惑星ができない！
- 理論観測両面から探る惑星形成 -片岡章雅（国立天文台）

• 自己紹介•

京大理学部・大学院修士 (2006-2012)•

総研大博士課程/国立天文台（2012-2014）2012年夏の学校会場係長••

東工大研究員 (2014.9-2015.3)•

ハイデルベルク大学研究員 (2015.4-2017.3)•

国立天文台 フェロー→助教 (2017.12-)•

博士から他大に行きたい人•

外国での研究生活について聞きたい人•

夏の学校について議論したい人

あとで捕まえて！
Akimasa Kataoka (NAOJ)

惑星ができない！
- 理論観測両面から探る惑星形成 -概要• 惑星形成と原始惑星系円盤• ミリ波偏光観測によるダスト成長の制限
片岡章雅（国立天文台）

惑星の研究？
1. 太陽系の研究
2. 系外惑星の研究
3. 惑星形成の研究
Akimasa Kataoka (NAOJ fellow)

TRAPPIST 1

太陽系の研究

Hayabusa 2 mission

Jupiter - JUNO mission

系外惑星の研究

惑星形成: 何を解き明かしたいか?

~ 1 μm~ 1000 km

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

小石(≈1cm)同士をぶつけたら、くっつくのか？

小石くっつかない問題
跳ね返り障壁 (e.g., Zsom et al. 2010)

Blum et al. (Braunschweig)

ダストは数 m/s の衝突で破壊される
衝突破壊問題 (e.g., Blum and Münch 1993)

一定密度合体成長の仮定は正しいのか？

ダスト(シリケイトや氷)は星間空間で固体なので、この仮定は正しくない。

ダストは付着時にすき間を持つ弾性応力

表面付着力 (分子間力・水素結合)
弾性体の力学 (Herz理論, 1896)→表面付着力を追加 (JKR理論, 1971)→接線応力/摩擦を追加 (Dominik andTielens 1997)→ポテンシャルエネルギーで記述 (Wadaet al. 2007)

Suyama et al. 2008

Kataoka et al. 2013aKataoka et al. 2013b, 国立天文台 理論研究部プレスリリース
Akimasa Kataoka (National Astronomical Observatory of Japan)

col

col

跳ね返り問題の解決
配位数≈11

E break

配位数≈4

Wada et al. 2011

スカスカのダスト集合体→配位数小→跳ね返らない
E aggregates for various nc and ucol . Panels are arranged by nc (row) and ucol (column). In each panel, the leftWada et al. 2009

ダスト集合体を破壊するのに必要な速度2(1/2) Nm0 v = (結合の数)(結合の強さ)~ N × Ebreak-5/6=> v ~ 1 m/s × (r0/0.1 µm) for silicate,-5/6
10 m/s × (r0/0.1 µm) for ice
Dominik and Tielens 1997

数値計算の結果-5/6
v = 8 m/s × (r0/0.1 µm)
for silicate,-5/6
80 m/s × (r0/0.1 µm) for ice
Wada et al. 2007, 2009, 2013

Bastian Gundlach

2016年6月, ブラウンシュバイク工科大学にて

吸入器

氷の粒馬用吸入器（粒径 ≈ 1.5 µm）◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆
Gundlach and Blum 2015

重要

微粒

く左

デル

学会

低密

盤磁

つい
奥住聡(天文月報2016)

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

惑星形成の現場：原始惑星系円盤

惑星形成の現場：原始惑星系円盤

惑星形成の現場：原始惑星系円盤

惑星形成の現場：原始惑星系円盤

惑星形成の現場：原始惑星系円盤

惑星形成の現場：原始惑星系円盤

円盤を“横から”見ている中心星は隠されている= 500 AU

MIR

原始惑星系円盤（想像）Scattered Light(sub-)mm

1

2

3
4

a
b
d

c

Distance in AU
1 Turbulent Mixing (radial or vertical)
2 Vertical Settling
3 Radial Drift4 a) Stickingb) Bouncingc) Fragmentation with mass transferd) Fragmentation

1
0.35 mm

10100

3.0 mmALMA
VLTI/MATISSE

10 µm
2 µm

10 µm

EELT
JWST/MIRI

Fig. 1.— Illustration of the structure, grain evolution processes and observational constraints for protoplanetary
On for a review
Testidisks.
et al. 2015,
the left side we show the main grain transport and collision mechanism properties. The different lengths of the arrows

