Millimeter-wave polarization of
protoplanetary disks due to dust scattering
Kataoka, et al., submitted to ApJ
2P[%]

I [mJy/arcsec ]
10

3

3.00

2
102
[arcsec][arcsec]

1
0

101

-1
-2

λ=870µm-2-1

01[arcsec]

2

2

2.50

1

2.00

0

1.50

-1

1.00

-2

0.50

λ=870µm

100

0.00
-2

-1

0
1
[arcsec]

2

Akimasa Kataoka (Tokyo Tech)collaborators：T. Muto (Kogakuin U.), M. Momose, T. Tsukagoshi (Ibaraki U.),M. Fukagawa, H. Shibai (Osaka U.), T. Hanawa (Chiba U.), K. Murakawa (Osaka-S.)

Lopsided disks observed with ALMAThe Astrophysical Journal Letters, 783:L13 (6pp), 20

M. Fukagawa et al.

RESEARCH LETTER

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

0

0.1

0.2

0.3

HD142527 (Band 6)
2

HD142527

a

2

1

0

b

–1

–2
CO

2

1

1

0

0

ag.org on June 6, 2013

Angular position north (arcsec)

The highly asymmetric crescent-shaped dust
-accretion picture, dust grains
submicrometer sizes to rocky structure revealed by the 0.44-mm ALMA con–1–1
e mass of Earth (MEarth) within tinuum (Fig. 1) traces emission from millimeterear lifetime of the circumstellar sized dust grains and is located between 45 andCassasus et al. 2013
his growth process is stymied 80 AU (T9 AU) from the star. The azimuthalContinuum–2–2
ly called the radial drift and extent is less than one-third of the ring, with noA22
rier: Particles of intermediate detected flux at a 3s level (2.4 mJy per beam) inc IRS 48d
SR 21
tronomical unit (AU) (1 AU = the northern part (fig. S1). The peak emission
stance from Earth to the Sun), has a very high signal-to-noise ratio of ~390, and11
AU from the star] acquire high the contrast with the upper limit on the opposite
ward the star with respect to the side of the ring is at least a factor of 130. The00
ads to two major problems for complete absence of dust emission in the north of: First, high-velocity collisions IRS 48 and resulting high contrast make thewith different drift velocities crescent-shaped feature more extreme than earlier–1–1
on. Second, even if particles dust asymmetries (10, 13). The spectral slope
ntation, they will rapidly drift a of the millimeter fluxes Fn [0.44 mm com2 μm
HCO+
–2
–2
e lost into the star before they bined with fluxes at lower frequencies n (14)]Ba–1et al.–22014
2 der 1Marel0 et al.–12013–2 2
10van
al. 2013
Perez
w to planetesimal size. This Fukagawa
is only 2.67et
T 0.25(Fn º n ), suggesting thatAngular position east (arcsec)
Figure 1. ALMA observations of dust and gas emission for tr is one of the most persistent millimeter-sized grains (15) dominate theTable 1. Left panels:
continuum(color d,scale)
1 | ALMA
Supplementary
Fig. 1 fordustan overlay
withemission
the continuum.
HCOa
ormation theories. A possible 0.44-mm continuum emission. Figure
However,theobservations of HD 142527, with a horseshoe dust
Figure1.
ALMA
observations
of
dust
and
gas
emissionforthecontinuum
surrounding
a
gap
that
still
contains
gas.
We
see
diffuseCO
gas
intensity
shown
by
white
contours
atfractions
of
0.1,
0.3,
0.5,
0.7
moment0map,
contours
start
and
are
spaced
by
3σ
,
where
−1Leftrapping in so-called pressure gas traced by the 12CO 6-5 line fromthe sameTable
dustvalue,
continuum(colorscale)
andbeam,
overlain Keplerianrotation (coded in Doppler-shifted colours), and filamentary
0.95
ofs1.
the
intensity
0.40 3 emission
10220 W per
1 km.peakpanels:
moment 0 map,image
contours
start1andare spacedby 3σ, whereσintensity
summedin threediffer
red–green–blueof HCOemissionin HCOssure maxima where the dust ALMA data set indicates a Kepleriandisk
pro-1, with non-Keplerian flows near the star (comparison(A color−1 version of this figure is available in the online journ
1 km (sees . Supplementary Fig. 8 for definitions). Insets show mag
models illustrative of Keplerian rotation are shown in Supplementary
bands
mple of such a pressure bump file characteristic of a gas disk Information).
with an inner
The near-infrared emission abuts the inner rim of the horseshoe- of(Athecolor
centralfeaturesthatfigure
cross thedust gap.in
The
indicates
versionof thisis available
thecross
onlinejournaltvortex, which can trap dust cavity around the central star (Fig. shaped
1B). 12outer
CO
6-5
disk.
The
star
is
at
the
originofthecoordinates.
North
is
up
and
origin,withaprecisionof
0.05
arcsec,andthearrowspoint
at thebthe left. a, Continuum at 345 GHz, with specific intensity units in Inset to a: same as in a, with a narrow exponential scale
Image
Prope
east
is
to
highlight
imuthal direction (6–10).
emission is detected down to a 20 AU radius,
Janskys per beam. It is shown on an exponential scale (colour scale). A beam
gap-crossing filaments. These featuresappear to growthe eaImage
Propertia fromTarget sides of the horseshoe.
R.A.aContours are at 0.0015
Dec
Atacama Large Millimeter/ which is consistent with the hot COellipse
ring isatshown
30 AU
in the bottom right of b, and contours are drawn at 0.01, 0.1, 0.3, westernand 0.005
0.5, 0.75
andsome
0.9 times the peak value. The noise level is 1s 5 0.5 mJy per beam. beam.
Informatio
TargetInset to d: deconvolved
R.A.amodels (SupplementaryDecaay (ALMA), we report a high- (14). This indicates that there is indeedstill
1
velocities where the gap-crossing
filameb, CO(3–2) line intensity shown by white contours at fractions of 0.3, 0.5, 0.75 HCO emission (green) at(J2000)(J2000)ncentration of millimeter-sized CO inside the dust hole, with a significant
drop
220
21
Sreν
W
per
beam.
The
underlying.
Intensity
maps
for
the
blue
and
that
is,
from
3.2
to
4.3
km
s
and
0.95
of
the
peak
intensity
value,
2.325
3
10
C
00
ı
(J2000)(J2000)(Jy
Akimasa
Kataoka
2 in coe side of the disk of the star of the gas surface density inside ofred–green–blue~25 T 5 AU.
SAO 206462
15:15:48.448−37:09:16.06
image also showsCO(3–2) line intensity, but integrated inranges(see Supplementary
Fig. 8 for definitions)
are shown

