ALMAによる原始惑星系円盤観測の進展と惑星形成過程への示唆

片岡章雅（国立天文台）

惑星形成: 何を解き明かしたいか
微惑星~ 1 μm~ 1 km~ 1000 km

ダストの合体成長
0.1μm

1m

衝突破壊/
跳ね返り問題

1km

中心星
落下問題

ダスト

微惑星

ダスト実験/数値計算
Initial(b=0)

102-4km

天文観測

太陽系内

惑星

系外惑星

Initial(cross section)

Kepler 宇宙望遠鏡
Blum & Münch 1993

Wada et al. 2013

Outcome(b=0, ucol=52 m/s)

Outcome
ALMA Partnership 2015
(cross section)

Akimasa Kataoka (NAOJ)

Rosetta mission→ TESS 望遠鏡

本日のお話• 第一部: ALMAを中心とした、原始惑星系円盤の描像のレビュー (~20分)• 高分解能で見えたリング・ギャップ等副構造• サーベイ観測で明らかとなった全体像• 第二部: 我々の進めてきたALMA偏光観測 (~25分)• ダスト散乱による偏光と、ダストミクロ物理への制限• (時間があれば、今進めているダスト組成への示唆の研究 ~ 10分)

天体としての原始惑星系円盤

Planck Collaboration: Comparison of polarized thermal emission from Galactic dust with simulations of MHD turbulence

Taurus702

L. A. Cieza et al.
Ophiuchus

Figure 2. The spatial distribution of the ODISEA targets (both Samples A and B) shown on top of the Spitzer map of the Ophiuchus molecular cloud fromthe ‘Cores to Discs’ Legacy Project.

Chamaeleon- 距離140pcのところに~10個くらい、星形成領域がある- cf. 1 秒角 = 140 au- 各星形成領域に、100-300くらい円盤がある

source that can be unambiguously identified as the target.4 We firstused the imstat task to search for the peak flux value within an
aperture of 1 arcsec in radius and calculated an rms from an annulus
with inner and outer radii of 1.0 arcsec and 1.2 arcsec, respectively.
For single objects with peak signal-to-noise ratios (S/N) > 5, weused the uvmodelfit task in CASA to derive basic parameters foreach source. The full spectral coverage was utilized. We fitted bothFig. 1. Locations of the selected nearby fields. The background map represents optical depth ⌧353 at 353 GHz on a logarithmica pointscale,source and Gaussian with all free parameters: the integrated
t 50 resolution (Planck Collaboration XI 2014). The map uses a Mollweide projection in Galactic coordinates, with (l, b)flux= density,(0 ,0 the) full width at half-maximum (FWHM) along the
major and minor axis, the position angle (PA), and small offsets (<t the centre.
1.0 arcsec) in right ascension and declination from the phase centre.
We find that for objects with peak S/N ! 30, the point source and
the Gaussian fits give similar fluxes, but the Gaussian fits produce
and PA values with very large uncertainties ("50 per centide clues on the physics of the early Universe, by measuring dust alignment efficiency in dense clouds (Lazarian etFWHM
al. 1997,
and "90 deg, respectively). For objects with high S/N, the Gaussian
he CMB polarization. However, dominant foreground emission Whittet et al. 2008, Chapman et al. 2011).
fit can measure FWHM values (deconvolved from the beam) down
Akimasa
Kataoka(NAOJ)s also partially polarized, masking the primordial signal. In theto a factorof ∼2 of the beam size, but the ability to measure theMagnetohydrodynamical (MHD) simulations provide
a the-

Planck XX, 2015, Cieza et al. 2019are likely to be underestimated by this task. Therefore, we use ad
hoc criteria to decide whether the source is spatially resolved (i.e.
sufficiently different from a point source to justify reporting discsizes and orientations). In particular, we provide size information
only if the source has a peak S/N > 30 and the Gaussian flux isgreater than the point source flux plus 3 times the rms of the sky
between 1 and 1.2 arcsec of the target. For resolved sources, wereport the 1σ uncertainties obtained for each parameter (except forthe position), but remind the reader that these uncertainties might beunderestimated. Otherwise, we consider the source to be unresolved
and only report the flux and its uncertainty. For the few objects withsignificant substructures (e.g. transition disc objects with cavities,
spiral arms, and/or wide gaps, targets # 12, 22A, 51, 41, 62, 127,
141, and 143, see Section 3.4), the Gaussian model does not provide an accurate fit. In these cases, we fit an elliptical disc model
to measure their sizes (also within uvmodelfit), but we use the 2D
fitting tool within the CASA Viewer to measure the flux using a

0

ARI

25 July 2008

4:42

天体としての原始惑星系円盤
100
NGC 1333

各星団の年齢はHR図で出す。

•

赤外線超過から、「星が円盤を保持する割合」がわかる

NGC 2068/71

80
NGC 2024

Disk frequency (%)•

Trapezium

Taurus60

Chal

NGC 7129

IC348 Tr37
η Cham

NGC 226440
NGC 2244

σOri

0B1b

•
25 Ori0•5

年齢500万年くらいの老いたUpperScoは、2割くらいの星しか円盤を持っていない

NGC 7160

γVel0

例えば、年齢2-300万年の若いTaurusは6割くらいの星が円盤を持っている。

λOri

UpperSco
NGC 236220•

ただし、円盤ダストの質量はわからなかった。

10

Age (Myr)
2

Wyatt et al. 2008; Hernandez et al. 2007

on of protoplanetary disks—fraction of sun-like stars with detectable near-IR excess asAkimasa
a functionof(NAOJ)
Kataoka

ALMAで観測する時の戦略
1天体に数時間費やす

1天体1分以下で100天体くらい見る

HL TauLupus survey
A&A 599, A113 (2017)

Full#disk##TD#
Edge(on#

Ansdell et al. 2016, Miotello et al. 2017
ALMA Partnership 2015

- (total flux) =1.4 Jy at 1.0 mm- (rms) = 12 µJy/beam- (spatial resolution) =25ミリ秒角 (3.5 AU)- (detection rate) = 62/89 sources- (rms) ~ 0.3 mJy/beam- (spatial resolution) ~ 300 ミリ秒角 (40-50 AU)--

Akimasa Kataoka (NAOJ)

観測された原始惑星系円盤 Elias 2-24

Perez et al. 2016

磁気流体シミュレーション

Tomida et al. 2017

Fig. 1. Thermal dust emission from the protoplanetary disk surrounding Elias 2-27. The disk was
imaged at a wavelength of 1.3 mm, with ALMA reaching an angular resolution of 0.26″ by 0.22″ (indicatedby the ellipse in the bottom left corner), which corresponds to 36 by 31 AU at the distance of the star.
The field-of-view center (at 0, 0) corresponds to the disk emission peak located at right ascension (J2000) =016

accretes materiala mass accretion25). Previous obr resolution werend axisymmetricdisk that extends
decreases monoe star (20, 23).
h of the observed
performed radiRADMC-3D (26)ous surface denas 2-27 disk (20).
muthally averaged
LMA 1.3-mm cona radial distanced to as radius and
10 AU, the emisraces the density

ALMAで見えた２本の「うで」ALMAで見えた「偏った円盤」
AB

原始惑星系円盤IRS48

van der Marel et al. 2013
想像図 (van der Marel et al. 2013), 2013

shaped dust
ALMA conmillimeterween 45 ande azimuthalng, with noer beam) in
ak emission
f ~390, andhe opposite
of 130. The
the north oft make thethan earlier
ectral slope
4 mm comcies n (14)]gesting thatminate theowever, them the same

ALMAで見えた「リング円盤」
PRL 117, 251101 (2016)

PHYSICAL REVIEW LETTE

ALMA-Taurus

A&A 610, A24 (2018)

Isella et al. 2016

DSHARP; Andrews et al. 2018, Long et al. 2018…

ALMA Partnership 2015

Figure 3. The 1.3 mm images for our full sample, made with a BriggsFedele
weightingof2018robustness parameter of 0.5. The fir
etal.
Fig. 1. ALMA 1.3 mm dust continuum image (uniform weighting). The main substructures are highlighted in the right panel.
12 panels show images for disks with substructures, followed by the 12 smooth disks around single stars. The last row show
images for the 8 smooth disks in binaries. The images
areof thedisplayedin orderof decreasing
in peaking
each atsub-sample.
T
The structure
paper is the following:
observations
and and twodisk
weakerradii
dust rings⇠75 and 130 au, res

d (22), accretes material
disk with a mass accretionyear−1 (25). Previous ob″ angular resolution weremooth and axisymmetricl in the disk that extends
phere and decreases monofrom the star (20, 23).
cal depth of the observed
sion, we performed radions using RADMC-3D (26)the previous surface denor the Elias 2-27 disk (20).
the azimuthally averaged
served ALMA 1.3-mm con1) (17). At a radial distancer referred to as radius andhan R ≈ 10 AU, the emisnd thus traces the density
n to the midplane of thethe spiral structures (fromthe azimuthally averaged
dust continuum emission
U, decreasing to t = 0.02
S1B), which is consistent
eak brightness tempera1.2 K at R = 150 AU.
es are even more evident
e data has been projected• アルマ以前は「円盤状のものがありそう」と思われていただけだったが…
L14-2

The Astrophysical Journal Letters, 820:L40 (5pp), 2016 April 1

M. Fukagawa et al.

Andrews et al.