可視光・赤外線望遠鏡

λ~ 0.1 - 1 μm

電波干渉計

λ ~ 1 mm

HL Tau (BIMA 2.7 mm)

100 AU

Mundy et al. 1996

HL Tau (CARMA 1.3 mm)

Kwon et al. 2011

th
co
at
bo
fit
R
T
th
ax
(ν
of
1.
in
ar

HL Tau (ALMA 1.0 mm)

100 AU

ALMA Partnership 2015

Lupus ALMA
Disk Survey
Megan Ansdell
IfA (University of Hawaii)
0.05

0.10

0.15

0.20

superuniform

A&A proofs: manuscript no. hd97048-gap

8
0.00

0.02

0.04

0.06

uvclip/superuniform

0.08

0.00

0.01

0.02

0.03

0.04

MEM model∆δ [arcseconds]

Jonathan Williams (IfA)
The Astrophysical Journal Letters, 783:L13 (6pp)
Nienkevan der Marel(IfA)
REPORTS
1.0
1.0
1.0
Carlo Manara (ESA)
The highly asymmetric crescent-shaped
dust
the standard
0.5 core-accretion picture, dust grains
0.5
0.5
Anna Miotello(Leiden)must grow
Marco Tazzari(ESO)from submicrometer sizes to rocky structure revealed by the 0.44-mm ALMA con0.0
0.0
millimetercores ~10 times
the mass of Earth (MEarth) within0.0 tinuum (Fig. 1) traces emission from
Michiel Hogerheijde(Leiden)the ~10-million-year lifetime of the circumstellar sized dust grains and is located between 45 andSierk vandisk.
Terwisga−0.5 (Leiden)
−0.5
−0.5
80 AU (T9 AU) from the star.
azimuthal
However,
this growth process is stymied
TheTheAstrophysicalJournal Letters, 783:L13 (6pp), 2014 March 1
Isa Oliveiraby (MCTI)
what is usually called the radial drift and extent is less than one-third of the ring, with no
−1.0
−1.0
−1.0
A
Leonardofragmentation
Testi (ESO,
INAF)
barrier: Particles of intermediate detected flux at a 3s level (2.4 mJy per beam) in
Ewine vansize
Dishoeck
MPE)[~1 m at 1(Leiden,
astronomical
unit (AU) (1 AU = the northern part (fig. S1). The peak emission
1.0
0.5
0.0
−0.5
−1.0
1.0
0.5
0.0
−0.5
−1.0
1.0
0.5
0.0
−0.5
−1.0
Juan Alcala[arcseconds]∆α high[arcseconds]∆α [arcseconds]
signal-to-noise ratio of ~390, and
1.5 (INAF)
× 108 km = distance∆αfrom
Earth to the Sun), has a veryof theAstronomical
SocietyJapan(2015),
67, No.
122-3John Carpenter(ALMA)
contrastwith Vol.
the upper
limit6 on the opposite
orPublications~1 mm
at 50 AUfromthe star] acquire
high ofthe
Greta Guidi
sideof7 theis at least
factorof 130.
drift(INAF)
velocities
toward thestar ofwith
theALMA
Fig. 2. Reconstructed
imagesHD respect
97048 fortothe
band
data.ring
The intensity
scalea for
all images
is inThe
units of Jy beam 1 . To highlightthe4).
small-scale
structure
we show
left to right)
reconstructed
progressively
smallercompleteabsencewithof dustemissionin thebeams.
northTheof left panel shows the imagegas (3,This leads
to twomajor(fromproblems
for images
Geoff Mathews(IfA)
carriedout
intheextendedarray
configuration
withamaxreconstructedusingsuperuniform
weighting.
The central IRS
panel48shows
superuniformly
reconstructed
andtheresulting
highweighted
contrast
make theimage resulting from clipping
growth(5):First,
high-velocity
collisions
Antonellafurther
Natta(INAF,
DIAS)
all baselines below 160 k . Finally, the right panel shows the MEM model image. The di↵erence in dynamic range between the panels is due toimumbaseline
ofdifferent
about
480velocities
m. The observations
confeature
extremethan earlier
betweenparticles
drift
flux loss
incurredwith
by clipping
the shortest
baselines for thecrescent-shaped
central panel, and dueto themore
smallerreconstructedbeam for the right panel.
(10, 13). The spectral slope
cause
fragmentation.
Second, evenif particles
sistedof six scheduling
blocksduring dust
the asymmetries
period fromof configured
themillimetertofluxes
F [0.44 mm comavoid
thisJunefragmentation,
they Thewill
rapidlydrift abeam
1
2012
to of
August.
correlator
dynamical
range⇡ 1200 and
a RMS
of 0.20 mJywas. We 2.3. ALMA
Cycle n1 band 3 data
inwardandbe using
lost into
the star
beforethey foundbinedinwith
shift
all thus
imagesthe propermotioncorrection
van fluxes at lower frequencies n (14)]
B
a
store
dual
polarizations
infour
separate
spectralwindows
have Leeuwen
time to (2007)
grow tosize.
This 1 andis only
andplanetesimalthese are shownin Figs.
2 for 2.67
the T 0.25 (Fn º n ), suggesting that
ALMA
Early Science
Cycle 1 observations
were conducted oncontinuum
emission.
Weappliedself-calibration
solutionseach,
with
469
MHz
3840 channels
andradialdrift
barrieris ofonebandwidthof themosttheandpersistentmillimeter-sizedgrains(15)
dominatethe1 Decemberemission.
2013 withHowever,
72.6 secondsof total time on HD 97048
obtained
fromformation
the continuum
emissionto the HCO+0.44-mm
J=4-3 andcontinuum
issuesinplanettheories.
A
possiblethe
12 central frequencies were 330.588, 329.331, 342.883
their
CO J=3-2 data and subtracted the continuum emission using (Program
12 ID 2012.1.00031.S, see also Dunham et al. 2016). The
solutionisdusttrapping
inso-calledpressuregas
tracedbythe
CO 6-5 linefrom thesame ranging between 15.8 andarray
configuration
providedbaselines
the
CASA
task
uvcontsub,
resultinginaper-channel
RMSofand 342.400
GHz,
respectively,
totargetthedatamolecular
1bumps:
pressuremaximawhere theThe
dust
ALMA
set
indicates
Kepleriandisk pro- the perceptible water va462.9
meters. aDuring
the observations
19.5localand 23.7
mJy beam
respectively.
resulting
momentLupus ALMA
Disks Survey
1318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「偏った円盤」

