Investigating the gas-to-dust ratio in the protoplanetary disk of HD 142527

We present ALMA observations of the $98.5~\mathrm{GHz}$ dust continuum and the $\mathrm{^{13}CO}~J = 1 - 0$ and $\mathrm{C^{18}O}~J = 1 - 0$ line emissions of the protoplanetary disk associated with HD~142527. The $98.5~\mathrm{GHz}$ continuum shows a strong azimuthal-asymmetric distribution similar to that of the previously reported $336~\mathrm{GHz}$ continuum, with a peak emission in dust concentrated region in the north. The disk is optically thin in both the $98.5~\mathrm{GHz}$ dust continuum and the $\mathrm{C^{18}O}~J = 1 - 0$ emissions. We derive the distributions of gas and dust surface densities, $\Sigma_\mathrm{g}$ and $\Sigma_\mathrm{d}$, and the dust spectral opacity index, $\beta$, 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 the peak brightness temperature of $\mathrm{^{13}CO}~J = 3 - 2$ with a continuum emission. The gas-to-dust ratio, $\mathrm{G/D}$, varies azimuthally with a relation $\mathrm{G/D} \propto \Sigma_\mathrm{d}^{-0.53}$, and $\beta$ is derived to be $\approx 1$ and $\approx 1.7$ in the northern and southern regions of the disk, respectively. These results are consistent with the accumulation of larger dust grains in a higher pressure region. In addition, our results show that the peak $\Sigma_\mathrm{d}$ is located ahead of the peak $\Sigma_\mathrm{g}$. If the latter corresponds to a vortex of high gas pressure, the results indicate that the dust is trapped ahead of the vortex, as predicted by some theoretical studies.


Introduction
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 in a radial direction, with surface densities that follow a piecewise power law (Weidenschilling 1977b;Hayashi 1981). The high angular resolution observations by the Atacama Large Millimeter/submillimeter Array (ALMA), however, revealed complicated morphologies in protoplanetary disks as traced by the dust continuum and molecular line emissions, such as dustdepleted gaps, spiral-arms, and crescent-like distributions van der Marel et al. 2013;Isella et al. 2013;Pérez et al. 2014; ALMA Partnership et al. 2015;van der Marel et 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 not necessarily 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 the gas and dust and thus result in spatial variation of the gas-to-dust ratio. For example, dust particles can lose their angular momentum due to gas-dust friction and radially drift towards the central star (Weidenschilling 1977a). The gas-dust friction may also result in the settling of larger grains toward the disk midplane (Dominik et al. 2007;Pinte et al. 2016). Dust filtration may also occur at the edges of gaps in the dust that has been cleared by planets, in which smaller particles migrate inward to the disk inner region while larger particles are retained at the edges (Rice et al. 2006). Large-scale high pressure gas vortices can also trap dust particles in the azimuthal direction, which may explain the asymmetric structure observed in some protoplanetary disks (Barge & Sommeria 1995;Klahr & Henning 1997;Birnstiel et al. 2013;; . Other mechanisms that can change the gasto-dust ratio are the growth and fragmentation of dust particles near the snowline (Zhang et al. 2 2015;Okuzumi et al. 2016), as well as secular gravitational instability (Takahashi & Inutsuka 2014;Takahashi & Inutsuka 2016). In these cases the dust particles tend to accumulate in concentric 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 can also dramatically alter the gas and dust disk structure (Dipierro et al. 2016;Kanagawa et al. 2016;Dong et al. 2017). While the dominant mechanisms that result in the distribution of the gas-to-dust ratio may differ from disk to disk, the ratio may provide clues concerning the processes that lead to the observed disk structures and is crucial in understanding the back-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 primary star HD 142527A and the secondary star HD 142527B. The distance to HD 142527 derived by Arun et al. (2019) based on the Gaia observations (Gaia Collaboration et al. 2016;Gaia Collaboration et al. 2016) is 157 pc ± 1 pc. The primary star is a Herbig F6 − F7IIIe (Malfait et al. 1998;van den Ancker et al. 1998) star with a mass of approximately 2.4 M ⊙ and age of 2.96 Myr (Fukagawa et al. 2013;Arun et al. 2019). The secondary star is a M dwarf with a mass of 0.13 M ⊙ , which orbits around the primary star at an angular distance of approximately 0. ′′ 1 (Biller et al. 2012;Close et al. 2014;Lacour et al. 2016). The binary system is surrounded by an inner disk close to 30 au and a massive outer disk