November 23 and 0.7 mm on the latter two executions. The
total on-target integration time was ∼2 hr.
These raw data were calibrated by NRAO staff. After
applying phase corrections from water vapor radiometermeasurements, the data were time-averaged into 2 s integrations and ﬂagged for problematic antennas and times. The
bandpass response of each spectral window was calibratedusing the observations of J1058+0133. The amplitude scale
was determined from J1037–2934 and J1107–4449. The
complex gain response of the system was calibrated using thefrequent observations of J1103–3251. Although images
generated from these data are relatively free of artifacts andrecover the integrated ﬂux density of the target (1.5 Jy), folding
in additional ALMA observations with a higher density of shortantenna spacings improves the image reconstruction.
To that end, we calibrated three archival ALMA data
observations of TW Hya, from 2012 May 20, 2012 November
20, and 2014 December 31, using 16, 25, and 34 antennas
spanning baselines from 15 to 375 m. The ﬁrst two observations had four 59 MHz wide spectral windows centered at
Figure 1. Synthesized image of the 870 μm continuum emission from the TW
333.8, 335.4, 345.8, and 347.4 GHz. The latter had two
Hya disk with a 30 mas FWHM (1.6 au) circular beam. The rms noise level isFig. 1. Thermal dust emission from the protoplanetary
disk surrounding Elias 2-27. The disk was
235 MHz windows (at 338.2 and 349.4 GHz), one 469 MHz∼35 μJy beam−1. The inset shows a 0 2 wide (10.8 au) zoom using an image
Fig.
1. window
Dust
continuum
mapandat one336 1875GHz(890window!m)forthe with
diskﬁnerofresolution (24×18 mas, or 1.3×1.0 au, FWHM beam).
imaged at a wavelength of 1.3 mm, with
ALMA
reaching
an angularof 0.26″
0.22″(indicated(at 352.0GHz), resolution
MHz by(at
HD 142527.
TheJ1037–2934
colortoscalebrightness
temperature
338.4corresponds
GHz).
employeda gaincalibrator,
by the ellipse in the bottom left corner),
which
36was
byshows
31 AUtheatasthedistanceof the star. on
and Titan
and 3C(May20), Ceres
and T
J0522-364
10, 15,= anda logarithmic
scale.
The279black
contours
denoteb = 5,
The field-of-view center (at 0, 0) corresponds
to
the
disk
emissionpeak
locatedatrightascension(J2000)(November 20), or Ganymede and J0158+0133 (December 31)
20
K,
while
the
white
one denotes
5 "Thelevel.
size of thewith
synthe16 hours 26 min 45.024 s, declination (J2000)–24
23 calibrators.
min the08.250s,weatherandThecoincidental
served= as
ﬂuxdegrees
or bandpass
for these
13 CO (uppe
sized
beam
is
shown
at
the
left
corner
of
the
image
with
a
white
ellipseFig.
2.
Moment0(left)
and1(right)maps
inobservations
wasexcellent,
with
PWV
levels
of
0.5–1
mm.
The
the position of the star Elias 2-27. (A)00 1.3-mm00 dust continuum image from the Elias 2-27 protoı.
combined
on-target
integrationtime
was a95major-axis
minutes. ThePA
basic
39
!
0:
34
(=
55
au
!
48
au)
with
of
57
of
0:
J = 3–2 (lower). The contours in the left panels show thplanetary disk over a 4″ by 4″ area. The color
scale
represents
flux
densitymeasured
in
units
of
Janskycalibration was as described above. As a check, we compared
−26
−2
−1
In the right panels, the first moment maps are presented
per beam (1 Jy = 10
W m Hz ). (B) Increased
contrast
image
from processing
the original ALMA
the amplitudes
from eachindividual
data set on overlapping
sion detected above 5 ". The contours for the integrated
and foundconsistency.
Cycle
0.spatial
Thefrequencies
maximum
andexceptional
minimumbaselines were 380 m
observations shown in (A) with anunsharpmaskingfilter (17).
The calibrated visibilities from each observation were shifted
overplotted, starting from 5 " and increasing by 5 " stepand 20 m,
respectively,
andthelattercorrespondedtotheto account for the proper motion of the target and thenin each panel denotes the position of the central star. The
00
combined after excising channels with potential emission fromlargest angularscale of the detectable component of 10 . The
beam size is displayed with a white ellipse in each panel,
spectral lines. Some modest improvements were made with around ofphase-onlyin
self-calibration.
imagesat a schedulingobservations
reported
this letterContinuum
consistedof four! 0:00 37 with a PA of 50ı for both 13 CO and C18 O.
mean frequency of 345.9 GHz (867 μm) were generated byblocks overtheperiodfrom 2012
June toFourier
invertingthe visibilities,
deconvolving
withAugust.
a multi- The corre-• 若い円盤→２本の腕が示すダイナミックな動き• 偏った円盤→惑星誕生中か？

rg/ on November 21, 2016

O R TS

アルマで見た原始惑星系円盤• リング・ギャップ構造→惑星がギャップの中にいる？

アルマで惑星形成の現場の姿がわかってきた。

ALMAで観測する時の戦略
1天体に数時間費やす

1天体1分以下で100天体くらい見る

HL TauLupus survey

A&A 599, A113 (2017)

Full#disk##TD#
Edge(on#

Ansdell et al. 2016, Miotello et al. 2017
ALMA Partnership 2015

- (total flux) =1.4 Jy at 1.0 mm- (rms) = 12 µJy/beam- (spatial resolution) =25ミリ秒角 (3.5 AU)- (detection rate) = 62/89 sources- (rms) ~ 0.3 mJy/beam- (spatial resolution) ~ 300 ミリ秒角 (30-50 AU)--

Akimasa Kataoka (NAOJ)

天体としての原始惑星系円盤

The Astrophysical Journal, 828:46 (15pp), 2016 September 1

Ansdell

cumulative distribution
•

領域の違い
•

Lupus, Taurus: 200-300万年 (若い)•Upper Sco: 500-1000 万年 (老いている)•Class II円盤のミリ波強度を測った。

•

結果
•

若い領域の円盤のほうが３倍くらい明るい。

•

明るい円盤は、おそらく円盤の質量が多い（横軸は、円盤のミリ波の明るさに比例するもの）
Figure 9. Comparisons of the dust mass distributions in Taurus and Upp
Figure 8. Dust mass cumulative distributions for Lupus, Taurus, and Upperto that of the Lupus reference sample. pG is the probability that the pote
Sco disks around host stars with M*  0.1 M: (Section 6.2). The average dust
Andrews et al. 2013, Ansdell et al. 2016, Barenfeld et al. 2016
incomplete and/or biased comparison samples are drawn from the same
masses for each region are given for reference. The distributions were
population as the complete reference sample. f (pG ) is the cum
calculated using the Kaplan–Meier estimator to include upper limits;
Akimasaline
Kataoka (NAOJ)pComparison of R68 Size Distributions

Summary Statistics for Resolved Disks

天体としての原始惑星系円盤

R68 (au)
RegionCount

MedianOph
Tau/Aur
Lupus
ChaI
USco

20
25
30
33
22

60.1
48.6
46.6
33.9
26.8

e.g., the Pearson’s r test, are based on the assumption that thedata follow a normal distribution. The Shapiro–Wilk p value isthe null hypothesis probability that the sample is normally
distributed. In cases where the p value is <0.05, we reject thenull hypothesis and conclude that the distribution is not normal.
Otherwise, we conclude that the distribution is likely normal.
The result of this determines which correlation test we use
afterward and is described in further detail below.
For all regions, we calculate both the Pearson correlation(hereafter Pearson r test) and Spearman’s rank
• coefﬁcient
領域の違い
correlation coefﬁcient (hereafter Spearman ρ test) and thecorresponding p values. For both tests, the p value gives theprobability of rejecting the null hypothesis that there is no
signiﬁcant Taurus,
relationship between
the variables,•statistically
Ophiucus,
Lupus,
ChaI: more
speciﬁcally, a linear relation for the Pearson’s r test and amonotonic
one for the
Spearmanρ test. In cases where the p
1-3 Megayear(若い)value for the chosen statistic is <0.05, we consider the data to
be correlated. As mentioned above, the Pearson’s r test requires
the data to be bivariate normal. For this reason, we use ther test Sco:to establish
if thereis a linear
correlation
only•Pearson’s
Upper
5-11
Mega
year
(老い
when our data are normally distributed, as found by the
Shapiro–Wilk test. In all other cases, we rely on the Spearmanρ toている)test for the existence of a monotonic relationship between
variables. Note that while the Spearman ρ does not need thevariables to be normally distributed, it does require that they areconverted into a rank-order (ordinal) data set.
• 結果
A limitation of all these statistical tests is that they do notinclude upper limits and uncertainties in the assessment. As
such, and for comparison with results already reported in theliterature, we might ﬁt linear relationships even if our•correlation
tests result in a probability larger than 0.05 that
結構明るい天体は、サイズが~30the variables are not correlated.

R90 (au)

R68 Distributions

Stat

Sig.a

Max

MedianMax

Region 1

138.0
167.0
128.1
140.9
100.8

L
L
63.2
43.1
33.4

L
L
213.1
231.3
126.2

USco
ChaI
3.4
0.014
USco
Lupus
3.4
0.013
Figureresolved disks in different1.2
regions, ordered by0.105
age.
ChaI 4. Swarmplots forLupus
R68 25%–75% quartiles,
The
boxplots include a shaded
Lupus
Oph region surrounding the1.2
0.104
the horizontal line denotes the median disk size, while whiskers deﬁne the 0%–
Tau/AurOph−0.2> 0.2525% and 75%–100% quartiles. The regions observed with the SMA are grayedout because they are biased to the brightest millimeter disks, hence their size
Note.
distributions
should not be directly compared to the regions observedabySig.,
ALMA.
also known as the error rate, indicates the signiﬁcance level at which thenull hypothesis that samples are drawn from the same/can not be rejected.

Note. Oph and Tau/Aur R68 values are from Andrews et al. (2018b).

Region 2

Anderson–Darling

cumulative distribution

5.1. Relations Between Stellar and Disk Properties

Figure 4. Swarmplots for resolved disks in different regions, ordered by age.
The boxplots include a shaded region surrounding the R68 25%–75% quartiles,
the horizontal line denotes the median disk size, while whiskers deﬁne the 0%–25% and 75%–100% quartiles. The regions observed with the SMA are grayedout because they are biased to the brightest millimeter disks, hence their size
distributions should not be directly compared to the regions observedby ALMA.

The following two subsections examine the disk size–diskluminosity (log Reff – log L mm ) and the disk size–stellar properties (log Reff – log M and log Reff – log L  ) relations. In order todetermine if empirical relationships can be established, weapply several statistical tests to the data.
We begin with the Shapiro–Wilk normality test (Shapiro &Wilk 1965) to determine if the distribution of our bivariate data
is normal or not. This is important as many correlation tests,
e.g., the Pearson’s r test, are based on the assumption that thedata follow a normal distribution. The Shapiro–Wilk p value isthe null hypothesis probability that the sample is normally
distributed. In cases where the p value is <0.05, we reject thenull hypothesis and conclude that the distribution is not normal.
Otherwise, we conclude that the distribution is likely normal.
The result of this determines which correlation test we use
Figure5. Cumulative
disk sizes distributions
our modeled
afterward
and is describedin furtherfordetailbelow.regions: Lupus,
et al.correlation
2020
ChaI,
Shadedweregions
indicateboth
1σHendler
conﬁdence
intervals.
ForandallUSco.
regions,
calculatethe Pearson
coefﬁcient (hereafter Pearson r test) and Spearman’s rank
100auくらいある。
To test if theseresults (hereafter
depend onSpearman
the selection
or RtheR68and90 ,correlation
coefﬁcient
ρ of
test)
5.1.1. Disk Radii and Millimeter Luminosities
Figureperformed
weproduced a pRvalues.
corresponding
For ofbothtests, 5,theandp valuegives the90 version
Anderson–Darling
tests on
ChaI, and that
UScothere
usingis our
probability of rejecting
theLupus,null hypothesisno
Recently, Andrews et al. (2018b) demonstrated that the dust
and foundno signiﬁcantchangethe observed
Rstatisticallysigniﬁcantrelationshipbetweenthe invariables,
more
effective radius (Reff ) and the millimeter luminosity (L mm )90 disk sizes•disk明るい天体の大きさは、UScoのほ
speciﬁcally, a linear relation for the Pearson’s r test and ascale in the same way for their Oph, Tau/Aur, and Lupus
trends.
monotonic one for the Spearman ρ test. In cases where the p
うがちょっと小さいかな。
value for the chosen statistic is <0.05, we consider the data to 7
be correlated. As mentioned above, the Pearson’s r test requires
the data to be bivariate normal. For this reason, we use thePearson’s r test to establish
if there is a linear correlation only
Akimasa Kataoka (NAOJ)
when our data are normally distributed, as found by theLupus
ChaI
USco

30
33
22

46.6
33.9
26.8

原始惑星系円盤の全体像

128.1
140.9
100.8

63.2
43.1
33.4

Note. Oph and Tau/Aur R68 values are from Andrews et al. (2018b).