The Astrophysical Journal Letters, 783:L13 (6pp), 2014 March 1

L14-2

M. Fukagawa et al.
原始惑星系円盤HD142527

Fukagawa et al. 2013

Fig. 1. Dust continuum map at 336 GHz (890 !m) for the disk of
HD 142527. The color scale shows the brightness temperature on
a logarithmic scale. The black contours denote Tb = 5, 10, 15, and20 K, while the white one denotes the 5 " level. The size of the synthesized beam is shown at the left corner of the image with a white ellipse

Perez et al. 2014

Fig. 2. Moment 0 (left) and 1 (right) maps in 13 CO (

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

PHYSICAL REVIEW LETTE

A&A 610, A24 (2018)

Isella et al. 2016

ALMA Partnership 2015
Fedele et al. 2018

Fig. 1. ALMA 1.3 mm dust continuum image (uniform weighting). The main substructures are highlighted in the right panel.

The structure of the paper is the following: observations andand two weaker dust rings peaking at ⇠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。

Protoplanetary disks - birthplace of planets

The Astrophysical Journal Letters, 829:L35 (6pp), 2016 October 1

Tsukagoshi et al.

MIRJ. Menu et al.: TW Hya: multiwavelength interferometry of a transition disk
λ=1.3 mm
• TW Hya (Mstar = 0.6 M⊙, Teff = 4000 K)

1

2

Scattered Light(sub-)mm

3
4

a
b

star

d

c

Distance in AU
1

1 Turbulent Mixing (radial or vertical)

0.35 mm

2 Vertical Settling
3 Radial Drift100

3.0 mmALMA
VLTI/MATISSE

10 µm

4 a) Stickingb) Bouncingc) Fragmentation with mass transferd) Fragmentation

disk

10

2 µm

10 µm

EELT
JWST/MIRI

Tsukagoshi et al. 2016

Testi et al. 2014

Fig. 1.— Illustration of the structure, grain evolution processes and observational constraints for protoplanetary disks. On
the left side we show the main grain transport and collision mechanism properties. The different lengths of the arrows
illustrate the different velocities of the different grains. On the right hand side, we show the areas of the disk that can beprobed by the various techniques. The axis shows the logarithmic radial distance from the central star. The horizontal
bars show the highest angular resolutions (left edge of the bars) that can be achieved with a set of upcoming facilities andinstruments for at the typical distance of the nearest star forming regions.

