-out and isotope-selective photodissociation are small, theabundance of CO relative to H still remains uncertain if carbon is locked up in other formof molecules. The detail thermochemical models show that the mass conversion from CO toH would be underestimated by a factor of about three to eight (Yu et al. 2016; Yu et al.2017; Molyarova et al. 2017). The depletion of more than a factor of ten, however, is unlikelybecause the gas disk would be gravitationally unstable (Fukagawa et al. 2013). In short, thoughΣ g , G / D, and the dust size estimated from equation (9) may be underestimated, the exponent23 ≈ . g and Σ d remains valid because p does notdepend on the absolute values of Σ g and Σ d . We present the ALMA Band 3 observations of the 98 . CO J = 1 − O J = 1 − ∼ . ′′
5, and compare the results to the ALMA observations at Band 7.The 98 . O J = 1 − / D, of the outer disk. The main conclusions are as follows.1. The 98 . . α is ≈ . ≈ . CO J = 1 − ∼ .
4. The C O J = 1 − . β is derived to be ≈ ≈ . β between the two regions indicate thedifference in dust properties. We use the J = 1 − J = 3 − O and the98 . g and Σ d . We assume the local thermodynamic equilibrium, the interstellar abundance χ (C O / H ) = 1 . × − , and the canonical dust opacity described by Beckwith et al. (1990)by varying β spatially. The derived surface densities are Σ g ∼ . − and Σ d ∼ . − in the northern regions, with results of Σ g ∼ . − and Σ d ∼ .
01 g cm − in the southernregions. The contrast along the Σ g and Σ d ridges are 5 and 33, respectively. The gas-to-dustratio, G / D ≡ Σ g / Σ d , is derived to vary smoothly in the azimuthal direction of the disk,where it is ∼ ∼
20 in the northern and southern regions, respectively.4. By using the results of Σ g and Σ d derived at the Σ d ridge, we found that Σ g varies approxi-mately as Σ . , or equivalently G / D ∝ Σ − . . This relation will be a critical test for futuretheoretical studies to understand the azimuthal-asymmetric disk structure.5. Our results show that the Σ d peak is slightly shifted ahead of the Σ g , which is predicted24y theoretical studies of the trapping of dust by vortices of high gaseous pressures. Theestimated dust size is > ∼ χ (C O / H ) in the disk is similar to the interstellar value.6. The CO J = 1 − . A . = 200 ◦ − ◦ is marginally optically thin, where wederive N tot ( CO) /N tot (C O) = 9 . ± .
67; the value agrees with the interstellar abundanceratio χ ( CO / C O) = 8 . ± . Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers 17H01103 and 18H05441. This paper makes use of the followingALMA data: ADS/JAO.ALMA
Appendix 1 Channel maps of CO J = 1 − and C O J = 1 − Figure 11 shows the channel maps of CO and C O line emission from which the momentmaps shown in figures 3 and 5 are created. When creating the moment maps, we first maskout the regions where Keplerian motion of the disk is not expected in the velocity channels(Salinas et al. 2017; Ansdell et al. 2018), and the emission below 3 . σ in the unmasked regionis then clipped. We adopt a stellar mass of M ∗ = 2 . M ⊙ and a disk inclination of i = 27 ◦ whencreating the Keplerian mask. Appendix 2 Two-layer disk model
To evaluate the uncertainties of G / D and the exponent p , we here adopt a two-layer diskmodel when deriving the surface densities, where the temperature of gas and dust particles aredifferent. The gas temperature T g is assumed to be the same as the brightness temperature atthe peak T B of CO J = 3 − T d , on the other hand, is simply taken to be 80% of the gas temperature acrossthe map; this physical condition mimics the effect of dust sedimentation. The 20% temperaturedrop results in a peak T d ≈
29 K in the dust temperature field. Indeed, this agrees with thepeak dust temperature derived by Casassus et al. (2015) using the continuum observations atBands 7 and 9, and therefore it is a reasonable estimate for the dust temperature.Figure 12 shows the optical depth of the continuum emission at 98 . β derived from the two-layer disk model; they are larger25 .
90 1 .
20 1 .
50 1 . .
10 2 .
40 2 .
70 3 . .
30 3 .
60 3 .
90 4 . .
50 4 .
80 5 .
10 5 . − − − ′′ ) − − − ∆ D e c ( ′′ ) .
70 6 .
00 6 .
30 6 . CO J = 1 − − ) .
90 1 .
20 1 .
50 1 . .
10 2 .
40 2 .
70 3 . .
30 3 .
60 3 .
90 4 . .
50 4 .
80 5 .
10 5 . − − − ′′ ) − − − ∆ D e c ( ′′ ) .
70 6 .
00 6 .