whose gas content extends to approximately 400 au (Verhoeff et al. 2011;Muto et al. 2015); the inner disk is separated from the outer disk by a dust-depleted region, or gap, that extends to a radius of 150 au. ALMA observations of HCO + hint at the existence of gas filaments across this gap, through which the material is funneled from the outer disk to the inner disk . The accretion rate is estimated to be 10 −7 M ⊙ yr −1 (Mendigutía et al. 2014). Near infrared images show that there are at least six spiral arms in the outer disk (Avenhaus et al. 2014). From the different spatial distribution of emission seen at the near-and mid-infrared wavelengths, the outer disk is thought to be inclined to the line-of-sight, with the northeastern half appearing to be the furthest 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 been derived as 27 • and 161 • , respectively, from the kinematics traced by the 13 CO J = 3 − 2 line emission (Fukagawa et al. 2013). On the other hand, the inner disk is modeled to be inclined at 70 • relative to the outer disk . The inner disk shadows the northern and southern regions of the outer disk from stellar irradiation causing a drastic drop in the intensity of infrared wavelengths in the two regions (Avenhaus et al. 2014). At the submillimeter and 3 longer wavelengths, the dust continuum emission of the outer disk shows a crescent structure in 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 features of the disk (e.g., spiral arms, cavity, HCO + streamers) may be explained by just considering the interaction between the disk and the binary system. Their results also predict that the disk-binary interaction can create the asymmetric dust disk without invoking a gas vortex in the disk northern region (see also Ragusa et al. 2017).
In previous research, Muto et al. (2015) and Boehler et al. (2017) derived the gas and dust surface densities and the gas-to-dust ratio of the outer disk of HD 142527 by modeling ALMA observations at Band 7. This research focused on the northern and southern regions of the outer disk, which correspond to the sectors where the dust continuum emission is brightest and faintest at Band 7, respectively. The gas-to-dust ratio was derived to be ∼ 3 and ∼ 30 in the northern and southern regions, respectively, and the results indicate that dust is concentrated in the northern region. However, discussions concerning the detailed spatial variations in the gasto-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 across the outer disk of HD 142527. We assume the local thermal equilibrium and derive the gas and dust surface densities by using ALMA observations of the 13 CO and C 18 O molecular line and dust 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 data as well as the previously published ALMA Band 7 data for the HD 142527 system. In Section 3, we present the calibrated images of the ALMA Band 3 data and compare them to that from Band 7. We describe the methods used to derive the gas and dust surface densities in Section 4 and discuss the results in Section 5. Section 6 provides a summary of our research.

Observations and data reduction
We used the ALMA Cycle 2 Band 3 1 and Cycle 0 Band 7 2 observational data of HD 142527 to investigate the distribution of the gas-to-dust ratio in the disk. The observational details are described in the following subsections. 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 the J1427−4206 or J1617−5848, while the absolute flux calibrator was either Ceres, Pallas, Titan, or J1427−4206 3 . The flux of the quasar J1427−4206 at 103.5 GHz was monitored once in every ≈ 20 days from the late June to the early August in 2015, and judging from these results, the flux variation during the observation period should be less than 10%. For all the execution blocks J1604−4228 was used as the phase calibrator. We used CASA pipeline version 4.3.1 to perform the data reduction and calibration, and during the data reduction two blocks were completely discarded for lacking calibration information. After flagging aberrant data, the total on-source integration time was 2.94 hours and the number of 12 m antennas involved were 37 to 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 four separate spectral windows. Two spectral windows were optimally configured for the continuum observation with frequencies centered at 97.50 GHz and 99.50 GHz, and both had an effective bandwidth of 1.875 GHz. The other two windows, each having 3840 channels, were centered at 109.78 GHz and 110.19 GHz to target the J = 1 − 0 line emission of C 18 O and 13 CO with a spectral resolution of 15.259 kHz (∆v ≈ 0.04 km s −1 ).
