Grain Growth Probed by ngVLA Polarimetric Observations
Takahiro Ueda, 1 Satoshi Ohashi 2 , Akimasa Kataoka 1
1

National Astoronomical Observatory of Japan, 2–21–1 Osawa, Mitaka-shi, Tokyo 181–8588, Japan
2
RIKEN Cluster for Pioneering Research, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan
takahiro.ueda@nao.ac.jp

Abstract
ALMA polarimetric observations have revealed interesting polarization morphologies in protoplanetary disks.
The polarization at millimeter wavelengths have been used for constraining dust sizes in disks since the polarization
efﬁciency is sensitive to the dust size. However, the ALMA polarimetric observations have optical depths andspatial resolution which might be not enough to probe the dust evolution at the disk mid-plane where the planet
formation occurs. We perform radiative transfer simulations with models based on the ALMA observations toderive predictions for ngVLA observations. We ﬁnd that the polarization fraction at ngVLA wavelenth is as highas ∼ 4% if the maximum dust size is 1 mm. If the disk is optically thick, ngVLA and ALMA traces the different
heights of the disk. Therefore, by combining ngVLA and ALMA, we can constrain how much the vertical mixing is
efﬁcient and hence we can estimate the turbulence strength and dust size. Owing to its high sensitivity, ngVLA canobserve the polarimetric morphology with a high spatial resolution and hence allows us to understand how dust size
varies across disk substructures which might link with the planetesimal/planet formation. These results show thatngVLA will provide us new insights on how dust grains grow into larger bodies.
Key words: dust, extinction1 — planets and satellites: formation2 — protoplanetary disks3

1. Introduction

μm

Dust grains are building materials of terrestrial planets andcore of giant planets. In protoplanetary disks, dust grains
are initially size of < 1 µm and stick together into mm/cmsized grains called as pebbles. The pebbles are thought togrow into km-sized bodies called planetesimals via direct coagulation (e.g., Okuzumi et al. 2012; Kataoka et al. 2013)
and/or local dust accumulation followed by hydro-dynamical
instabilities (e.g., Youdin & Goodman 2005; Carrera et al.
2015; Dra̧żkowska & Alibert 2017; Ueda et al. 2019). The
planetesimals collide each other (e.g., Ida & Lin 2004) and/or
accrete pebbles (e.g., Ormel & Klahr 2010; Lambrechts &Johansen 2012) and eventually form planets (Figure 1). Even
though the evolution from dust to planetesimals has a key rolein the planet formation, it is still unclear because dust grains
are thought to radially drift quickly (Whipple 1972; Adachi
et al. 1976) and are easy to fragment (e.g., Blum & Wurm
2000; Wada et al. 2013).
Polarimetric observation is one of the best ways to probegrain size evolution in protoplanetary disks. ALMA polarimetric observations have detected successfully the polarization
at the millimeter wavelengths and have provided us new insights on the grain growth. In protoplanetary disks, millimeter polarization is thought to originate from self-scattering of
dust thermal emission (Kataoka et al. 2015; Yang et al. 2016)
and dust alignment with a magnetic and radiation ﬁeld (Cho &Lazarian 2007; Guillet et al. 2020). The polarization morphology of these mechanisms are very different from each other;polarization vector is perpendicular to the disk minor axis for
self-scattering and is azimuthal/radial direction for alignment.
Since the polarization efﬁciency is sensitive to the maximum
dust size amax , we can constrain the dust size from the polar-

mm

Dust
Direct coagulation
Pebblesm
km

Instabilities
Planetesimals

103km

Fig. 1.
Schematic
view
of
solid
materials
in

Pebble accretion
Planetsofsize
protoplanetaryevolution
disks.

ization morphology.
One of the most interesting ﬁndings from the ALMA polarimetric observations is a prevalence of 100 µm-sized grains
in disks. ALMA have revealed that many disks, regardless of
their ages, show the scattering-induced polarization pattern at
λ ∼ 1 mm, indicating that the grain growth is halted at ∼100
µm in these disks even though they should contain mm-sizedgrains (Stephens et al. 2017; Bacciotti et al. 2018; Hull et al.
2018; Dent et al. 2019; Sadavoy et al. 2019)
However, there are some concerns on the interpretation of
the ALMA polarimetric observations. One of them is an opticaldepth effect. Because of a sensitivity limit, current ALMA polarimetric observations focus mainly on bright disks and hence
they might be optically thick at the ALMA wavelength (Ohashi
et al. 2020; Ueda et al. submitted). If the disk is optically thick,