712

•

•

距離100-150pcの場所に、円盤を~100個持つ領域が~10個ある。

•

ミリ波連続波でダスト円盤が観測できるダスト円盤の質量 (Class II)••

質量中央値は5-15地球質量。分散大きい(0.1-100地球質量)

ダスト円盤の大きさ (Class II)

Note.
aSig., also know
null hypothesis

L. A. Cieza et al.

5.1. ReThe follow
luminosity (lties (log Reff –determine if
apply several
We begin
Wilk 1965) tois normal ore.g., the Peardata follow a
the null hyp
distributed. I
null hypothes
Otherwise, w
Figure 4. Swarmplots for resolved disks in different regions, ordered by age.
The result o
The boxplots include a shaded region surrounding the R68 25%–75% quartiles,
afterward andthe horizontal line denotes the median disk size, while whiskers deﬁne the 0%–
For all reg
25% and 75%–100% quartiles. The regions observed with the SMA are grayed
coefﬁcient (hout dust
becausethey aretosamplethe brightest
millimeterdisks,
hence
size
Figure 13. The cumulative
mass distribution
in ourbiased
Ophiuchuscompared to thoseof otheryoung
regions.
The
linetheir
widthsindicate
1σ confidence
Cieza
et
al.
2019
intervals. Average dust distributions
masses and ages areshould
listed for reference.
Ophiuchuspresents
a disc mass distribution
is very similar
to those seen in Taurus
andnot bedirectlycomparedto thethatregions
observed
correlationc
Lupus, and more massive discs than older regions. However, the distributions shown are not corrected by sample selection biases or the dependence on stellar
by ALMA.
correspondin
mass and thus should be interpreted with caution.
probability o
the Ophiuchus Molecular Cloud, and present the initial continuum(5) A simple conversion between flux and dust mass (adopting
statistically s
data. Our main results are the following:standard assumptions for dust opacities and temperatures) indicatesthat all sources detected at 1.3 mm have enough solid mass tospeciﬁcally,form
one or more rocky planets. In contrast, only ∼50 discs (∼1/3 of(1) We detect 120 of our 147 targets in 1.3 mm continuum, formonotonico
the sample) have enough mass in the form of dust to formthean overall detection rate of 82 per cent. Among these detections,canonical 10 M⊕ core needed to trigger runaway gas accretion
value for the
we find 11 binary systems and a triple system, for a total of 133
andtheformation
of
gas
giant
planets.
In
thiscontext,
themainindividual discs detected. Out of these 133 detected discs, 60 werebeuncertainty is the total mass of solids already incorporated to largecorrelated
spatially resolved and we measure fluxes, sizes, and position angles.
bodies (e.g. cm to km scales) that are not detectable by ALMA.
the data to b
The other 73 detected objects remain unresolved and we can only
(6) The distribution in disc sizes in our sample is heavily
measure flux and set an upper limit to their size (approximately
Pearson’srtweighted towards compact discs. Most discs have radii < 15au,corresponding to the resolution of our observations).
while only 22 discs (∼15 per cent of the targets) have radii > 30
au.
when
our d
(2) 27 of our targets remain undetected, with 4σ upper limits of
The
discs
that
remainunresolvedin
oursamplewould
benefitfrom∼1.0 mJy, but a stacking of the non-detections shows a 4σ detection
higher resolution data at longer wavelengths to better constrainShapiro–Wilk
bothof 0.16 mJy, suggesting a typical dust mass of just ∼0.1 M⊕ for
their
sizes
and
masses.
ρ to test for tthese objects.
(3) Among our sample, we find eight sources with clear subThe detailed study of disc properties as a function of the variables.
mass
No
structures. Six of them have inner dust opacity cavities and two ofand age of the host stars, the effects of (sub)stellar companions on
variables to bthem show narrow gaps/rings (one object, WSV 82, shows both andisc properties, and the gas content in the discs based on the 12 CO,
inner cavity and a gap/ring structure). Another object, Elias 2-27,
13
converted int
CO, and C18 O observations will be presented in future papers
shows two spiral arms. Four additional sources show hints of subof this series, along with radiative transfer modelling of resolved
A limitatio
structures based on their deprojected radial profiles. Most of thesesources.
features are seen among the brightest sources in the sample. If they
include uppe
are all confirmed, it would imply that ∼50 per cent (11/21) of thesuch, and forsources brighter than ∼50 mJy show some type of substructure.
AC K N OW L E D G E M E N T S(4) We performed a preliminary comparison of the dust mass
literature, w
We thank the anonymous referee for his/her comments, which wefunction in Ophiuchus to those of other regions. We find that thetebelieve have
us to improvethe manuscript
significantly.correlationThis
dust mass distributionFigure
in Ophiuchus
is very similar disk
to thoseof other
5. Cumulative
sizes
distributions
for helped
our modeled
regions:
Lupus,
paper makesHendleruse of the following ALMA
young regions (1–2 Myr) as Taurus and Lupus. However, significant
al.ADS/JAO.ALMA2020
the variables
ChaI, and USco. Shaded regions indicate
1σ conﬁdence
intervals. et data:•

明るい天体の半径は30-100auくらい(でも分解能も~30au程度の情報)•

まだ暗い天体の大きさはわからない。
Akimasa Kataoka (NAOJ)

ChaI
Lupus
Tau/Aur

evolution is seen towards older ages, as already shown by previous
results.

Downloaded from https://academic.oup.com/mnras/article-abstract/482/1/698/5114271 by National Astronomical Observatory of Japan user on 19 August 2019•

原始惑星系円盤

213.1
231.3
126.2

#2016.1.00545.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA), and NINS (Japan), together with NRC

本日のお話• 第一部: ALMAを中心とした、原始惑星系円盤の描像のレビュー (~20分)• 高分解能で見えたリング・ギャップ等副構造• サーベイ観測で明らかとなった全体像• 第二部: 我々の進めてきたALMA偏光観測 (~25分)• ダスト散乱による偏光と、ダストミクロ物理への制限• (時間があれば、今進めているダスト組成への示唆の研究 ~ 10分)

ALMA偏光観測は、明るい天体のみ

Astrophysical Journal Letters, 831:L12 (6pp), 2016 November 10

Kataoka et al.

•

ダスト連続波の偏光を観測する•

偏光度は0.1-10%程度•を受信する必要がある•

e 1. In the left panel, the colorscale represents the polarized intensity in units of mJy beam−1 with a log scale, the gray contours show the continuum emission,e white vectors show the polarization vectors. Note that the lengths of the polarization vectors are set to be the same. The levels of the contours are (3, 10, 30,
300, 600, 900, 1200, 1500, 1800)×σI(=185 μJy beam−1) for Stokes I. Polarization vectors are plotted where the polarized intensity is larger than=0.128 mJy beam−1. In the right panel, the colorscale displays the polarization fraction overlaid with the polarization vectors. The gray contours display theuum emission with the same levels of the left panel. The colorscale is only shown with the same threshold of the polarization vectors in the left panel.

bility is the difference in the grain size and its effects onalignment efﬁciency; the radiative torque efﬁciency
ases with decreasing grain size if the grain size is smaller
the wavelength. Therefore, if the peak emission of Stokes I
ainly coming from grains smaller than the wavelengths, it
d decrease the alignment efﬁciency and thus the polarizafraction (e.g., Cho & Lazarian 2007; Lazarian &→普通の連続波の1/100の暗い信号

Kataoka et al. 2016

power-law size distribution with a power of −3.5 and the
maximum grain size 150 μm, which is the most efﬁcient grain
size to scatter the thermal emission and make it polarized at theobserved wavelength of λ = 0.87 mm. The density distribution
is based on a previous modeling of the continuum at the same
wavelength (Muto et al. 2015). The density distribution of dust
distribution
in radial andgrains Σd is taken to be a Gaussian
Akimasa Kataoka(NAOJ)