We used CASA version 5.1.0 to image the calibrated visibility and combined the two wide band spectral windows to obtain a continuum centered at 98.5 GHz with a total bandwidth of 4 GHz. We then applied the multi-scale CLEAN algorithm with Briggs weighting (robust parameter 0.5) 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 imaging process. In order to improve the signal-to-noise ratio, we performed self-calibration to the continuum image as follows. First, we solved the gain phase of the initial CLEAN model for the continuum image starting from a time interval equal to the total time duration of each scan (which is between 2 minutes and 7 minutes) of the target, followed by shorter time intervals in the order of 240 s, 120 s, and 60 s. After every phase calibration, we performed CLEAN to the continuum image to obtain a new model that could be used in the succeeding phase calibration. Once the phase calibration was completed, we solved the gain amplitude of 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 3 The source name for J1427−4206 was designated as J1427−421 by mistake in the execution block of ADS/JAO.ALMA#2013.1.00670S. We use the correct source name in this paper. 5 the 98.5 GHz continuum and performed final CLEAN to create an image of the continuum.
With self-calibration, the resulting noise of the continuum image is lowered by a factor of approximately five, and a root mean square noise level of σ = 9.6 µJy beam −1 is reached. The synthesized beam in full width at half maximum (FWHM) of the final image is 0. ′′ 54 × 0. ′′ 44, oriented along P.A. = 78.1 • .
Before imaging the J = 1 − 0 line emission of 13 CO and C 18 O, we applied the phase and amplitude solutions that were derived from the self-calibration to the visibility data of the continuum 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 equivalent velocity resolution of 0.30 km s −1 . The velocity resolution is set at a slightly smaller value than the observed velocity dispersion, which is approximately 0.4 km s −1 as shown in figures 3 and 4 of Muto et al. (2015) as well as in figure 3(d) in this paper, to reveal the emission with the best sensitivity. Finally, we applied a CASA task imsmooth to smooth the image cubes of 13 CO and C 18 O so that they had the same angular resolution in the 98.5 GHz continuum image, i.e., 0. ′′ 54 × 0. ′′ 44 (P.A. = 78.1 • ). The noise level is σ = 2.0 mJy beam −1 .
We also created a spectral cube of ∆v = 0.12 km s −1 for both the 13 CO and C 18 O line emissions to derive their peak brightness temperature. The beam size was also smoothed to match that of the 98.5 GHz continuum image. The noise level is σ = 2.9 mJy beam −1 .

ALMA band 7 data
The observational setup and calibration process of the Band 7 data are described in detail by Fukagawa et al. (2013) and Muto et al. (2015). In this study, we use the calibrated images of the 336 GHz continuum and the 13 CO J = 3 − 2 and C 18 O J = 3 − 2 lines produced by Muto et al. (2015). The velocity resolution of the line images is 0.12 km s −1 . The synthesized beams of the Band 7 images are smaller than that from Band 3, so we applied imsmooth to the Band 7 images to obtain a spatial resolution identical to that of the Band 3 images, i.e., a synthesized beam of 0. ′′ 54 × 0. ′′ 44 (P.A. = 78.1 • ) The resultant noise rms was 150 µJy beam −1 for the continuum, and 5.9 mJy beam −1 and 7.5 mJy beam −1 for the 13 CO and C 18 O image cubes, respectively.
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 as where θ maj and θ min are the FHWM of the beam major and minor axes, respectively. The signal-to-noise ratio of the peak continuum flux at 98.5 GHz is 240. The spatially integrated flux at 98.5 GHz, considering only emission above 5σ level, is 72.1 mJy. On the other hand, the integrated flux at 86.3 GHz (equivalent wavelength 3.476 mm) obtained with the Australia 8 Telescope Compact Array (ATCA) at a coarser beam of 16. ′′ 2 × 2. ′′ 9 is 47.1 mJy ± 6.5 mJy, and the spectral index between 800 µm and 3.476 mm is derived to be ≈ 3 (Verhoeff et al. 2011).
With this spectral index, the integrated flux at 98.5 GHz corresponds to 48.5 mJy at 86.3 GHz, indicating that the ALMA observation recovers all the flux.