2

1.2
1
0.8
Pω

we no longer observe the disk mid-plane where large grains
exist and planet formation takes place. In addition to that, thecurrent spatial resolution for polarimetric observations is notenough to resolve substructures which have been already foundwith higher angular resolution observations. If disk properties
changes dramatically within a small scale compared to the observing beam size, the interpretation of the polarimetric observations would need to be modiﬁed (Lin et al. 2020) Since
the substructures are thought to be associated with on goingplanetesimal/planet formation, spatially resolved polarimericobservations on the substructures are of most importace for understanding how dust evolves into larger bodies.
Grain alignment mechanisms are still an issue even at thedisk scale. First, in which scale and at which wavelengths thealignment-induced polarization dominate over self-scattering?
It is believed that millimeter-wave polarization is dominated byintrinsic polarization from ellipsoidal dust grains aligned withmagnetic ﬁelds down to sub-parsec scales (e.g., Girart et al.
2006). While many disks show the polarimetric pattern withthe central part dominated by self-scattering at 0.9 mm, somedisks show alignment-induced polarization at 3.1 mm (Kataoka
et al. 2017) or at the outer part of even at 0.9 mm (Mori et al.
2019). Lopsided disks show the grain-size dependent polarimetric pattern (Ohashi et al. 2018). Furthermore, the direction of the alignment is uncertain. While the radiative torquealignment theory achieved a great success in B-ﬁeld alignment in star-forming clouds, the direction of grain alignment
may not be with the magnetic ﬁelds but with gas-ﬂow or withanisotropic radiation (Tazaki et al. 2017; Kataoka et al. 2019)
since dust grains in disks are much bigger than the interstellar
medium and surrounded by dense gas. Phenomenological discussions on interpreting disk polarimetric pattern have shownthat magnetic ﬁeld direction may not be the dominant direction of intrinsic polarization (Ohashi et al. 2018; Mori et al.
2019; Yang et al. 2019; Mori & Kataoka 2020), while more
fundamental discussion on microphyiscs of grain alignment isneeded.
The Next Generation Very Large Array (ngVLA) will
have an technical capability of the polarimetric observation at(sub-)cm wavelengths. As shown in Figure 2, the polarization
due to self-scattering is sensitive to the grain size. With the current ALMA sensitivity, knowledge on polarization has developed for the wavelength of 0.9 mm, which revealed the ∼ 150
micron-sized dust grains. In contrast, the ngVLA wavelengths
are sensitive to the dust size of ∼ 1 mm which is the most importance in the context of planet formation. Owing to its highsensitivity and long wavelength, the ngVLA polarimetric observations will allow us to see the polarimetric morphology at
the disk mid-plane where planet formation occurs with a reasonable observation time. In this project, we perform radiativetransfer simulations with models based on ALMA observations
to derive predictions for ngVLA polarimetric observations. In
Section 2, we investigate how vertical mixing of dust grains
affect the polarization. In Section 3, we demonstrate the capability of high angular resolution polarimetric observations with
ngVLA with taking the HD 163296 disk as an example. The
detection limit of the polarization at ngVLA wavelength is discussed in Section 4 and conclusions are given in Section 5[Vol. ,

3.1 mm0.87 mm (Band 3)(Band 7)7 mm
(Band 1)0.34 mm(Band 10)

0.6
0.4
0.2
0
0.001

0.01
0.1
Maximum grain size [cm]1

Fig. 2. The predicted polarization efﬁciency due to self-scattering as afunction of the grain size. See Kataoka et al. (2015) for more details.