あんまり高くない分解能(0.5秒角~50auくらい)でたくさん積分(~数時間)しないと取れないimages, as seen in Figure 2. Speciﬁcally, at 3.1 mm the
StokesQ image shows negative regions from north to southand positive regions from east to west. At 1.3 mm, the negative
regions are much brighter than the positive regions, and at
870 μm, the positive regions almost completely disappear.
StokesU shows two positive and two negative regions at
3.1 mm. The negative blobs disappear at 1.3 mm, while thepositive regions connect, and at 870 μm, the positive regions
turn into a single, large region.
4
F. Bacciotti et a
For the Stokes V images (Figure 2), 3.1 mm appears to be
purely noise. For both 1.3 mm and 870 μm, StokesV has anegative ﬂux blob offset to the top-right of the Stokes I
F. Bacciotti eintensity, and this blob 4is signiﬁcantly brighter in 870 μm.
The Astrophysical Journal Letters, 831:L12 (6pp), 2016 November 10 Although circular polarization can in principle be produced by Kataoka et al.
L30 W. R. F. Dent etscattering
al.
of linearly polarized light off non-spherical grains
4
Hull
et al.
HD 142527
IM LupCWwellTau(e.g., Tazaki
et al. 2017), StokesV has not beencharacterized for ALMA, so its detection could be spurious
IM Lupand will not be discussed in detail in this paper.
The central polarization vectors for 1.3 mm and 870 μm are
55°. 4 ±0°. 96 and 55°. 3 ±0°. 41, respectively. The major axisof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnership et al.
2015), indicating the polarization vectors are ∼7° from being
perpendicular to the major axis. We would expect thepolarization to be perfectly perpendicular to the major axis.
The reason for this small 7° discrepancy is uncertain, but could
indicate asymmetry in the disk.
The right panels of Figure 2 show P for each wavelength.
For 1.3 mm and 870 μm, there is a slight asymmetry for P
along the major axis of1%the disk, with the southeast morepolarized than the northwest. For 1.3 mm, the absoluteAUdifference between the 200
two
P peaks along the major axis(a)is0.0013 ± 0.0014, which is not statistically signiﬁcant. The
asymmetry for 870 μm is more apparent, although the southeast
HL TauHD 163296
DG Taupart of the disk −1
does not peak (i.e., it is still increasing at the
Figure 1. In the left panel, the colorscale represents the polarized intensity in units
witha log scale,the grayThecontours
show
the continuum emission,edgeofofmJy
thebeamdetectedpolarized
emission).
P peaktowardand the white vectors show the polarization vectors. Note that the lengths of thethepolarization
are setbe the same.
The alevels
the (a)contours are (3, 10, 30,
northwestvectors
is 0.0077
±to0.0010.
Drawingline offromthe−1
I. Polarization
vectors theare center
plotted ofwhere
the polarized
intensity is larger than100, 300, 600, 900, 1200, 1500, 1800)×σI(=185 μJy beam ) for Stokesnorthwest
peak throughthe disk,
at the same−1
fraction
overlaid withpolarization±
vectors.
TheP gray
3σPI=0.128 mJy beam . In the right panel, the colorscale displays the polarization
radius on
the southeastside,theP=0.0094
0.0010.
risescontours display thecontinuum emission with the same levels of the left panel. The colorscale is only
shown withtheedgesameof the polarization
vectors in the left panel.
to ∼0.0115
at theofthresholdthe disk. Therefore,
the P asymmetry
along the major axis for 870 μm is ∼0.002–0.004. These
are relatively
moderate, butwith
the fact
that they
possibility is the difference in the grain size and its effects on asymmetries
power-lawsize distribution
a powerof −3.5 and theboth at 1.3
mm sizeand 870they
the alignment efﬁciency; the radiative torque efﬁciency appearmaximum
grain
150μm
μm,suggests
which isthecould
most efﬁcient grain
be a real feature. If we consider total polarization PT 
decreases with decreasing grain size if the grain size is smaller Contours:
size to scatter the thermal
emission and make it polarized at theContours:
Q 2 U 2 V 2 I , the asymmetry
is similar; for 1.3 mm, it isIntensity
P
Polarization
than the wavelength. Therefore, if the peak emission of Stokes Polarized
I 0.0012
observed
wavelengthof fraction
λ = P0.87
mm. The density distributionfrac
± 0.0014, while for 870 μm it is ∼0.001–0.004.
is mainly coming from grains smaller than the wavelengths, it Yangis etbasedon ashowed
previousof thethecontinuumat the sameal. (2017)that modelingasymmetry along
major
would decrease the alignment efﬁciency andFigure
thus
the polariza- axis
(Muto
et al. 2015). The
densityindistributionof dustiswavelength
not disk
expectedscattering-induced
polarizationan
1. 870 µm ALMA maps of the Class
II protoplanetary
IM Lup. The forpeak valuesof the total intensity (Stokes I),
polarized
intensity (P ), and polarization fraction images are 120.74 mJy beam , 1.37 mJy beam , and 0.011, respectively. The rms noise values inaxisymmetricdisk,
axisymmetry
must
be broken if thetaken
Gaussiantion fraction (e.g., Cho & Lazarian 2007;
Lazarian& thermal
Σared is= so
the total intensityand polarized intensity
dust grainsemission images
100µJy beam toand be= 22 aµJy beam, respectively. distribution in radial and
The black ellipses in the lower-left corners of all panels represent the ALMA synthesized beam (resolution element), which measures 0. 50 ⇥polarizationdue ofto161 scattering
evenetthough
the total
0. 40 at a position angle of 76.9 , corresponding
to a linear
resolutionisof ⇠really
72 au direction
at a distance±as
10 pc (Gaia Collaboration
al. 2016).
azimuthal
Hoang 2007).
Top: Polarization map of IM Lup. Contours are the total intensity thermal dust emission, plotted at 3, 8, 16, 32, 64, 128, 256, 512, 1024 ⇥ .
Grayscale is the polarized thermal dust emission,plotted (Stokes
starting at 3 I .) Linesegments are
the polarization orientationof the other hand,
intensity
is highly
axisymmetric.
On thedust vectors
emission, with lengths
proportional to the polarization fraction P. Bottom left: Grayscale is the total intensity thermal dust
The azimuthal direction of the polarization
asshown
emission; contours are the polarized intensitythe
P , plotted
at 0.06, 0.1, 0.2, 0.3, 0.4,
0.5, 0.6, 0.7,the0.8, 0.9 ⇥minor
the peak of 1.37
mJy beam. Bottompolarization
along
axis
is expected
to be⎡right:
Grayscaleis the total
intensity thermal dust emission; contours are
the polarization fraction P= P/I, plotted at levels of⎛⎞⎤
Figure1.
ALMApolarimetricobservations
at
3.1
mm
(top,
Kataokaetal.
2percentage
in the outer regions indicates the Figure
poloidalmagneticﬁeld
0.005,
0.006,
0.007,
0.008,
0.009,
0.01.
The
coordinates
andthegrayscaleareidentical
in
the
two
bottompanels.
The
ALMA
data
used
to
1.
Sub-mmcontinuumpolarizationin
HD163296.
The
top
panels
show
(a)
the
total
intensity
and
(b)
the
polarization at band 7 in th
R

R
(
)
asymmetric
if
the
dust
disk
is
optically
thick
and
has
a
d
make
figure areshow
availablethein the online version of this publication.
2017), 1.3 mm (middle), and 870 μm (bottom), where theredthisvectors⎢40,min (40,max  40,min ) exp ⎜⎜ (c)
⎥
⎟
4

d
⎟ ⎥(b). The lower panels are (c) the p
conﬁguration,
while
the radial
direction
on rotated).
the inner
ringareregion.
as ellipses
representations
ofwidththe threein theillustration,
total intensity
signiﬁcantangular(forrings
a cartoon
seeimage,
Figuremarked
6 2G 21–3 in>3σ polarization
morphology(i.e., vectors
have
notSuperimposed
been
Vector⎢⎝⎠ are⎣⎦ shown at their actual angle, whdlengthsthe
are linearly
proportional
to P. The
color
scale
shows
the(d)
polarized
flux intensity
andthepolarization
angle,etboth
the HL
polarization
vectors
superimposed.
In (c), the vectors
al. with2017).
Tau disk
is known
to be opticallyindicates
toroidalmagnetic
ﬁeld.
There
has
been
no in Yang
◦ is multiplied
intensity, which is masked to only show 3σ detections.
Stokes
I contours
in to the2. Linearlypolarized
P andpolarization
at t8(d) theof
vectorrotation
relativemeanatof 870
44.1μmby a factorof⎞et3, totheintensity
relative
twist.
Polarization
fractionfraction
and anglep are
thick(Carrasco-González
al.emphasize2016), but
no2⎛Figuremechanism
locally
toforrotate
the50,direction
the750,magnetic
each panel
are shown[3, 10, 25,
100, 200, 325,500,1000] × TI ,ﬁeldr
rcminor
(DG
) au)
Tau
(panels
as in(beams
Fig.
1. Polarization
angle,−1atpolarized
flux andlevelsof
5σ per beam
(250µJy).
Imagesare⎜and3arcsec(315
across.
Resolution
isof∼0.2 arcsec
areshown lower left).
Pola
asymmetryisdetectedalong
theaxis.(c),(d)).
The lackContours
exp
,
1
q
(
)
T
is
44,
154,
and
460
μJy
bm
for
3.1
mm,
1.3
mm,
870
μm,
where
⎟
I
by 90°. Therefore, at least at that position, the mechanism
2
indicate
jet
Disk near-side lies towards the receding jet lo
asymmetryfor P along
optically
minor axis implies
vectors have 1/2 beam spacing, withlengths proportional
to thepolarization
fraction.
respectively.
2rthe⎠ orientation.
⎝thew thick
should be different from the grain alignment.
−1
total intensity is I > 10 mJy beam
for CW Tau and I > 30 mJy beam(c)

ALMA偏光観測
The Astrophysical Journal Supplement Series, 245:2 (50pp), 2019 November

Sadavoy et al.

1

1

I

1

P

1

00

00

I

P
frac

1

frac

Figure 3. The 14 continuum sources with polarization detections. Background images show the Stokes I maps on a logarithmic color scale (see Appendix A for theﬂux scale), and the black line segments show the normalized e-vectors. Sources with ‡are outside of the inner third of the primary beam FWHM. The blue and red
arrows indicate the outﬂow position angle, if known (see Section 4.1 for details). The gray bars show the major-axis position angle of the continuum sources detectedin polarization, except IRAS 16293B, as this source is near face-on and does not have a well-constrained continuum position angle. For VLA 1623 A, we show twogray bars: the ﬁlled one shows the position angle of the compact disk from Harris et al. (2018), and the open one shows the position angle of the extended disk.

Kataoka et al. 2016, Hull et al. 2018, Bacciotti et al. 2018, Dent et al. 2019, Stephens et al. 2017, Kataoka et al. 2017,
Theal.
polarizationin the south
is as high as
Ohashi et2018,fraction
Sadavoy
et regional.observations
2019…
sub-mmfound an upper
limit rofand
1 per
centthetoetradial
the
total
on-source
20,max
h,
where
θ are
andTheazimuthalcoordinates,◦ although some 15 min
Piétual. (2014)
andthetimeoneof jet, i was=449
reportedof the11jet
13.9±0.7%, which is higher than thepredicted value (e.g.,polarization fraction in a 1 arcsec beam
(Hughesetal.
2009).
Pinte
were
flaggedinthesecondsessionthe target
transite
Figure2.
Linearlypolarized
intensityP
andapolarization
fraction
p=
4
and
are
the
maximumandminimum
surfacedensity
atwhile0,minHartiganetal.
(2004).
The
same
fit
gives
disk
posiini
Cho & Lazarian2007).
The
highfractionofpolarization
means
jet
Akimasa Kataoka (NAOJ)et al. (2018) and Teague et
also
found
the(c),(d)).
zenith.
3 al. (2018)
and
DG
as in
Fig. 1. Polarization ang◦◦ center andthe havecenterof recently
the
ring,
θTau
and(panels
f torepresent
theContours
width

d PA
tion angle,

d = 60.7 ±1.9 , in good agreement withhigher回転方向と平行

短軸と平行

The Astrophysical Journal Letters, 844:L5 (5pp), 2017 July 20163296 of(0.9themm)essential. The wavelength HD
dependence
polarization
fraction is not strong in the case of the grain alignment,
while it is strong in the case of the self-scattering because
the scattering-induced polarization is efﬁcient only when the
maximum grain size is around M 2Q where λ is the
wavelengths (Kataoka et al. 2015).
To obtain the wavelength-dependent polarimetric images, weobserve the HL Tau disk with the Atacama Large Millimeter/
submillimeter Array (ALMA) using Band 3. HL Tau is a youngstar in the Taurus molecular cloud with a distance of 140pc(Rebull et al. 2004). The circumstellar disk is around in∼100 au scale (Kwon et al. 2011). The disk has several ringand gap structures with tens of au scales (ALMA Partnershipet al. 2015). The observed band corresponds to wavelengths of
3.1 mm, which is sufﬁciently longer than the previous
CARMA
4polarimetric observations at 1.3 mm (Stephens et al. 2014).
The Astrophysical Journal, 851:55 (6pp), 2017 December 10

Kataoka et al.