- We observe midplane at millimeter wavelengths- Disks have sub-structures at ~10 au scales- Physical origin is under discussion

with respect to the gas. The force exerted on them depends
not only on the relative motion between gas and dust, butalso on the particle size: small particles that are observable
at up to cm wavelength can quite safely be assumed to besmaller than the mean free path of the gas molecules and arethus in the Epstein regime. If the particles are larger than
Akimasa Kataoka (NAOJ)
about the mean free path of the gas molecules, a flow struc-

Menu et al. 2014a dimensionless number, which relates the stopping time tothe orbital period ⌦K . The concept of the Stokes number isuseful because particles of different shapes, sizes, or composition, or in a different environment have identical aerodynamical behavior if they have the same Stokes number.
2.1.2. Radial drift

Infrared polarization

VLT/SPHERE (Avenhaus et al. 2018)

IR scattered light

Infrareddisk

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

Muto et al.

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

The Astrophysical Journal Letters, 729:L17 (6pp), 2011 March 10- We observe scattered light with infrared

Subaru/HiCIAO

S2 S1
S3
S4

polarization

S8

Gemini/GPI

S7
S5- Infrared polarization traces the surface layer- Full of structures (such as spiral arms)

S6N
1″ =144AU(Muto
Akimasa Kataoka(NAOJ) et al. 2012, Hashimoto et al. 2011)

E

1″ =144AU(Rapson et al. 2015)

Scattering-induced polarization
IR scattered light
0.1μm

10

4

κabs,sca [cm /g]

2
millimeter

102-4km

amax=1 µm, κabs
amax=1 µm, κsca
amax=100 µm, κabs
amax=100 µm, κsca

10

radio scattered light ?

1km

dust opacity

5

disk

Infrared

1m

1mm

3

10

2

10

scattering> absorption

1

10

0

10

-1

10

-2

10

-3

10

10

0

10

1

2

10
λ [µm]

3

10

10

4

Polarization due to scattering
incident light(unpolarized)
a dust grain

an observer

an observer
an observer
http://sites.sinauer.com/animalcommunication2e/chapter05.02.html

Akimasa Kataoka (NAOJ)

Polarization due to scattering
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)

Polarization due to scattering

Horizontal Polarization

Akimasa Kataoka (NAOJ)

Polarization due to scattering

Unpolarized

Akimasa Kataoka (NAOJ)

Polarization due to scattering

Unpolarized

Akimasa Kataoka (NAOJ)

Polarization due to scattering

Vertical Polarization

Akimasa Kataoka (NAOJ)

Akimasa Kataoka (NAOJ)

Akimasa Kataoka (NAOJ)

Theoretical prediction
2
StokesI (continuum)
I [mJy/arcsec]

P[%]fraction [%]Polarization
103

ring @ 170AU, d=140pc

3.00

2
102
[arcsec][arcsec]

1
0

101

-1
-2

λ=870µm-2-1

01[arcsec]

2

2.50

1

2.00

0

1.50

-1

1.00

-2

0.50

λ=870µm

100

0.00
-2

2

-1

0

1

2

[arcsec]

The polarization degree is ashigh as 2.5%→detectable with ALMA
Anisotropy → net polarization
Akimasa Kataoka (NAOJ fellow)

Kataoka, et al., 2015

散乱偏光の理論予測

ALMA 観測100 AU

Cycle 3 観測提案書 (PI:Kataoka)cf.) Kataoka et al. 2015

Kataoka, et al. 2016b

Yang, Li, et al. 2016
See also Kataoka et al. 2016aof the disc closer to the observer (the right half) brighter. The polarization fraction is, however, higher on the far side (especiallytowards the outer part of the disc) because the polarization degreeof the scattered light is higher for backward scattering than forforward scattering (see Fig. 6). The most striking difference between this case and the Rayleigh scattering case shown in Fig. 5lies in the polarization direction. The difference comes from thepolarization reversal in the large grain case, which yields an intrinsic (or face-on) polarization direction in the radial (as opposed toazimuthal) direction and an inclination-induced polarization along
the major (rather than minor) axis. The interplay between the intrinsic and inclination-induced polarization leads to polarization
directions in the region of high polarized intensity (the most easily(disk, edge-on view)

Figure 7. Scattering-induced polarization by large grains. As in Fig. 5,plotted are the polarized intensity (colour map) and polarization vectors(line segments, with length proportional to the polarization fraction). Notethe strong asymmetry with respect to the major axis in both the polarized
intensity and the polarization vectors. The polarization along the major axis
in the central region is due to polarization reversal, which may be a robust
indicator of scattering by large, mm/cm-sized, grains. The near side of thedisc is on the right.