2. Probing vertical mixing of dust grains
As mentioned in Section 1, polarimetric observations by
ALMA have provided us many insights on the dust growth.
However, the disks can be optically thick at mm wavelengths
and hence we cannot observe the disk mid-plane. Owing to its
long observing wavelengths, ngVLA would be able to observe
the disk mid-plane. We expect that by combining ALMA andngVLA observations, we can constrain the vertical dust distribution and hence the dust size and turbulence strength. In thissection, we investigate how dust settling affects the disk polarization by performing radiative transfer simulations.
2.1. ModelWe carry out radiative transfer simulations with taking vertical dust settling and mixing into account. The model used inthis section is based on the model of Ueda et al. submitted. In
this subsection, we brieﬂy summarize key points in the modeland refer readers to Ueda et al. submitted for details.
In protoplanetary disks, the vertical dust distribution is determined by the equilibrium between the settling and turbulent
mixing and the dust scale height can be written as (Dubrulle
et al. 1995; Youdin & Lithwick 2007)()−1/2
St 1 + 2St
hd = hg 1 +,(1)
αt 1 + St
where hg is the gas scale height, αt is the strength of the turbulence and St is the normalized stopping time which is proportional to the dust radius.
At each radial grid, the vertically integrated dust size distribution is assumed to be a power-law distribution ranging from
0.1 µm to amax with a power-law index of 3.5. We consider
two cases where amax = 160 µm and 1 mm. The dust size distribution is logarithmically divided into 15 size bins per decadeand Equation 1 is applied to each size bin. The radial proﬁles ofthe dust surface density and temperature are determined fromthe millimeter SED of the HL Tau disk within the ∼ 20 au andNo. ]

3

λ = 0.87 mm

λ = 3.0 mm

λ = 11.0 mm

Fig. 3. Simulated polarization fraction of the disks with amax = 160 µm (top) and amax = 1000 µm (middle and bottom) at the observing wavelength of 870 µm (left), 3 mm (center) and 11 mm (right). The gray solid lines denote the intensity contours linearly separated into 10 bins from the maximum to 0. The white ﬁlled circle at the bottom left in each panel denotes the observing beam size.

hence we ignore the substructures observed in the outer disk.
2.2. Results
Figure 3 shows the simulated polarizartion fraction of themodel disk at different observing wavelengths. Interestingly,
both models with amax = 160 µm and amax = 1000 µm predictcomparable level of polarization at λ = 870 µm when αt =10−5 (top and middle panels). This is because large grains are
hidden in the mid-plane and we can only observe small grainsat the upper layer at λ = 870 µm. As the observing wavelength
increases, we can observe a layer closer to the mid-plane where
the large grains reside and hence difference in the polarization
fraction is more signiﬁcant.
If we compare models of amax = 1 mm with different αt(middle and bottom panels), we can see that the polarization
fraction at λ = 11 mm is almost the same, while only modelwith αt = 10−5 predict the polarization level observed in the

HL Tau disk at λ = 870 µm. Therefore, we can know the true
dust size and turbulence strength by combining the ALMA andngVLA polarimetric observations.
3. Dust size variation across the substructures
ALMA observations have revealed that many disks have gap
and ring-like structures which might be associated with the formation of planets. Therefore, it is important to understand how
dust size varies with the observed substructures. ngVLA will
have a capability to observe the polarized emission with an angular resolution high enough to resolve some of the observed
substructures. In this section, we demonstrate the capability of
ngVLA high angular polarimetric observations with taking the
HD 163296 disk as an example.
One big improvement is the high sensitivity observations at
3 and 7 mm with ngVLA compared with ALMA. Polarimetric4[Vol. ,

log I [mJy/beam]
5.0

4.5

4.0

3.5

log PI [mJy/beam]

3.0

2.5

2.0

7.0

6.5

6.0

5.5

PF [%]

5.0

4.5

4.0

0.00 0.25 0.50 0.75 1.00 1.25 1.50

1.00
0.75

dDec. [arcsec]

0.50
0.25
0.00
0.25
0.50
0.75
1.00

30 au
1.0

0.5

Fig. 4.
Simulated
theHD
1632960.0

0.5

intensity
disk
at

7

dR.A. [arcsec](left),
mm.

30 au
1.0

1.0

polarized
The

0.5

0.0

dR.A. [arcsec]