4

F. Bacciotti et al.
Harrison et al.

(a)
複合的

DG Tau (0.9 mm)

HL Tau (3 mm)

Stephens et al.

The transition of polarization morphologies from one
wavelength to another is also apparent in the StokesQ and U
images, as seen in Figure 2. Speciﬁcally, at 3.1 mm the
StokesQ image shows negative regions from north to southand positive regions from east to west. At 1.3 mm, the negative
regions are much brighter than the positive regions, and at
870 μm, the positive regions almost completely disappear.
StokesU shows two positive and two negative regions at
3.1 mm. The negative blobs disappear at 1.3 mm, while thepositive regions connect, and at 870 μm, the positive regions
turn into a single, large region.
For the Stokes V images (Figure 2), 3.1 mm appears to be
purely noise. For both 1.3 mm and 870 μm, StokesV has anegative ﬂux blob offset to the top-right of the Stokes I
intensity, and this blob is signiﬁcantly brighter in 870 μm.
Although circular polarization can in principle be produced byscattering of linearly polarized light off non-spherical grains(e.g., Tazaki et al. 2017), StokesV has not been wellcharacterized for ALMA, so its detection could be spurious
and will not be discussed in detail in this paper.
The central polarization vectors for 1.3 mm and 870 μm are
55°. 4 ±0°. 96 and 55°. 3 ±0°. 41, respectively. The major axisof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnership et al.
2015), indicating the polarization vectors are ∼7° from being
perpendicular to the major axis. We would expect thepolarization to be perfectly perpendicular to the major axis.
The reason for this small 7° discrepancy is uncertain, but could
indicate asymmetry in the disk.
The right panels of Figure 2 show P for each wavelength.
For 1.3 mm and 870 μm, there is a slight asymmetry for P
along the major axis of the disk, with the southeast morepolarized than the northwest. For 1.3 mm, the absolutedifference between the two P peaks along the major axis is0.0013 ± 0.0014,
which is not statistically signiﬁcant. The
The Astrophysical Journal Letters, 877:L2 (8pp), 2019 May 20
asymmetry for 870 μm is more apparent, although the southeast
4
Hull et al.
part of the disk does not peak (i.e., it is still increasing at theedge of the detected polarized emission). The P peak toward
IM Lupthe northwest is 0.0077 ± 0.0010. Drawing a line from thenorthwest peak through the center of the disk, at the sameradius on the southeast side, P=0.0094 ± 0.0010. P rises
to ∼0.0115 at the edge of the disk. Therefore, the P asymmetry
along the major axis for 870 μm is ∼0.002–0.004. These
asymmetries are relatively moderate, but the fact that they
appear both at 1.3 mm and 870 μm suggests they could
be a real feature. If we consider total polarization PT 
Q 2 U 2 ◦ V 2 I , the asymmetry is similar; for 1.3 mm, it is0.0012 ± 0.0014, while for 870 μm it is ∼0.001–0.004.
Yang et al. (2017) showedthat asymmetry along the major
1%axis is not expected for scattering-induced polarization in an
200axisymmetryAUaxisymmetric disk, so
must be broken if thepolarization is really due to scattering even though the total
intensity (Stokes I ) is highly axisymmetric. On the other hand,the polarization along the minor axis is expected to be
Figure 1. ALMA polarimetric observations at 3.1 mm (top, Kataoka et al.
asymmetric if the dust disk is optically thick and has a2017), 1.3 mm (middle), and 870 μm (bottom), where the red vectors show thesigniﬁcant angular width (for a cartoon illustration, see (a)Figure 6>3σ polarization morphology (i.e., vectors have not been rotated). Vector
lengths are linearly proportional to P. The color scale shows the polarizedin Yang et al. 2017). HL Tau disk is known to be opticallyintensity, which is masked to only show 3σ detections. Stokes I contours inthick at 870 μm (Carrasco-González et al. 2016), but noeach panel are shown for [3, 10, 25, 50, 100, 200, 325, 500, 750, 1000] × TI ,asymmetry is detected along the minor axis. The lack ofwhere TI is 44, 154, and 460 μJy bm−1 for 3.1 mm, 1.3 mm, and 870 μm,
asymmetry for P along the optically thick minor axis implies
respectively.

ownloaded from https://academic.oup.com/mnrasl/article-abstract/482/1/L29/5107365 by Universidad Nacional Autonoma d

ALMA偏光の向き

Mori et al.

Figure 1. Sub-mm continuum
polarization in HD163296. The top panels show (a) the total intensity and (b) the percentage polarization at band 7 in the central
2. Observations
region. Superimposed as ellipses are representations of the three rings in the total intensity image, marked 1–3 in (b). The lower panels are (c) the polarized(c)
Tau andwas(d)observedby ALMA
onwith2016
October 12,
fluxHLintensity
the polarization
angle, boththe polarization
vectors superimposed. In (c), the vectors are shown at their actual angle, whereas induringits Cycle
4 operation(2016.1.00115.S,
PI: A. Kataoka).
(d) the vector
rotation
relative to themean of 44.1 is multiplied
by a factor of 3, to emphasize the relative twist. Polarization fraction and angle
are truncatedFigure2. Linearly polarized intensity P and polarization fraction p at 870 µm
TheantennaandImages
41 antennas
were
at polarized
fluxconﬁgurationlevels of 5σ perwas
beamC40-6,(250µJy).
are 3 arcsec(315 au) across. Resolution is ∼0.2 arcsec (beams are shown lowerandleft).DG
Polarization
Tau (panels (c),(d)). Contours as in Fig. 1. Polarization angle, χ, is invectors have 1/2
spacing, withlengths proportional
to the windows
polarization fraction.
operating.
Thebeamcorrelator
processed
four spectral
indicate the jet orientation. Disk near-side lies towards the receding jet lobe (red102.5,
and2019,104.5 Stephens
GHz with aetbandwidth
centered at 90.5, 92.5,
Dent
et al.
al. 2017,
of
1.75 GHz
each. The
bandpass,
amplitude,
were
sub-mmobservations
found
limit
of 1andpercent2018…
to
the
Hull
et an
al. upper
2018,
Bacciotti
etphaseal.
calibrated
observationsof J0510+1800,
andpolarizationby
fractionin a 1 arcsec
beam (HughesJ0423-0120,
et al. 2009). Pinte
J0431+1731,
respectively,
polarization
was
et al. (2018) and
Teague etand
al. the(2018)
have alsocalibration
recently foundperformed
by observationsof J0510+1800.
The raw data were
dynamical evidenceof massive
planets in the system.
reducedthe EA-ARC
In thisby
paper,
we presentstaff.
ALMA observations of polarized dust
We further perform the iterative CLEAN deconvolution
emission of HD163296 at 870 µm with a resolution of ∼0.2arcsec –imaging with self-calibration to improve the image quality. We
sufficient to resolve the rings. We also combine the intensity images
employ the briggs weighting with the robust parameter of 0.5
Contours:

3Polarized Intensity P

Contours:
Polarization fraction Pfrac

Figure 1. 870 µm ALMA maps of the Class II protoplanetary disk IM Lup. The peak values of the total intensity (Stokes I), polarized
intensity (P ), and polarization fraction images are 120.74 mJy beam 1 , 1.37 mJy beam 1 , and 0.011, respectively. The rms noise values inthe total intensity and polarized intensity thermal dust emission images are I = 100 µJy beam 1 and P = 22 µJy beam 1 , respectively.
The black ellipses in the lower-left corners of all panels represent the ALMA synthesized beam (resolution element), which measures 0.00 50 ⇥0.00 40 at a position angle of 76.9 , corresponding to a linear resolution of ⇠ 72 au at a distance of 161 ± 10 pc (Gaia Collaboration et al. 2016).
Top: Polarization map of IM Lup. Contours are the total intensity thermal dust emission, plotted at 3, 8, 16, 32, 64, 128, 256, 512, 1024 ⇥ I .
Grayscale is the polarized thermal dust emission, plotted starting at 3 P . Line segments are the polarization orientationof thedust emission, with lengths proportional to the polarization fraction Pfrac . Bottom left: Grayscale is the total intensity thermal dust
emission; contours are the polarized intensity P , plotted at 0.06, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 ⇥ the peak of 1.37 mJy beam 1 . Bottom
right: Grayscale is the total intensity thermal dust emission; contours are the polarization fraction Pfrac = P/I, plotted at levels of
0.005, 0.006, 0.007, 0.008, 0.009, 0.01. The coordinates and the grayscale are identical in the two bottom panels. The ALMA data used tomake this figure are available in the online version of this publication.

−1−1
total intensity isBacciotti
I > 10 mJy
beam
for
CW
Tau
and
I
>
30
mJy
beam
for D
et al. 2018, Mori et al. 2019…
Kataoka et al. 2017, Harrison et al. 2019…
The total time on-source was 2 h, although some 15 min of data◦
Piétuetal.
(2014)
and
the
one
of
jet,
i
=
49
reportedof these valu
jetwere flagged in the second session while the target transited close◦
Hartiganetal.
(2004).
The
same
fit
gives
a
disk
posiin
i
=
38
(E
jet
to the zenith.
angle,
PAadisk = 60.7◦ ±1.9◦ , in good agreement withhigher than d
The system was set up to observe continuumtion
in band
7 at
思ってたのと違う…
mean frequencyof 343.5 GHz, with spectral windows
at 336.494,
PAdisk= 62◦ ± 3◦ (Piétu et al. 2014), and almost per2010). The 2
338.432, 348.494, and 350.494 GHz, each having 31.25
MHz chanpendicular
to the jet PAjet =-29◦ (Hartigan et al. 2004).
almost perpe
nel spacing and 2 Akimasa
GHz nominal
with aFor
total
usableDG
Tau, the integrated flux is 880.2 ± 9.4 mJy,
1998).
Kataoka bandwidth,(NAOJ)(b)

Figure 1. Upper left (a): The total intensity (Stokes I) of the continuum emission at 870 µm. The solid contours represent total
intensity with levels of 100 10000 ⇥ I (=60 µJy beam 1 ) in log space. The beam with the size of 0.00 94 ⇥ 0.00 62 and position
angle of 75. 3 is shown in the bottom left with the white ellipse. Upper right (b): Polarized intensity on a linear scale. The
solid contour levels are (3, 5, 7, 10) ⇥ P I (= 27 µJy beam 1 ). The polarization vectors are presented where polarized intensity
is larger than 3 P I . We set the length of the polarization vectors to be the same. Lower left (c): The polarization fraction
overlaid with the vectors. The solid contours show polarized intensity as with the P I map. The polarization fraction wherepolarized intensity is less than 3 P I is removed. The synthesized beam is also presented with the black ellipse. Lower right (d):星・惑星形成におけるミリ波偏光
ダスト整列による偏光理論•

偏光観測の例

星・惑星形成領域において、ミリ波帯では、~10-100K程度の熱放射が見える。

•

熱放射を偏光させる有力なメカニ
ズムは、ダストの整列

Linear polarization

Akimasa Kataoka (NAOJ)

et al. 2006
Fig. 1. (A) Sketch of the axisGirart
directions:
red/bluearrows show the direction of the redshifted/
blueshifted lobes of the molecular outflow,
probably driven by IRAS 4B (8); solid lines show
the main axis of the magnetic field; and dashedlines show the envelope axes. The solid triangles

L30

W. R. F. Dent et al.

原始惑星系円盤におけるミリ波偏光
円盤偏光予測The Astrophysical Journal Letters, 844:L5 (5pp), 2017 July 20•

ALMA偏光観測 Kataoka et al.