Both 98.5 GHz and 336 GHz continuum images reveal an asymmetric ring-like structure in their emission. The FWHM radial width of the continuum emission from the outer disk is approximately 100 au, which means that the observation beam (linear scale ≈ 76 au) marginally resolves the disk in the radial direction. The 98.5 GHz continuum emission shows a radial extent of approximately 2 arcsec above the 5σ level, and it shares a similar distribution with that observed at 336 GHz, i.e., the outer disk exhibits a crescent-like structure as a result of the concentration of dust in the northern region. Hereafter, we use the word ridge to refer to the line that connects the radial peak of a physical quantity in every P.A. direction (as seen from the central star) on the outer disk. To search for the maximum and minimum values along the ridge, the averaged values from an area of radial size 0. ′′ 1 and angular size 6 • with coordinates indicated by (r, P.A.) will be used. The maximum and minimum values of the continuum emission along the ridge are listed in Table 1. The contrast of the 98.5 GHz emission along its ridge is approximately 58 and is higher than that at 336 GHz, which is 25 (see also Fukagawa et al. 2013). This difference is because of the lower optical depth at 98.5 GHz; the optical depth at 336 GHz in the northern region of the disk is > ∼ 1, hence its emission is saturated . The lower optical depth at 98.5 GHz also accounts for the lower peak T B , i.e., 8.1 K, compared to 21.5 K at 336 GHz.
The spectral index α is defined as and is shown in figure 1(c). The index varies smoothly in the azimuthal direction; in the northern region α ≈ 2.8, while in the southern region α ≈ 3.4. When the Rayleigh-Jeans approximation is valid, the flux density is proportional to ν 2+β , where β is the dust opacity spectral 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 flatter as the optical depth at 336 GHz gets higher. We will derive β and optical depth from the dust continuum 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 of P.A.. A dip in intensity at P.A. ∼ 0 • is seen at 336 GHz, rendering the emission morphology to be a double-peaked structure; however, there is no dip at the same P.A. direction at 98.5 GHz. 9 The 336 GHz emission is so opaque that it would be more sensitive to dust temperature than dust surface density; the dip may therefore reflect a temperature drop in the disk atmosphere . In fact, the intensity at infrared wavelengths is also lower at P.A. ∼ 0 • (as well as at P.A. ∼ 160 • , see Avenhaus et al. 2014) and is thought to be the result of a shadow from a warped inner disk . On the other hand, the 98.5 GHz emission is optically thin and should also depend on the dust surface density; here, the shadow is not apparent.
3.2 13 CO J = 1 − 0 line emission  (a) and (c), the white contours denote the 3.5σ level, which are 6.53 K and 6.70 K, respectively.
In panels (b) and (d), the white contours denote the 5σ 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. ′′ 9,27 • ), close to the continuum peak with F int = 28.7 mJy beam −1 km s −1 . The ridge of 0th-moment is lowest at (0. ′′ 9, 225 • ) where F int = 6.95 mJy beam −1 km s −1 . The contrast of the ridge is thus 4.13. The peak T B is ≈ 25 K in the north while it is ≈ 10 K in the south, and its distribution is similar to that of the continuum emission.

Analyses
In this section, we derived the gas and dust surface density for the disk of HD 142527 under the assumptions of local thermodynamic equilibrium (LTE). We do not consider dust sedimentation at the midplane and assume that the gas and dust are well-mixed in the disk. We assume the physical temperatures of the gas and dust, T d and T g , to be identical. These temperatures are taken from the peak T B of 13 CO J = 3 − 2 including the continuum emission, as shown in figure 4(d); this temperature is referred to as the disk temperature in the following. Since the 13 CO J = 3 − 2 emission in the disk inner region is optically thin and does not reflect the physical temperature, in the following analyses we mask out the inner region in which the brightness temperature is less than 30 K. Due to the disk inclination, the western region of the disk (P.A. = 161 • − 341 • ) 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 that is irradiated by the central star is exposed to us. The disk is assumed to be isothermal in a vertical direction. A model where T d is assumed to be 80% of T g is discussed in Appendix 2.