Akimasa Kataoka (NAOJ)

i=45°

0.50

H. Yang et al.

[arcsec]-2[arcsec]

2802

1.00

0

Parallel to thedisk minor axis

Kataoka, et al., 2016a

see also Yang et al. 2016

Figure 7. Scattering-induced polarization by large grains. As in Fig.
plotted are the polarized intensity (colour map) and polarization vect

Akimasa Kataoka (NAOJ)

0.00

100

Kataoka, et al., 2015
2
0
1
[arcsec]
-1
-2

2
0
1
[arcsec]
-1
-2

-1

-2

1.50

101

0

Radial inside,
azimuthal outside
2.00

102

1

2

2.50

-1

3

10

2

1

3.00

Pol. vectors
P[%]

I [mJy/arcsec2]

based mostly on CARMA observations at 1.3 and 2.7 mm. It is inagreement with the spatially averaged value obtained from ALMA
observations from 0.87 to 2.9 mm (ALMA Partnership: Brogan
et al. 2015). This value is significantly lower than the typical ISM
value of β ∼ 1.5–2. The difference is usually taken as evidence
for grain growth to millimetre size or larger (Testi et al. 2014), although other interpretations are possible. For example, Ricci et al.
(2012) showed that a value of β ∼ 1 or lower can be obtained without mm/cm-sized grains if part of the disc is optically thick. Somesupport for this possibility is provided by the spatially resolved distribution of β derived from the ALMA data, which shows β ∼ 0
indicative of optically thick emission at the central continuum peak
and two rings (B1 and B6, ALMA Partnership: Brogan et al. 2015,
see their fig. 3). Another possibility is that the index β is sensitive to not only the size but also the shape of the grains. Indeed,
Verhoeff et al. (2011) were able to reproduce the spectral energy
distribution (SED) of the disc of HD 142527 (with β ∼ 1 in the
millimetre regime) with irregular grains of sizes up to only 2.5 µm;

Radiative transfer calculations

Conditions of dust grains for polarization
λ=870 µm (ALMA Band 7)

・For efficient scattering

1.4
1.2

(grain size) >~ λ(grain size) <~ λPolarization requires(grain size) ~ λ/2π

P・For efficient polarization

1

P90

1

P
ω

1

Albedo

1

0.8

0

0.6

0

0.4

0

0.2

0

0

0

-0.2
0.001

-0

Akimasa Kataoka (NAOJ)

0.01
0.1
Maximum
grain
size
[cm]
maximum grain size [cm]1

gle of 90 and the albedo ! = sca /(abs + sca ) as a function of maximum grain size.
3.5
w of n(a) / a. The wavelengths are assumed to be 1.3 mm for the left panel ande maximum grain size which has the most efficient polarization by 90 scattering.

Grain size constraints by polarization
1.2

ed

1

max

velengthon due to 90
nly when thealbedo (§2.2)
ering (§2.3).
etected.

Expected polarization fraction (scalable)

Pω

0.8

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
Kataoka, et al., 2015

Multi-wave polarization → constraints on the grain size
Fig. 4.— The polarization
times
the albedo P ! against the maxAkimasa
Kataoka (NAOJ)

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 4the two P peaks along the major axis is
F. Bacciotti et al.
0.0013 ±  0.0014, which is not statistically signiﬁcant. The
HD163296 submillimetre dust polarisation and opacity
asymmetryfor
4
Hull etal. 870 μm is more apparent, although the southeast
part of the disk does not peak (i.e., it is still increasing at the
IM Lup edge of the detected polarized emission). The P peak toward
the 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
The Astrophysical Journal, 832:200 (8pp), 2016 December 1
Fernández-López et al.
to ∼0.0115 at the edge of the disk. Therefore, the P asymmetry
Table 1along the major axis for 870 μm is ∼0.002–0.004. These
Parameters of the Cepheus 1 mm Continuum Sources
asymmetries are relatively moderate, but the fact that they
a
b
c
P%
P.A.
SourceR.A.
Decl.
Stokes I Peak
Stokes I FluxP
appear both at 1.3 mm and 870 μm suggests they could
−1
J2000
J2000
(mJy beam )
(mJy)
(mJy)
(%)
be a real feature. If we consider total polarization PT =shm
62 01¢49. 60
22 56 17. 989423±10863±209±1
2.0±0.4
57±6
HW2
2 + U 2 + V 2 I , the asymmetry is similar; for 1.3 mm, it isQshm
22 56 17. 976
62 01¢46. 10
HW3c68±10160±6
L
L
L
0.0012 ±  0.0014, while for 870 μm it is ∼0.001–0.004.
Notes.
Yang et al. (2017) showed that asymmetry along the majora1%Polarized intensity ﬂux.
axis
is
not
expectedforscattering-induced polarization in anb
Fraction of polarized emission (percentage average).
(a) if thecaxisymmetric disk, 200
so AU
axisymmetry must be broken
Position angles of the polarized emission are measured counterclockwise. 100 AU
polarization 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] × sI ,asymmetry is detected along the minor axis. The lack ofwhere sI 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.