0.5

2%
1.0

intensity(center)
and
image
is
smoothedtosubstructures have been observed only at 0.9 mm, which is thecurrently available shortest wavelength for polarization with
ALMA because sensitivity is not high enough at longer wavelengths, such as 3 mm, with spatial resolution high enough toresolve the ring and gap structures. Therefore, current analysis is limited to the brightest disks and at single band analysis.
Once ngVLA reaches the spatial resolution as high as 0.1 arcsec to resolve the rings and gaps and the high sensivitity down
to detecting 1% of thermal dust emission, we will be ﬁnallyable to discuss the polarimetric SEDs at rings and gaps, anddifference of the grain sizes between rings and gaps.
3.1. Model
Here, we show an example of the polarization images obtained by the radiative transfer simulations of self-scattering
suitable for ngVLA observations in Figure 4. The disk is assumed to be HD 163296 because this is the only disk where
the rings and gaps are spatially resolved and investigated inmillimeter-wave polarization measurements so far.
Ohashi & Kataoka (2019) have investigated the grain sizeand dust scale height structures of the HD 163296 disk by reproducing the observed polarization features with the simulations. They suggested that the maximum grain size is amax ∼140 µm in the gaps, while it becomes signiﬁcantly larger orsmaller in the rings. By taking into account that the ring structures are formed by pressure bumps and the grain growth proceeds, we consider the maximum grain size of 1.4 millimeterin the rings and inner part of the disk.
3.2. Results
Figure 4 shows the simulated images of the total intensity, polarized intensity, and polarization fraction of the HD
163296 disk at a 7 mm observing wavelength. The images aresmoothed to the beam size of 0.2 arcsec.
As shown in the ﬁgure, the ring and gap structure can be imaged by the ngVLA observations. Furthermore, the polarized
emission will be observed in the ring regions by ngVLA 7 mmdust continuum observations, while it was observed in the gap
regions by the ALMA 0.87 mm dust continuum observations.

1.0

0.5

0.0

dR.A. [arcsec]

polarization
the
beam

fraction
size
of

0.5

1.0

(right)of
0.2
arcsec.

Thus, the observations of ngVLA together with ALMA will allow us to reveal the different grain size distributions related tothe disk structure.
The polarized intensity can be detected with 0.01 − 0.2 µJybeam−1 and a beam size of 0.2 arcsec. An integration time of
4 − 5 hours on source will allow us to detect the polarizationfrom inner 30 au with above 3 σ. Furthermore, if the beam size
is as large as 0.4 arcsec, the polarized emission is detectablefrom the ring region with an integration time of ∼ 10 hours.
4. Sensitivity comparison
In this section, we estimate the detection limit of the polarized emission by comparing the expected noise level of ngVLA
observations and the intensity proﬁle of the HL Tau disk as an
example. Figure 5 compares the radial intensity proﬁle of the
HL Tau disk at λ = 7.9 mm observed with VLA (CarrascoGonzález et al. 2019) and expected noise level for an observation with 1 hr integration time by ngVLA. The observing beam
size is set to be 0.1 arcsec, which is ∼3 times or more better
than the typical ALMA polarimetric observations. As shownin Section 2 and 3, we expect ∼ 1–5% polarization at ngVLA
wavelengths. If the polarization fraction is 1% at λ = 7.9 mm,
the polarized emission from the HL Tau disk can be detected
within ∼ 30 au with > 3σ noise level. If the polarization fraction is 5%, the polarization can be detectable even at ∼ 65 au.
With increasing the integration time and/or lowering the resolution, we would be able to observe the polarized emission
more outer region.
5. Conclusions
We performed radiative tranfer simulations with models
based on the ALMA observations to derive predictions for
ngVLA polarimetric observations.
First, we examine the effect of dust settling and mixing on
the polarization. At the sub-mm wavelength, polarization fraction of 0.5% which is observed in the HL Tau disk, can begenerated either of 100 µm-sized and mm-sized grains be-

No. ]

5

I38GHz
1% of I38GHz
3% of I38GHz
5% of I38GHz

Intensity [mJy/beam]

10 1
10 2
10 3
10

3 detection
rms for 1 hr integration
4

10 5

0

20

40
60
80
Radial distance [au]

100

120

Fig. 5. Comparison between the intensity proﬁle of the HL Tau
disk at λ = 7.9 mm (ν = 38 GHz) and the expected noise levelof the ngVLA observation. The black solid line denotes the observed intensity proﬁle at λ = 7.9 mm and the uncertainty causedby the thermal noise is denoted with the translucent color (original data is from (Carrasco-González et al. 2019)). The red, green
and blue solid lines denote 1%, 3% and 5% of the observed intensity, respectively. The gray and black dashed lines show the expected root mean square (rms) of the noise and 3×rms for 1 hour
integration, respectively. The beam size is set to be 0.1 arcsec.