30 6 . C O J = 1 − − ) Fig. 11: The velocity channel maps of the CO J = 1 − O J = 1 − − ) is written in the top left cornerin each channel map. The white ellipse in the bottom left indicates the synthesized beam,which is identical to that of the 98 . . ′′ × . ′′ . A . = 78 . ◦ . σ = 7 mJy beam − and the black contours aredrawn at (20 , , ,
80) mJy beam − . The white shaded regions denote the Keplerian masksused to create the moment maps in figures 3 and 5.than those derived from the one-layer disk model due to the lower temperature. In addition,the larger β results in a smaller dust opacity κ d , where it is smaller than that of the one-layerdisk model by ≈
10% in the disk southern region and by ≈ −
50% in the dust concentratednorthern region.The radiative transfer for the gas molecular line in the two-layer disk model reads I g+d = [ B ν ( T g ) − B ν ( T bg )] [1 − exp( − τ g / B ν ( T d ) − B ν ( T bg )] [1 − exp( − τ g )] exp( − τ g / B ν ( T g ) − B ν ( T bg )] [1 − exp( − τ g / − τ g / − τ d ) , (A1)where I g+d denotes the line emission including the continuum emission (Nomura et al. 2016).In the line of sight, the first term accounts for the line emission from the disk atmosphere at26 − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) . . . . . . .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 . τ d at 98 . − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b) . . . . .
00 0 .
30 0 .
60 0 .
90 1 .
20 1 . τ d at 336 GHz − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Opacity index β Fig. 12: Similar to figure 7, for the results derived from the two-layer disk model.the front side, the second term the dust emission in the disk midplane, while the last term theline emission from the back side that will propagate through the disk midplane and the frontatmosphere.Figure 13 shows the results derived from this two-layer disk model. We mask out thedisk inner region in which the disk temperature is lower than 24 K, i.e., 80% of the temperaturecriteria used to mask out the disk inner region in the one-layer disk model (Section 4). Theoverall distributions of Σ g , Σ d , and G / D are similar to the one-layer disk model; due to thelower κ d , however, in the northern region Σ d is derived to be twice as high as that in theone-layer disk model, and therefore the G / D distribution is derived to be lower. Figure 14(a)shows the correlation between Σ g and Σ d . Similar to figure 9(a) we find a power law with anexponent p = 0 .
44 to be a good fit to the results. The derived value of exponent p is consistentwith that of the one-layer disk model despite the different temperature assumption betweenthese two disk models. Figure 14(b) is analogous to figure 9(b), where the derived values of p are also consistent between the two models. Appendix 3 Mock-up dust continuum image at
700 GHz
By using the dust surface density Σ d distribution derived from the one layer-disk model (figure8a), we create a mock-up image at 700 GHz to compare with the continuum observations at thesame frequency reported by Casassus et al. (2015). We use the same temperature distribution,i.e., the peak T B of CO J = 3 − β distribution (figure 7c) to calculate the dust opacity κ d at 700 GHz (Equation 5).The radiative transfer follows Equation (4). Figure 15 shows the mock-up image. Though27 a) . . . . . (b) . . . . . . . (c) (d) . . . . . . − − − − − − . A . ( ◦ )0 . . . . . . r ( ′′ ) (e) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Σ g ( g c m − ) . . . . . . . . Σ d ( g c m − ) G / D ≡ Σ g / Σ d . . . . . . . τ d a t . G H z . . . . . . . β Fig. 13: Similar to figure 10, but the results are derived from the two-layer disk model. Notethat only the color scale range of (b) is twice wider than that in figure 10(b), while the othershave the same scaling range. 28 − − − Σ d (g cm − )10 − Σ g ( g c m − ) (a) Σ g = (0 . ± . (cid:18) Σ d .
10 g cm − (cid:19) . ± . G / D = G / D = G / D = P . A . sector (000 ◦ , ◦ )(060 ◦ , ◦ )(120 ◦ , ◦ ) (180 ◦ , ◦ )(240 ◦ , ◦ )(300 ◦ , ◦ ) − − − τ d − Σ g ( g c m − ) (b) Σ g = (1 . ± . (cid:18) τ d . (cid:19) . ± . P . A . sector (000 ◦ , ◦ )(060 ◦ , ◦ )(120 ◦ , ◦ ) (180 ◦ , ◦ )(240 ◦ , ◦ )(300 ◦ , ◦ ) Fig. 14: Similar to figure 9, for the results derived from the two-layer disk model. − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (a) . . . . . . . . . . . . . . . . . . . . Mock - up 700 GHz continuum (Jy beam − ) − − − . A . ( ′′ ) − − − ∆ D e c . ( ′′ ) (b) . . . . . . . . . . . . . . . . . Mock - up 700 GHz continuum (K) Fig. 15: The mock-up dust continuum image at 700 GHz. Panels (a) and (b) present the con-tinuum emission in units of Jy beam − and K, respectively. The ellipse in the lower left cornerindicates the beam size (0 . ′′ × . ′′
44, P . A , = 78 . ◦
1) of the Band 3 and Band 7 observations,which are used to the derive the Σ d distribution.the beam size is larger than that of the image obtained by Casassus et al. (2015), our mockup image successfully reproduces the observed intensity distribution, in which there are twoemission peaks and the northwestern one is brighter (because the temperature in this region ishigher). This comparison shows that the disk parameters estimated from Bands 3 and 7 arereasonable. References
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