Millimeter-wave polarization of disks

3 Contours:

Polarized Intensity P

3Contours:
Polarization fraction Pfrac

10 au
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 atover
a position
angle of 76.9Black, corresponding to a linear resolution of ⇠ 72 au at a distance of 161 ± 10 pc (Gaia Collaboration et al. 2016).
3s displayed.
Figure 2. Left: polarimetric map (polarization E-vectors) of the CepheusAHW2 disk-like structure. Fractional polarization red vectors
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 .
contours are Stokes I data with the same levels as in Figure 1. Green contours correspond to the VLA Cband continuum emission showing
the radio
at −6,thermal−3, 3,dust emission, plotted starting at 3 P . Line segments are the polarization orientation of theGrayscaleis the jetpolarized
1
dust
emission,withlengths
proportional
to the polarization fraction Pfrac . Bottom left: Grayscale is the total intensity thermal dust
6, 10, 20, 40, 80, 100, and 140 times the rms noise level of the 6 cm radio map, 28 m Jy beam ) associated with the HW2 massive protostar. The color scale shows theemission; 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
corner.
Right:issame
mapintensity
as in thermal dust emission; contours are the polarization fraction Pfrac = P/I, plotted at levels ofpolarized intensity over 3s . The synthesized beam of both CARMA (gray) and VLA (green) observations are shown at the bottom leftright:
Grayscalethe total
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 toleft panel but including orange vectors between 2s and 3s . The polarized intensity (color scale) also shows emission over 2s .
make this figure are available in the online version of this publication.

HD 142527; Kataoka et al. 2016, HL Tau; Stephenset al.
2017, continuum
IM Lup; polarisation
Hull et al.in2018,
CWThe
Tautopand
DGshow
Tau;
et al. and (b) the percentage polarisation
Figure1. Sub-mm
HD163296.
panels(a)Bacciotti
the total intensity(c) rings in the total intensity image marked 1 - 3 inat band 7 in the central region. Superimposed as ellipses are representations of the three
2018, Cepheus A HW2 ; Fernández-Lopez et al. 2016, HD 163296; Dent et al. 2019, HD100546; Pohl et al. in prep.

(b). Lower panels are (c) the polarised flux intensity and (d) the polarisation angle, both with the polarisation vectors superimposed. In
Figure2. theLinearly
intensitytoPthe
andpolarization
p atby870µm in t(c), the vectors are shown at their actual angle, whereasin (d)
vectorpolarized
rotation relativemeanof 44.1 isfraction
multiplieda factorand DGand
Tauangle(panels
Contours
as influx
Fig.levels
1. Polarization
angle,(250µJ
χ, is indica
4.2.2. Toroidal Magnetic
Field
Model
of 3, toemphasise
the relative twist. Polarisation fraction
are(c),(d)).
truncated
at polarisedof 5 per beamy).
indicate thenear-sidelies towards
the receding
jet lobearro
are 300one,(315
across. The images have a resolutionof jet0.200orientation.
(beams areDisk
shownlower left).
Polarization
vectors have
1/2(redbeam
The second model that we Images
test is a simple
withau)grainstotal
intensity is I > 10 mJy beam−1 for CW Tau and I > 30 mJy beam−1 for DGaligned with a toroidal magnetic
ﬁeld.with
Toroidalﬁeldsproportionalarespacing,
lengths
to the polarization
fraction.
proposed for MRI (magneto-rotational instability) dominated(c)◦Inclined disks: self-scattering at 870 µm
et al. (2014) and the one
jet, i = 49 reported
a lopsided disk: self-scattering at north andPiétualignment
atofsouth