cause large grains are hidden at the mid-plane where sub-mm
wavelength cannot observe. However, at the ngVLA wavelengths, owing to the low optical depth, the polarization fraction changes sensitively with the dust size and the degeneracy
can be solved.
Second, we demonstrate that the high angular polarimetricobservation with ngVLA allows us to constrain the dust size
varying with sub-structures with taking the HD 163296 disk
as an example. The observed rings and gaps in HD 163296
are expected to contain different dust population; large dust
in rings and small dust in gaps. Our model predicted higher
polarization fraction at innerdisk and rings and lower at gaps at
the ngVLA wavelength. The spatial variation can be detectedwith a reasonable observing time.
Finally, we compared the observed radial intensity proﬁle ofthe HL Tau disk with the expected noise level in the ngVLA
observation to see the detection limit of the polarization quantitatively. We found that the polarization within ∼ 30 au can bedetectable with 1 hr integration time if the polarization fraction
is 1% . If the polarization fraction is 5%, the detectable region
expands to 65 au.
These results showed that ngVLA untangles the concerns invoked from ALMA polarimetric observations and will be able
to tell us how dust grains evolve into larger bodies.
References
Adachi, I., Hayashi, C., & Nakazawa, K. 1976, Progress ofTheoretical Physics, 56, 1756
Bacciotti, F., Girart, J. M., Padovani, M., et al. 2018, ApJL, 865, L12
Blum, J., & Wurm, G. 2000, Icarus, 143, 138
Carrasco-González, C., Sierra, A., Flock, M., et al. 2019, ApJ, 883,

71
Carrera, D., Johansen, A., & Davies, M. B. 2015, A&A, 579, A43
Cho, J., & Lazarian, A. 2007, ApJ, 669, 1085
Dent, W. R. F., Pinte, C., Cortes, P. C., et al. 2019, MNRAS, 482, L29
Dra̧żkowska, J., & Alibert, Y. 2017, A&A, 608, A92
Dubrulle, B., Morﬁll, G., & Sterzik, M. 1995, Icarus, 114, 237
Girart, J. M., Rao, R., & Marrone, D. P. 2006, Science, 313, 812
Guillet, V., Girart, J. M., Maury, A. J., & Alves, F. O. 2020, A&A,
634, L15
Hull, C. L. H., Yang, H., Li, Z.-Y., et al. 2018, ApJ, 860, 82
Ida, S., & Lin, D. N. C. 2004, ApJ, 604, 388
Kataoka, A., Okuzumi, S., & Tazaki, R. 2019, ApJL, 874, L6
Kataoka, A., Tanaka, H., Okuzumi, S., & Wada, K. 2013, A&A, 557,
L4
Kataoka, A., Tsukagoshi, T., Pohl, A., et al. 2017, ApJL, 844, L5
Kataoka, A., Muto, T., Momose, M., et al. 2015, ApJ, 809, 78
Lambrechts, M., & Johansen, A. 2012, A&A, 544, A32
Lin, Z.-Y. D., Li, Z.-Y., Yang, H., et al. 2020, MNRAS, 496, 169
Mori, T., & Kataoka, A. 2020, arXiv e-prints, arXiv:2012.01735
Mori, T., Kataoka, A., Ohashi, S., et al. 2019, ApJ, 883, 16
Ohashi, S., & Kataoka, A. 2019, ApJ, 886, 103
Ohashi, S., Kataoka, A., Nagai, H., et al. 2018, ApJ, 864, 81
Ohashi, S., Kataoka, A., van der Marel, N., et al. 2020, ApJ, 900, 81
Okuzumi, S., Tanaka, H., Kobayashi, H., & Wada, K. 2012, ApJ, 752,
106
Ormel, C. W., & Klahr, H. H. 2010, A&A, 520, A43
Sadavoy, S. I., Stephens, I. W., Myers, P. C., et al. 2019, ApJS, 245, 2
Stephens, I. W., Yang, H., Li, Z.-Y., et al. 2017, ApJ, 851, 55
Tazaki, R., Lazarian, A., & Nomura, H. 2017, ApJ, 839, 56
Ueda, T., Flock, M., & Okuzumi, S. 2019, ApJ, 871, 10
Wada, K., Tanaka, H., Okuzumi, S., et al. 2013, A&A, 559, A62
Whipple, F. L. 1972, in From Plasma to Planet, ed. A. Elvius, 211
Yang, H., Li, Z.-Y., Looney, L., & Stephens, I. 2016, MNRAS, 456,
2794
Yang, H., Li, Z.-Y., Stephens, I. W., Kataoka, A., & Looney, L. 2019,
MNRAS, 483, 2371
Youdin, A. N., & Goodman, J. 2005, ApJ, 620, 459
Youdin, A. N., & Lithwick, Y. 2007, Icarus, 192, 588