Derivation of dust surface density
The dust surface density is derived from Σ d = τ d /κ d , where τ d is the optical depth of the dust continuum emission and κ d is the dust opacity. We first calculate τ d at 98.5 GHz and 336 GHz from the radiative transfer equation where I d denotes the intensity of the continuum emission, B ν is the Planck function, T bg = 2.7 K the temperature of the cosmic background radiation. The results are shown in figures 7(a) and (b). The peak τ d at 98.5 GHz is 0.24 and is co-spatial to its peak continuum emission. On the other hand, peak τ d at 336 GHz is 0.82, and is located at the western component of the doublepeaked structure seen at the 336 GHz emission; this is due to the lower disk temperature at the near side. The dust opacity is highly uncertain and depends on the particle compositions, structures, as well as size distributions (Miyake & Nakagawa 1993;Draine 2006;Kataoka et al. 2014;Birnstiel et al. 2018); in the analyses, we adopt the canonical dust opacity (per dust mass) κ d described by Beckwith et al. (1990), where β is the dust opacity spectral index and is calculated from the τ d distributions via Figure 8(a) shows the derived dust surface density Σ d . Along the ridge of Σ d , the maximum is located at (1. ′′ 2, 315 • ) where Σ d = 3.08 × 10 −1 g cm −2 and the minimum is located at (1. ′′ 2,225 • ) where Σ d = 9.14 × 10 −3 g cm −2 . The derived spatial location of the peak Σ d does not correspond to that of the peak continuum emission at 98.5 GHz which is optically thin; this is mainly due to the lower temperature in the near side of the disk as well as the β distribution.
Similarly, because of the temperature and β distributions, the derived Σ d ridge contrast of 33 is lower than that of the 98.5 GHz continuum emission, which is 58. This inconsistency may be due to the high optical depth of the dust continuum in the northern regions; 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 et al. 2017;Birnstiel et al. 2018).

Derivation of gas surface density
We derived the disk H 2 gas surface density Σ g from the J = 1 − 0 and J = 3 − 2 line emission of C 18 O by assuming the interstellar abundance χ(C 18 O/H 2 ) = 1.79 × 10 −7 (Wilson 1999); the validity of the abundance is discussed in Section 5.3. The J = 3 − 2 emission is used for the derivation of Σ g in the region of P.A. = 180 • − 240 • , where the J = 1 − 0 emission is weak.
The optical depth of the molecular line τ g in the velocity channels is calculated from the radiative transfer equation, which is similar to Equation (4) but takes the form i.e., the factor exp(−τ d ) is included to account for the line emission absorbed by the dust. Here,  figure 1(b). The optical depth τ g is related to the total (particle number) column density N tot of the CO isotopologue by where µ, J u , and B 0 , are the dipole moment, the rotational quantum number of the line transition upper level, and the rigid rotor rotational constant, respectively (Mangum & Shirley 2015). The excitation temperature T ex is equal to T g in the LTE analysis. The gas surface density is then calculated by Σ g = m H 2 N tot /χ, where m H 2 is the molecular mass of H 2 .   The exponent in this case is smaller than that of the relation shown in figure 9(a), since there is an azimuthal variation of 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 figures 3(c), 5(c), and the infrared images (Fujiwara et al. 2006), the disk is thought to be rotating in a clockwise rotation. Comparing figures 10(a) and 10(b), we see that the peak Σ d is located at P.A. ≈ 315 • , which is downstream of the peak Σ g located at P.A. ≈ 3 • . If the northern region of high Σ g corresponds to a vortex with higher pressure, then the dust will accumulate at a region shifted ahead of the vortex. This picture is consistent with the theoretical prediction by  if the Stokes number, St, of the dust particles is > ∼ 1; we estimate the 20 physical radius of the dust particle s by using equation (1) in the paper by the same authors, i.e.,

Relative spatial distribution of gas and dust surface densities
where ρ pc is the internal mass density of the particles. The gas surface density is Σ g ≈ 0.7 g cm −2 where Σ d peaks, and by assuming that ρ pc = 1 g cm −3 , s > ∼ 5 mm if St > ∼ 1. If the lower β in the north indicates a particle growth, β ≈ 1 implies a particle size of ≈ 1 mm − 10 mm, and it agrees with the above size estimation. In addition, the estimated size is also consistent with the continuum observations at 34 GHz which should be dominated by thermal emission from particles of size ∼ 1 mm; at 34 GHz one of two clumps of concentrated dust is observed at P.A. ≈ 330 • (the other is at P.A. ≈ 15 • , Casassus et al. 2015). On the other hand, the dust size estimated here is larger than the estimated size of 150 µm based on polarization modeling (Ohashi et al. 2018). One possible explanation to the discrepancy is a segregation of dust size in the disk vertical direction, such that smaller particles (efficient scatterers) float at the upper atmosphere while larger particles (efficient emitters) sediment at the midplane. Comparing figures 10(a) and 10(d), we see that the peaks of τ d and Σ g share a similar spatial location 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 Appendix 3, our derived parameters of the dust disk can also reproduce the intensity distributions of the continuum 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, and this is beyond the scope of this study.