もし空間分解能が上がれば、原essential. The wavelength dependence of the polarization
fraction is not strong in the case of the grain alignment,
while it is strong in the case of the self-scattering because
始惑星系円盤の偏光が見えるは
the scattering-induced polarization is efﬁcient only when the
maximum grain size is around M 2Q where λ is theずwavelengths (Kataoka et al. 2015).
•

To obtain the wavelength-dependent polarimetric images, weobserve the HL Tau disk with the Atacama Large Millimeter/
submillimeter Array (ALMA) using Band 3. HL Tau is a youngstar in the Taurus molecular cloud with a distance of 140pc(Rebull et al. 2004). The circumstellar disk is around in∼100 au scale (Kwon et al. 2011). The disk has several ringand gap structures with tens of au scales (ALMA Partnershipet al. 2015). The observed band corresponds to wavelengths of
3.1 mm, which is sufﬁciently longer than the previous CARMA
polarimetric observations at 1.3 mm (Stephens et al. 2014).

原始惑星系円盤全体の大きさは100 au くらい ~ 1秒角くらい•

磁場に整列していれば、トロイ
2. Observations
ダル磁場の証明ができるはず HL Tau was observed by ALMA on 2016 October 12,
during its Cycle 4 operation (2016.1.00115.S, PI: A. Kataoka).
The antenna conﬁguration was Fig.
C40-6,
and 41 antennasobservations.
were11.—SimulatedDegree of polarization is calculated for the radiation from thだ。
operating. The correlator processed four spectral windows

centered at 90.5, 92.5, 102.5, and 104.5 GHz with a bandwidthof 1.75 GHz each.
Thebandpass,
amplitude,
and phase 1997,
were
Figure 1. Sub-mm continuum polarization in HD163296. The top panels shoe.g.,
DraineandWeingartner
Kataoka
et
al.
2017,
disk
symmetry
axis
and
the
line
of
sight.
Weplot
thedirectionofregion. Superimposed as ellipses are representations of the three rings in thecalibrated by observations of J0510+1800, J0423-0120, and思ってたのと違う…
flux intensity
andDent(d) the polarization
angle, both with the polarization vect
J0431+1731,
respectively,
the polarization
was2007…
Lazarian
2007,
Cho andcalibration
Lazarian
et al. 2019…
polarization
for andthree
different
wavelengths
and twodifferent(d) the vector rotation relative to the mean of 44.1◦ is multiplied by a factor
performed by observations of J0510+1800. The raw data wereviewing angles. The lines represent the direction of polarization.
at polarized flux levels of 5σ per beam (250µJy). Images are 3 arcsec (315
reduced by the EA-ARC staff.
vectors
have 1/2 beam spacing, with lengths proportional to the polarization
Since
weperform
assumemagnetic
field is azimuthal, thedirectionWefurther
the that
iterative
CLEAN deconvolution
Kataoka (NAOJ)
imaging with self-calibrationAkimasa
to improve
the image quality. We

ダスト偏光によるミリ波偏光
Self-scattering

VLT/SPHERE (Avenhaus et al. 2018)

IR scattered light

disk

Infrared

The Astrophysical Journal Letters, 748:L22 (7pp), 2012 April 1

radio scattered light(self-scattering)

Muto et al.

The Astrophysical Journal Letters, 815:L26 (7pp), 2015 December 20

The Astrophysical Journal Letters, 729:L17 (6pp), 2011 March 10

Subaru/HiCIAO

S2 S1
S3
S4

HashimoGemini/GPI

S8
S7

S5

S6

millimeterN
1″ =144AU

1″ =144AUE(Muto et al. 2012, Hashimoto et al. 2011)

Kataoka et al. 2015

1

Akimasa Kataoka (NAOJ)(Rapson et al. 2015)10(mJy/arcsec 2 ) 100

Figure 1. Near-infrared (H band) PI and I images of AB Aur. Left: the HiCIAO PI image with a coronagraphic occulting mask of 0.!! 3 diameter. The multstructures we refer to as S1 to S8 are identified in the top right inset, of which S7 and S8 are newly found. Right: the CIAO reference PSF-subtracted I ima software mask of 1.!! 7 diameter (Fukagawa et al. 2004). In contrast to the original image, this image shown here is not divided by the square of the radia
from the star. The field of view in both images is 7.!! 5 × 7.!! 5. The solid circles in the left bottom inset in both images represent the spatial resolution of 0.!! 06

ダスト偏光によるミリ波偏光
thermal dust emissionof other dust grainsa dust grain

The observer is you.

Horizontal Polarization(the line of sight isperpendicular to the planeof this slide)

Akimasa Kataoka (NAOJ)

ダスト偏光によるミリ波偏光

Horizontal Polarization

Akimasa Kataoka (NAOJ)

ダスト偏光によるミリ波偏光

Unpolarized

Akimasa Kataoka (NAOJ)

ダスト偏光によるミリ波偏光

Vertical Polarization

Akimasa Kataoka (NAOJ)

ダスト偏光によるミリ波偏光
偏光ベクトルはチューブ構造に対して垂直

リング円盤

偏った円盤

真横から見た円盤

傾いた円盤

動径

動径

鉛直

短軸に平行

Akimasa Kataoka (NAOJ)

輻射輸送計算結果
I [mJy/arcsec2]

P[%]

10

3

3.00

2
102
[arcsec][arcsec]

1
0

101

-1
-2

2

2.50

1

2.00

0

1.50

-1

1.00

-2

0.50

100
-2

-1

0
1
[arcsec]2

偏光ベクトル

内側動径方向、
外側回転方向

0.00
-2

-1

0
1
[arcsec]

2

Kataoka, et al., 2015, Ohashi et al. 2020,…

短軸と平行Akimasa Kataoka (NAOJ)

Kataoka, et al., 2016a, Yang et al. 2016,
Dent et al. 2019, Okuzumi and Tazaki 2019,
Ohashi and Kataoka 2019, Lin et al. 2020,
Brunngräber and Wolf 2020 …

散乱偏光で可能となったサイエンス
Assumption: spherical dust grains

アルベド（散乱効率）

a=λ/2π１回散乱における９０度散乱の偏光度

grain size

a=λ/2π散乱偏光は、(ダスト半径)=2π×(波長)くらいのときだけ検出できる

grain size

ALMA偏光観測を利用したダストサイズ測定
d the albedo ! =  /(+  ) as a function of maximum grain size.
sca

abs

sca

a 3.5 . The wavelengths are assumed to be 1.3 mm for the left panel andgrain size which has the most efficient polarization by 90 scattering.

0
he
2)
).

ffihs

1.2

Prediction of polarization fraction

1

Pω

0.8

•
3.1 mm0.87 mm (Band 3)(Band 7)7 mm
(Band 1)

例•

0.34 mm(Band 10)

ALMA Band 7 (0.87mm)で散乱偏光が受かったけど、

0.6

ALMA Band 3 (3.1 mm)では散0.4

乱偏光が受からなかった

0.2
•

0
0.001

→ダストサイズは~150 µmく
らい

0.01
0.1
Maximum grain size [cm]1
Kataoka et al., 2015

(grain size) ~ λ/2π
Fig. 4.— The polarization times the albedo P ! against the maximum grain size. This figure represents the sensitive grain sizefor detection of polarization. Each line corresponds to the wave-