4.2.1. Uniform Magnetic Field Model

The ﬁrst model that we test is one with grains aligned with auniform magnetic ﬁeld threading the disk-like structure
approximately along its major axis, which would cause a
distribution of polarization vectors perpendicular to the ﬁeld
(i.e., northeast–southwest, along the minor axis). This distribution of vectors has the same morphology as the large-scale

disks of low-mass protostars (e.g., Cho & Lazarian 2007). It isof these values ijettherefore an appropriate model to test against the CARMA◦
Hartiganetal.
(2004).
The
same
fit
gives
a
disk
posiini=38
jetLinearly4 polarized
intensity PAND
and polarization
fraction p at 870 (Eislöµm i(Isella et al. 2007). The relative flux calibrationsFigure
across 2.
each
DISCUSSION
MODELING
observations.

wavelengths can occur
sometimes scattering,
the polarization mor-

Polarization mechanisms

polarization morpholowith what would be exdust grains. In particuhe Combined Array forronomy (CARMA) to2
morphology in HL Tau.
nt with grains aligned2015), the Class 0 disk candidate of NGC 1333 IRAS 4A
roidal magnetic fields(Cox et al. 2015), the Herbig AE late-stage protoplaneributed radially in thetary disk HD 142527 (Kataoka et al. 2016), and the diske oriented more or lesscandidate of the high-mass protostar Cepheus A HW2
Kataoka et al. (2015,(Fernández-López et al. 2016). Polarization toward disks
ested that the polarizahave also been detected at mid-infrared wavelengths oftent with that expected
hl et al. 2016; Yang 8.7,
et 10.3, and 12.5 µm (Li et al. 2016, 2017). However,
emission at mid-infrared wavelengths can occur
where polarization polarizedisdue to absorption, emission, and sometimes scattering,
the polarization morcausing difficulty in interpreting the polarization morring rather than grains
phology.
However, except for
42527 (Kataoka et al. Despite these detections, the polarization morphologies usually were not consistent with what would be exl. 2017), the published
pected from magnetically aligned dust grains. In particusolve more than a fewlar, Stephens et al. (2014) used the Combined Array forsk, making it difficult
Research in Millimeter-wave Astronomy (CARMA) toand other polarization
measure the 1.3 mm polarization morphology in HL Tau.2
The morphology was inconsistent with grains aligned
ervations of HD 142527
2015), the Class 0 disk candidate of NGC 1333 IRAS 4A
with the commonly-expected toroidal magnetic fields
polarization for many
(Cox et al. 2015), the Herbig AE late-stage protoplane(polarization/E-field vectors distributed radially in thements across the disk.
tary disk HD 142527 (Kataoka et al. 2016), and the diskdisk). Instead, the E-vectors were oriented more or lessghout most of the disk,
candidate of the high-mass protostar Cepheus A HW2along the minor axis of the disk. Kataoka et al. (2015,
ed with a toroidal field,(Fernández-López et al. 2016). Polarization toward disks
2016) and Yang et al. (2016) suggested that the polarizalogy changed from rahave also been detected at mid-infrared wavelengths oftion morphology is actually consistent with that expected
onsistent with scatter8.7, 10.3, and 12.5 µm (Li et al. 2016, 2017). However,from self-scattering (also see Pohl et al. 2016; Yang et16) found that scatterpolarized emission at mid-infrared wavelengths can occur
al. 2017). Indeed, several disks where polarization istures observed in partsdue to absorption, emission, and sometimes scattering,detected show consistency with the polarization more polarization orientacausing difficulty in interpreting the polarization morphology expected from self-scattering rather than grains
erywhere. A complete
phology.
case is still missing. aligned with the magnetic field. However, except for
the ALMA observations of HD 142527 (Kataoka et al. Despite these detections, the polarization morpholoClass I/II in the sky atgies usually were not consistent with what would be ex2016) and HL Tau (Kataoka et al. 2017), the publishedthus the polarization
pected from magnetically aligned dust grains. In particuobservations are too coarse to resolve more than a few
t high resolution withlar, Stephens et al. (2014) used the Combined Array forindependent beams across the disk, making it difficult
taoka et al. (2017) folResearch in Millimeter-wave Astronomy (CARMA) toto distinguish between scattering and other polarization
014) observations withmeasure the 1.3 mm polarization morphology in HL Tau.
mechanisms.
urprisingly, they foundThe morphology was inconsistent with grains aligned
was azimuthal, which The high-resolution ALMA observations of HD 142527
with the commonly-expected toroidal magnetic fields
by Kataoka et al. (2016) resolved polarization for manylong axes perpendicuFigure 1.
ALMA polarimetric observations at 3 mm
(top,(polarization/E-field
vectors distributed radially in the
10s of independent
resolution
elements
acrossthedisk.
dicted by Tazaki et al.
Kataoka et al. 2017), 1.3 mm (middle), and 870 µm (bottom),disk).(i.e.,
Instead, the E-vectors were oriented more or lessThe
polarization
wasradialthroughout
most of thedisk,where the red
vectors
show
the >3 polarization
morphology
this grain alignmentalong
the minor axis of the disk. Kataoka et al. (2015,
have notrotated).
are linearly
proporexpected
for beengrainsalignedVector
withlengths
a toroidal
field,
adiation anisotropy.”which isvectors
tionalthe
to Pedges. The color
scale shows thechanged
polarized from
intensity,
whichandis Yang et al. Akimasa
2016)(2016) suggested
that thepolarizaKataoka (NAOJ
fellow)
but toward
the morphology
ramorphologies observed
masked to only show 3 detections. Stokes I contours in each panel(alignment with B-fields)