The observations of asymmetric protoplanetary disk around HD 135444B reveal a frequency dependent azimuthal shift in the peak continuum position, which can be interpreted as a 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 the 98.5 GHz and 336 GHz peaks in the north. The peak shift in the case of HD 142527, however, may not be due to the size segregation since the 336 GHz emission is fairly optically thick. In fact, the β distribution in the outer disk shown in figure 10(e) is nearly mirror symmetric with respect to P.A. = 0 • , and there is no gradient along the azimuthal direction from upstream to downstream indicative of dust size segregation. The dynamic range of the observed frequencies in this study may be insufficient to discuss size segregation in the disk (cf. Casassus et al. 2015).

Effects of uncertainties in CO abundance
In a protoplanetary disk, the abundance of CO as relative to H 2 can be lower than that in the interstellar medium if CO is depleted due to freeze-out onto dust grains. In addition, CO can also 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 disks derived from the HD J = 1 − 0 transition, which are considered to be a reliable mass tracer, are found to be a factor of five greater than the masses derived independently from the CO observations without accounting for these CO depleting processes (Bergin et al. 2013;McClure et al. 2016).
Here, we discuss the effects of CO freeze-out and photodissociation in the outer disk HD 142527. CO freeze-out occurs in the disk midplane where the disk temperature is lower than the CO freeze-out temperature, i.e., approximately 20 K (Qi et al. 2011). The disk models used by Muto et al. (2015) show that the temperature in the outer disk of HD 142527 varies radially, and in the disk midplane the temperature is mostly higher than 20 K (see Figure 8 of their paper), implying that the CO freeze-out may be insignificant. On the other hand, the photodissociation is subject to self-shielding and therefore the process is isotopeselective. The less abundant isotopologue will have a thicker photodissociation layer, and the relative abundances among CO, 13 CO, and C 18 O are thus expected to be varying spatially (Shimajiri et al. 2014). In Section 4.2 we derived N tot ( 13 CO)/N tot (C 18 O) to be similar to the 13 CO to C 18 O ratio in the local interstellar medium; these results might suggest that isotope-selective photodissociation is insignificant in the case of HD 142527. The abundances of these isotopologues relative to CO, however, are still currently unknown and therefore further investigation is required to confirm the photodissociation of CO.
Even if the effects of freeze-out and isotope-selective photodissociation are small, the abundance of CO relative to H 2 still remains uncertain if carbon is locked up in other form of molecules. The detail thermochemical models show that the mass conversion from CO to H 2 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 unlikely because the gas disk would be gravitationally unstable (Fukagawa et al. 2013). In short, though Σ g , G/D, and the dust size estimated from equation (9) may be underestimated, the exponent p ≈ 0.5 found in the power law relation between Σ g and Σ d remains valid because p does not depend on the absolute values of Σ g and Σ d .

Summary
We present the ALMA Band 3 observations of the 98.5 GHz dust continuum and the 13 CO J = 1 − 0 and C 18 O J = 1 − 0 lines of the protoplanetary disk associated with HD 142527 at a spatial resolution of ∼ 0. ′′ 5, and compare the results to the ALMA observations at Band 7.
The 98.5 GHz continuum and C 18 O J = 1 − 0 is optically thin, and we derived the gas-to-dust ratio, G/D, of the outer disk. The main conclusions are as follows.