3.1 mm. The negative blobs disappear at 1.3 mm, while thepositive regions connect, and at 870 μm, the positive regions
turn into a single, large region.
For the Stokes V images (Figure 2), 3.1 mm appears to be
purely noise. For both 1.3 mm and 870 μm, StokesV has anegative ﬂux blob offset to the top-right of the Stokes I
intensity, and this blob is signiﬁcantly brighter in 870 μm.
Although circular polarization can in principle be produced by
The Astrophysicalscattering
Journal, 851:55(6pp), 2017
December
10 off non-spherical grains
Stephens et al.
of linearlypolarized
light
urnal Letters, 808:L3 (10pp), 2015 July 20
ALMA
Partnershipetal.
The Astrophysical(10pp), 2015 July 20
ALMA Partnership et al.
(e.g., Tazaki
et al. 2017), Journal
StokesV Letters,
has not 808:L3
been well
The transition of polarization morphologies from one
characterized for ALMA, so its detection could be spurious
and will not be discussed in detail in this paper. wavelength to another is also apparent in the StokesQ and U
images,as seen in Figure 2. Speciﬁcally, at 3.1 mm the
The central polarization vectors for 1.3 mm and 870
μm are55°. 4 ±0°. 96 and 55°. 3 ±0°. 41, respectively. The StokesQmajor axisimage shows negative regions from north to southand positiveof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnershipet al. regions from east to west. At 1.3 mm, the negative
regions
are much brighter than the positive regions, and at2015), indicating the polarization vectors are ∼7° frombeing
ALMA Band 7
870
μm,
the
positive
regions
almostcompletely
disappear.
to the Journal
major axis.Letters,
We would
expect(5pp),
the 2017 July 20
Theperpendicular
Astrophysical
844:L5
Kataoka et al.
StokesU
shows
twopositiveandtwonegative
regions
at
ALMA Band 6
polarization to be perfectly perpendicular to the major axis.
3.1
mm.
The
negative
blobs
disappear
at
1.3
mm,
while
the
The reason for this small 7° discrepancy is uncertain, but could
However,
we cannotalignment
withtheμm, the positive regions
positive regions
connect, andat 870indicate asymmetry
in the disk.rule out the grain
turn into a single, large region.
The right
panels of Figure
2 showInP for
wavelength.
poloidalmagneticﬁelds.
theeachcase
ofthethe
1.3
mm (Figure
image,
For
StokesV
images2), 3.1 mm appears to be
For 1.3 mm and 870 μm, there is a slight asymmetry for P
however,
we axisinterpret
it with
withthe (c)the moreself-scatteringof andthe870 μm, StokesV has apurelynoise. For both 1.3 mm
along the majorof the disk,
southeast
ﬂux blob offset to the top-right of the Stokes I
polarizeddustthan emission,
the northwest.which
For 1.3provides
mm, thenegative
absolute
thermalthepolarization
vectors brighter in 870 μm.
intensity,
and
this
blob
is
signiﬁcantly
difference between the two P peaks along the major axis isparallel
to0.0014,
the minor
However,
there
be2017also
some
Althoughcircular polarizationcanin principle be produced by
0.0013 ±
which isaxis.
not statisticallysigniﬁcant.
Thecould
The AstrophysicalJournal,851:55(6pp),
December
10 off non-spherical grains
Stephens et al.
scatteringof linearly polarized lightasymmetry
for
870
μm
is
more
apparent,
althoughthesoutheast
contributions of (b) the alignment withtheradiationﬁelds
to has not been well(e.g.,
Tazakietal.
2017),
StokesVof the disk does not peak (i.e., it is still increasing at the
The transition of polarization morphologies from one
thepartpolarization,
which
enhancesthepolarization
vectorsatthecharacterized
for
ALMA,
so
its
detection
couldbespuriousedge of the detected polarized emission). The P peak toward
wavelength to another is also apparent in the StokesQ and U
and
will
not
be
discussedindetailin
thispaper.
the northwest andis 0.0077
± 0.0010. regions
Drawing a linefrom theimages, as seen in Figure 2. Speciﬁcally, at 3.1 mm thenorth–west
south–east(alongthe major
axis)
while
The
centralpolarization
vectors
for
1.3
mm
and
870
μm are image shows negative regions from north to south
northwest peak through the center of the disk, at the same
StokesQ
decreasingpolarization
thenorth–east
55°. P
4at±0°. 96 and
55°. 3 ±0°. 41, andrespectively. The major
axis regions from east to west. At 1.3 mm, the negative
radius on the thesoutheast
side, P=0.0094fraction
± 0.0010.
rises
and positiveof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnershipet al.are much brighter than the positive regions, and at
to ∼0.0115 at theedge of the
disk. Therefore,
the P asymmetry
regions
south–west
regions(alongthe minoraxis).
2015),
indicating the polarization vectors are ∼7° fromalong the major axis for 870 μm is ∼0.002–0.004.
These
870being
μm, the positive regions almost completely disappear.
The
wavelength
dependenceinthepolarization
fractioninperpendicular
to
the
major
axis.
We
would
expectthe shows two positive and two negative regions atasymmetries are relatively moderate, but the fact that they
StokesUpolarization
to be perfectly perpendicular to the majoraxis.The negative blobs disappear at 1.3 mm, while themm and 870 μm suggests
they
could
3.1 mm.
theappear
casebothof atthe1.3self-scattering
is strong(Kataokaetal.
2015),The reason
couldregions connect, and at 870 μm, the positive regions
PT  for this small 7° discrepancy is uncertain, but
be a real feature. If we consider total polarization
positivewhile
it is weaker in the case of the grain
Therefore,
indicatealignment.
asymmetry in thedisk.
turn into a single, large region.
Q 2 U 2 V 2 I , the asymmetry is similar; for 1.3 mm, it is
The right panels of Figure 2 show P for each wavelength.
For the Stokes V images (Figure 2), 3.1 mm appears to be
the0.0012
mostinterpretationis thatthe alignment with the
± natural
0.0014, while
for 870 μm it is ∼0.001–0.004.
For 1.3 mm and 870 μm, there is a slight asymmetry
for noise.
PpurelyFor both 1.3 mm and 870 μm, StokesV has a
Yang et al. (2017) showed that asymmetry along the majorradiationﬁelds
providestheaxisymmetricalong the azimuthal
major axis of polarizathe disk, with the southeast
more
negative ﬂux blob offset to the top-right of the Stokes I
axis is not expected for scattering-induced polarization in an
4. Total
fraction as brightera functionof μm.
the observedALMA
wavelengths.
polarized than the northwest. For 1.3 mm, Figure
the intensity,
absolute
Band 3and polarization
this blob is signiﬁcantlyin 870tion
vectorsdisk,
onsobothwavelengths,
while
axisymmetricaxisymmetry
must be broken
if the the self-scattering
difference between the two P peaks along the The
majoraxis polarization
is circular polarization
total
fractioncan
is derived
bybeintegrating
Althoughin principle
produced byeach Stokes I, Q, and U
polarizationisreallydue
toscattering
eventhoughthetotaldominates
at 1.3mm.
0.0013 ± 0.0014, which is not statistically signiﬁcant.
The Thescatteringof linearlypolarized
lighttheoff prediction
non-sphericalofgrains
component.
curvesrepresent
the HL Tau disk with theintensity(StokesI)ishighlyaxisymmetric.
On
the
other
hand,
show 2.9, 1.3, and 0.87 mm ALMA continuum images of HL Tau. Panel (d) shows the 1.3 mm PSF for the same FOV
as the forotherasymmetry
870 μm is more apparent, although the (e.g.,southeast
Tazakimodel
et al. where
2017), theStokesV
has not
been
well
the polarization along the minor axis is expected
to show
be theself-scattering
maximumgrain
sizes
are a max  50, 70, 100 ,enlargedview of theobservations
inner 300atmas
centeredon the PSF’sand (f)
1.
ALMA polarimetric
3.1 mm(top, Kataoka
et al. peak (the other bands show similar patterns). Panels (e) partof the disk
does not peak (i.e., it is still increasingatthecharacterized for ALMA, so its detection could be spurious
asymmetric
if theis opticallythick andhas<a4 . The
αedge
αerroresultingfrom thecombination
the the1.3redand
0.87showmmthedata. The
spectral index(α)dustmapdisk
has beenmasked where.3 mm (middle),
and 870μm (bottom),ofwhere
vectors(Kataoka
et al.in 2016a)andwith the radiative alignment model. The
150
N mnotof the detected polarized emission). The Pandpeaktowardandwillbediscussed
detailin
thispaper.
signiﬁcantangular
width
(for
a
cartoonillustration,
see
Figure6larization
morphology(i.e.,
vectors
have
not
been
rotated).
Vector
4.2.forModelingtheComponents
to 0.0077 ± 0.0010. Drawing a dashed,
he lower left of each panel; also see Table 1. The range of the color bar shown
panel (b) at 1.3
mmScatteredcorresponds−2× rms isthetonorthwest
line fromthesolid,
dotted vectors
lines represent
with the local alignmentThecentralandpolarizationfor 1.3 mmthe
and models
870 μm arearelinearly
proportional
to
P.
The
color
scale
shows
the
polarized
in
Yang
et
al.
2017).
HL
Tau
disk
is
known
to
be
opticallyvalues in Table 1. The color scales for panels (a), (c), and (e) are the same except using the values of rms northwest
and imagepeak
peakthrough the center of the disk, at the same
, which is masked to only show 3σ detections. Stokes I contours in, respectively.
efﬁciency
of. 96p
3.6%55°. 4 ±0°
and0%,
55°. 31.8%,±0°. 41,
respectively.
The major axis
thickat 870 μm (Carrasco-González
et components
al. 2016), but noof the polarization,
wavelengthin[3,Table
By
modeling
thescatterednel
are shown for
10, 25,1.50, 100, 200, 325, 500, 750, 1000] × TI ,radius on the southeast side, P=0.0094 ± 0.0010.of PHLrises
Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnership et al.
−1
asymmetryisdetected
along
the
minor
axis.
The
lack offor 3.1 mm, 1.3 mm, and 870 μm,
I is 44, 154, and 460 μJy bm
to ∼0.0115
at thedisk.
edge ofTo
the disk.
Therefore, the P asymmetry2015), indicating the polarization vectors are ∼7° from being
weasymmetry
can constrain
grain thicksizeminor
in theTau
model
for P alongthe
the opticallyaxis HL
impliesvely.
along thethe bestmajor axis for 870 μm is ∼0.002–0.004.
These
perpendicular
to the major axis. We would expect theeach point was moved to the nearest
the average disk geometry over large scales. However,the scattering components in polarization,
we consider
total but the fact
asymmetries
are relativelythe
moderate,that
theypolarization
be perfectly perpendicular
to themajor axis.
thespatialtoresolution
is better orsmaller
if it is diluted by theminimum for dark rings). To avoid
ﬁt ellipses have their centers offset with respect tothe peakof 1.3 mm and 870 μm suggestsif they
appearboth atcould

HL Tau のALMA偏光観測

ALMA Partnership 2015, Stephens et al. 2017

散乱が卓越 at 0.87 mm

散乱成分消える at 3.1 mm

Kataoka et al. 2017, modifiedスペクトルからのダストサイズ推定
SED

Optically thick, transition to Wien’s law

λFλOptically thick, Rayleigh-Jeans law (α =2 )Optically thin, Rayleigh-Jeans law

赤外

~ミリ波

センチ波

λ

スペクトルからのダストサイズ推定
8λFλM. Tazzari et al.

SED
α=2 (光学的に厚い)
α=中間の値：光学的に薄いかつ大ダスト
α=3.7 (光学的に薄い・
ISMダストを仮定)

1 mm

3 mm

λ

α = 2.0 - 3.0: 中間の値

Figure 5. (Left) Spectral index between 1 and 3 mm as a function of integrated 1 mm flux
Lupus TDs are marked with an additional red circle. The dark shaded region represents theare not sensitive anymore. The dashed line is the typical U1 3 mm of the optically thin em
spectral index measurements shown in the left panel. Tazzari et al. 2020a→ 大きな(ミリサイズの)ダスト！

See: Beckwith and Sargent 1991, Isella et al. 2007 …

y 20

ダストサイズの不一致
ALMA Band 7

8

M. Tazzari et al.

Kataoka et al.

ALMA Band 6

with them image,ng of theon vectors
also somen ﬁelds totors at thexis) while–east andraction inal. 2015),
Therefore,
with thepolarizascatteringlarization,
To modelr the total
grate theectors areovides the

ALMA Band 3

Figure 4. Total polarization fraction as a function of the observed wavelengths.
The total polarization fraction is derived by integrating each Stokes I, Q, and U
Kataoka et al. 2017
component. The curves represent the prediction of the HL Tau disk with theself-scattering model where the maximum grain sizes are a max  50, 70, 100 ,and 150 N m (Kataoka et al. 2016a) and with the radiative alignment model. The
dashed, solid, and dotted lines represent the models with the local alignment
efﬁciency of p  0%, 1.8%, 3.6%, respectively.