self-scattering

self-scatteringalignment with radiation

Stephens et al. 2017 (see also Kataoka et al. 2017)alignment with radiation

What can we learn? - grain size

Kataoka, et al., 2017
The maximum grain size is ~ 70 µm
Akimasa Kataoka (NAOJ)

Effects of porosity on self-scattering

ucture in Protoplanetary
Disks
Prediction on polarization
fraction
15Modeling of HL Tau

Unveiling Dust Aggregate Structure in Protoplanetary Disks

f = 1.00
f = 0.10
f = 0.01

0.6
0.4

Figure 6. Polarized intensity [mJy/beam] at = 1 mm for solid spheres (f = 1) and compact dust aggregates (f = 00.01) with amax f = 160 µm. From left to right panel, the volume filling factor is decreased. Red bars and their length repres
polarization orientations and polarization fraction, where the reference length for 1% polarization fraction is shown in ribottom in each panel. Total intensity contours in each panel are shown for [3, 12, 25, 35, 50, 100, 200, 300] ⇥ 0.03 [mJy/bea
FWHM of the beam size is 0”.1 as shown in the left bottom circle. Inclination angle of the disk is 45 degrees and the dista
between the observer and the disk is assumed to be 100 pc. Bottom side of each image corresponds to the near side of the d- Porosity widen the window forpolarization to be detected

0.2
0
3
10

10

2

1

0
10

10
amax (cm)1
10

f = 1.00
f = 0.10
f = 0.01

2
10

1

hPdisk i (%)

P ! e↵ , P !

0.8- Extremely fluffy aggregates (f<0.01) is
not likely

0.1

act dust aggregates (f = 0.1, 0.01) at = 1 mm. (Left) Solidfor the volume filling factor of f = 1, 0.1, and 0.01, respectively.
Akimasa Kataoka (NAOJ)
0.01

Tazaki et al. 2019

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

Mass budget problem

Manara et al.: Planet and disk masses

nets, exoplanetary systems, and disks of their host star, as in Fig. 1. The
0th and 90th percentile of the distribuesent the median of the distributions,Fig. 3. Masses of the cores of single exoplanets and the sum of thecores in exoplanetary systems, as well as disk masses, as a function of
the mass of their host star. The colored regions encompass the 10th and90th percentile of the distributions, while the dashed lines represent themedian of the distributions, as labeled.
Manara et al. 2018• おわりに•

これまでの研究
修士時代に星形成磁場における偏光観測予測。博士時代は•

完全に理論。PDで初めて観測論文を書く。
••

理論屋が観測にも手を出せる時代•

ALMAはキャリブレーション済みのデータをくれる。

•

プロポーザルは理論的背景があると強い研究する上では、良い問題を見つけることが大事•

博士から他大に行きたい人•

外国での研究生活について聞きたい人•

夏の学校について議論したい人

あとで捕まえて！
Akimasa Kataoka (NAOJ)

まとめ• 弾性体の力学を応用し、ダストは惑星形成の初期段階で隙間の多い構造を取ることを理論的に証明• すき間の多いダスト集合体は跳ね返り障壁を回避• 氷粒子の場合、衝突破壊問題を回避可能• （中心星落下問題を回避）• 散乱に起因するミリ波偏光理論の確立• ALMA観測によりミリ波偏光を実証

t=0 (φ=0.0003)

100 AUt=