1. The 98.5 GHz dust continuum shows a similar distribution to that at 336 GHz, where the northern region is brighter than the southern region. The contrast of the 98.5 GHz along its ridge is approximately 58. The spectral index α is ≈ 2.8 and ≈ 3.4 in the northern and southern regions, respectively.
2. The integrated intensity of the 13 CO J = 1 − 0 line emission is more axisymmetric compared to the dust continuum emission, where the northern region is brighter than the south by a factor of ∼ 1.4. The C 18 O J = 1 −0 emission is confined in a narrower radial extent, where its peak emission is located near to the 98.5 GHz dust continuum peak; the integrated intensity of the line in the northern region is brighter than the south by a factor of 4.
3. The dust opacity spectral index β is derived to be ≈ 1 and ≈ 1.7 in the northern and southern regions of the disk, respectively; the difference in β between the two regions indicate the difference in dust properties. We use the J = 1 − 0 and J = 3 − 2 lines of C 18 O and the 98.5 GHz and 336 GHz continuum emission to derive the disk gas and dust surface densities, Σ g and Σ d . We assume the local thermodynamic equilibrium, the interstellar abundance χ(C 18 O/H 2 ) = 1.79×10 −7 , and the canonical dust opacity described by Beckwith et al. (1990) by varying β spatially. The derived surface densities are Σ g ∼ 0.9 g cm −2 and Σ d ∼ 0.3 g cm −2 in the northern regions, with results of Σ g ∼ 0.2 g cm −2 and Σ d ∼ 0.01 g cm −2 in the southern regions. The contrast along the Σ g and Σ d ridges are 5 and 33, respectively. The gas-to-dust ratio, G/D ≡ Σ g /Σ d , is derived to vary smoothly in the azimuthal direction of the disk, where it is ∼ 3 and ∼ 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 approximately as Σ 0.47 d , or equivalently G/D ∝ Σ −0.53 d . This relation will be a critical test for future theoretical 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 predicted 24 by theoretical studies of the trapping of dust by vortices of high gaseous pressures. The estimated dust size is > ∼ 5 mm if χ(C 18 O/H 2 ) in the disk is similar to the interstellar value. 6. The 13 CO J = 1 − 0 line emission in P.A. = 200 • − 240 • is marginally optically thin, where we derive N tot ( 13 CO)/N tot (C 18 O) = 9.99 ± 1.67; the value agrees with the interstellar abundance ratio χ( 13 CO/C 18 O) = 8.11 ± 1.1 within uncertainties.  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-layer disk model by ≈ 10% in the disk southern region and by ≈ 30% − 50% in the dust concentrated northern region.
The radiative transfer for the gas molecular line in the two-layer disk model reads where I g+d denotes the line emission including the continuum emission ).
In the line of sight, the first term accounts for the line emission from the disk atmosphere at   the front side, the second term the dust emission in the disk midplane, while the last term the line emission from the back side that will propagate through the disk midplane and the front atmosphere. Figure 13 shows the results derived from this two-layer disk model. We mask out the disk inner region in which the disk temperature is lower than 24 K, i.e., 80% of the temperature criteria used to mask out the disk inner region in the one-layer disk model (Section 4). The overall distributions of Σ g , Σ d , and G/D are similar to the one-layer disk model; due to the lower κ d , however, in the northern region Σ d is derived to be twice as high as that in the one-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 an exponent p = 0.44 to be a good fit to the results. The derived value of exponent p is consistent with that of the one-layer disk model despite the different temperature assumption between these 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 ( figure   8a), we create a mock-up image at 700 GHz to compare with the continuum observations at the same frequency reported by Casassus et al. (2015). We use the same temperature distribution, i.e., the peak T B of 13 CO J = 3 − 2 including the continuum (figure 4d) as the disk temperature and the 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. Though   the beam size is larger than that of the image obtained by Casassus et al. (2015), our mock up image successfully reproduces the observed intensity distribution, in which there are two emission peaks and the northwestern one is brighter (because the temperature in this region is higher). This comparison shows that the disk parameters estimated from Bands 3 and 7 are reasonable.