偏光観測は~100µmを示唆

0.9-3mmのスペクトルが取れたもの：HL Tau, DG Tau
0.9mmの偏光検出~10-20天体
if the spatial resolution
is better or smaller
if it is diluted by thebeam. Then, we obtain the contribution to the total polarization
fraction of 0.114 q p  0, 0.21, and 0.41, respectively.
To explain the results of SMA and CARMA, the self-

Figure 5. (Left) Spectral index between 1 and 3 mm as a function of integrated 1 mm flux for Lupus discs (Lupus TDs are marked with an additional red circle. The dark shaded region represents the sensitivity cut-off
are not sensitive anymore. The dashed line is the typical U1 3 mm of the optically thin emission of ISM dus
spectral index measurements shown in the left panel.

Tazzari et al. 2021

スペクトル観測は~1mm-1cmを示唆
5 DISCUSSION
Spectral indices at sub-mm/mm wavelengths provide us with valu各領域の明るい数十天体
able information on the optical properties of the population of large
grains residing in the discs midplane. In Sect. 5.1 we discuss the constraints that our new 3 mm measurements set on the average grainproperties in the Lupus discs assuming that most of the observed
emission is optically thin. In Sect. 5.2 we discuss the millimeter continuum size-luminosity relation (Tripathi et al. 2017; Andrews et al.

(0 max 1mm) for asize distribution (seeUsing the new 3
spectral index in thecorresponds to a noaccording to Eq. (3).
opacity models base(e.g., Draine 2006; Bκabs [cm2

κabs [cm2

1

10

0

1

10

0

仮定が間違っている？

10

10-1
-2

10

10-1
-2

10

10

-3

10

-3

-4

10

10
10

-4

0

10

1

10

2

3

10

10

4

10

5

10

0

1

10

2

10

3

10

10

λ [µm]

λ [µm](e) af = 1 mm(f) af = 1 cm

4

10

5

10

吸収係数；空隙あっても情報が縮退
偏光強さ；赤がコンパクト、青緑が空隙あり
Unveiling Dust Aggregate
Structure in Protoplanetary Disks
5
4

10

3

0.8

2

10

1

10

P!

κabs [cm2 g-1]

10

0

10

0

f=10-1
f=10 -2
f=10 -3
f=10 -4
f=10

0.6
0.4

10-1
-2

4

10

3

10

2

10

1

10

0

10

f -1
= 1.00f
10 = 0.10
f = 0.01-30

f=10-1
f = 1.00
f = 0.10 f=10 -2
f = 0.01 f=10
-3
f=10 -4
f=10

0.6
0.4
0.2

10

-3

10

10

-4

10

0.8

-2

0.2

10

1

P ! e↵ , P !

1105

κabs [cm2 g-1]

105

0

10

1

10

0
2
33
10
10
10
λ [µm]

42
10
10

51
10
10
10
amax (cm)

-4

010

0

10

101

1

10

102

0
3 3
2
10 10
10
λ [µm]

2 4
10 10

1 5
10 10
100
amax (cm)

101

102

e↵
2. Pa !
for spacesolid spherescompact
aggregates(f = 0.1,
at Tazaki
Solid
KataokaetP !al.
2014
et (Left)al. 2019
Fig. 3. Absorption mass opacity in cases Figureof different
f . anda) Parameterof f and(fa =in 1)theandcasesof b) todustf). Themass opacities
are0.01)shown
in =the1 mm.
cases of b) a f = 1 µm, c) a f = 10 µm, d)linesa f represent= 100 µm,P !.
e) aRed,f = blue,
1 mm,and
andgreenf) a flines= 10showmm.the results for the volume filling factor of f = 1, 0.1, and 0.01, respectively.

Dotted and dot-dashed lines indicate the single scattering albedo ! and the degree of linear polarization P at scattering angle of
90 , respectively. Filled circles indicate P ! at the position of amax f = 160 µm. (Right) Solid and dashed lines indicate results
suggests that the scattering mass opacityise↵not
by Filledhand,circles
the scatteringmass
the Pabsorptione↵for P !
andcharacterized
P !, respectively.
indicate P !
atopacity
amax f =dominates
160 µm. The! e↵ -values mass
at x > 1 is significantlya f at the longer wavelengths. At the
shorter bywavelengths,thee↵ective
opacity
inscattering
fluffy cases
when a f = 0.1 µm. This greatly affects theattenuatedconsidering thesinglealbedo.

•吸収・散乱係数の情報があるとサイズと空隙が区別可能

mass opacity corresponds to the geometric cross section. In the infrared observations of dust grains. For example, Pagani et al.
compact case, the mass opacity scalestheasdegree
λ−4 at ofthepolarization
longer wave(2010)
dense interstellar
mediumweisuse d = 2.0 andbecomeshighreported
even if xthat> 1.dust grains
flu↵yinaggregates.
In this section,flengths. On the other hand, in the fluffy
case,
the
mass
opacitycomposedof
micron-sizedgrains
(and
not
0.1
µm)
becauseofThis is due to the fact thatk0 = 1.0 in order to attain clear physical insights into−2
−4 aggregates with f ⌧ 1
scales as λ at the inter mediate wavelengths,
thenrefractive
scales asindex
λ closethe highscattering
efficiencytheirobserved
the Spitzer space telehave e↵ective
to thatof vacuum,
opticalby
properties.
scope. Thus,
they infer that themonomersize
mustofbelinear
micron.
at the longer wavelengths. We will comeback they
to thiswithas opticallyand then,arepoint
regardedthin particles.
Firstof all, thedegreepolarization of flu↵yHowever,Fig.optically
5 suggests thateven
if the monomers
0.1becauseµm multiple scata physical explanation in Sect. 4. Since multiple scattering is suppressed
insidedust
aggregate
is as high asare100%
in size, theisaggregatesµm sizedmonomers
represent
thin particles, high degree of polarization
obtained. of 0.1
teringis suppressedwhen
x0 ⌧ 1 theand df  2 (Tazaki

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まあまあ詰まっている！

でも結構小さい！！(100ミクロン)
)
m
(µ

まとめ
•

ALMAで、原始惑星系円盤の全体像がわかってきた。

•

明るい円盤は、ミリ波偏光も取れる

The Astrophysical Journal Letters, 831:L12 (6pp), 2016 November 10•

非検出円盤に注意
The Astrophysical Journal Letters, 844:L5 (5pp), 2017 July 20••

偏光から、ダストサイズ、空隙もわかる
Kataoka et al.

ミリ波の吸収・散乱効率が議論できるようになった
Kataoka et al.

However, we cannot rule out the grain alignment withKataoka
theet al.
poloidal magnetic ﬁelds. In the case of the 1.3 mm image,
however, we interpret it with (c) the self-scattering of thethermal dust emission, which provides the polarization vectors
parallel to the minor axis. However, there could be also some
contributions of (b) the alignment with the radiation ﬁelds tothe polarization, which enhances the polarization vectors at the
Full#disk##north–west and south–east regions (along the major axis) whileTD#
decreasing the polarization fraction at the north–east andEdge(on#south–west regions (along the minor axis).
The wavelength dependence in the polarization fraction in
Miotello et al. 2017
the case of the self-scattering is strong (Kataoka et al. 2015),−1
whilerepresents
it is weaker
the caseintensityof the grainalignment.
Therefore,
Figure 1. In the left panel, the colorscale
the inpolarized
in unitsof mJy beamwith a log scale, the gray contours show the continuum emission,
the most
naturalinterpretationis thatthepolarizationalignment vectors
with theand the white vectors show the polarization
vectors.
Notethat the lengthsof theare set to be the same. The levels of the contours are (3, 10, 30,−1
radiation ﬁelds
provides the axisymmetric azimuthal polarizaplotted
where
the polarized
intensity
isof thelargerthanwavelengths.
100, 300, 600, 900, 1200, 1500, 1800)×σ
I(=185 μJy beam ) for Stokes I. Polarization vectors are Figure4.
Total
polarization
fractionasafunction
observed−1
tionpanel,
vectors
on both wavelengths,
while thefraction
self-scattering
the colorscale
displays the polarization
overlaid with The
the total
polarization
vectors.
graybycontours
display
the I, Q, and U
3σPI=0.128 mJy beam . In the rightpolarization
fraction The
is derived
integratingeach Stokes
Kataokaetal. 2017
dominates
1.3panel.
mm. The colorscale is only shown with the same threshold
continuum emission with the same levelsof theatleftof thevectors
in the left
panel.
component.
Thepolarization
curves represent
the predictionof theHL Tau disk with the

The Astrophysical Journal Letters, 831:L12 (6pp), 2016 November 10
A&A 599, A113 (2017)self-scattering model where the maximum grain sizes are a max  50, 70, 100 ,and 150 N m (Kataoka et al. 2016a) and with the radiative alignment model. The
dashed, solid, anddottedalines
representofthe−3.5
models withlocal alignment
distribution
with
power
andthetheefﬁciency of p  0%, 1.8%, 3.6%, respectively.

4.2.size
Modeling
Scatteredpossibility is the difference in the grain
and itstheeffects
onComponents
power-law size
the alignment efﬁciency; theBy radiative
torqueefﬁciency
maximum
grain size 150 μm, which is the most efﬁcient grainmodeling thescatteredcomponents of thepolarization,−1
Figure 1. In the left panel, the colorscale represents
the polarized
intensityin unitsgrainof mJybeam
withgrainatheloggrainscale,
thesmallergrayemission,
we sizecanconstrainin thecontours
HL Taushow
disk.themodel thedecreases
withdecreasing
if thesize sizeissize
toTocontinuum
scatterthermal emission and make it polarized at the
Kataokaetal.
2016
and the white vectors show the polarization vectors. Note that the lengths of the polarization
vectors are
set to be thesame. The levelsof the contours
are (3, 10, 30,
theifscattering
componentsinpolarization,
we consider
the wavelength
total
than
the
wavelength.
Therefore,thepeakemissionof
StokesI
observed
ofspatial
λ = 0.87
mm.isThedensity
distribution
if theresolution
betteror smaller
if it is diluted by the−1
vectors
areplottedwherethepolarized
intensityislargerthan
100, 300, 600, 900, 1200, 1500, 1800)×σI(=185 μJy beam ) for Stokes I. Polarization
polarization
fractionacross
HL
Tau.
If
we
integratetheAkimasa
Kataokabeam.
Then, we obtain
contributionat
to thethe total
polarization
mainly displays
comingthefrom
grainspolarization
smallerthanthe(NAOJ)
wavelengths,
itis basedonare
a previousof thethecontinuumsamepolarization
fraction
overlaid
withthevectors.
The
graycontours
display
themodeling
3σPI=0.128 mJy beam−1. In the right panel, theiscolorscale
all overthe polarization
disk, the axisymmetricvectors