Dust continuum map at 336 GHz (890 !m) for the disk of527. The color scale shows the brightness temperature on
10, 15, and emission is ~2-100
thmic scale.The
The contrast
black contours
T = 5,continuumof denote
mm-wave
hile the white one denotes the 5 " level. The size of the syntheeam is shown at the left corner of the image with a white ellipse
Fig. 2. Moment 0 (left) and 1! 0: 34 (= 55 au ! 48 au) with a major-axis PA of 57 .
J = 3–2 (lower). The contou

Planet formation in vortex?
1135

4x105 particles
2

Gas

1

Y

80
0

vortex→dust accumulation−1

Kepler rotation

−2
2

Dust

Dust accumulation→Planet formation?

1

Y

2

0

−1

−2
2

−2

−1

0
X

1

2

Observational constraints on
grain size should be necessary.

Lyra etal.at2009
ltiple particle species. Four rocky planetsform
the outerplot as very bright small dots. A movie of this simulation
Akimasa Kataoka

3κabs [cm2/g]

L. Ricci et al.: Protoplanetary disks iGrain size constraint with opacity index
The opacity index constrains the grain size (e.g., Beckwith et al. 1990)
compact
Grain(b)opacity510

a=0.1 µm, f=1
a=1 µm, f=1
1mm
a=10 µm, f=1
a=100 µm, f=1
a=1 mm, f=1

4

10

103
102

opacity slope at mm wavelength

101
100
-1

10

-2

10

a=0.1μma=10 μma=100μm
a=1mm(Ricci et al. 2010a)

grain size

Fig. 3. Millimeter dust opacity for the adopted dust model. Left top panel: dust opa
n(a) ∝ a−q between amin = 0.1 µm and amax . Different curves are for different val
10abs =
composite spheres made of astronomical silicates (≈10% in volume), carbonace-4
10
references
to the optical constants). Left bottom panel: β between 1 and 3 mm as a
1
10-4
10-3
10-2
10-1
100
10
3. Millimeter
dustfor
opacityfor theadoptedust opacity at 1 mm as function of β Fig.
between1 and 3 mm
the same
grain
dist
−q
2
∝ adustbetween
= 0.1
and
mincm
max .
λ [cm]
shown. In the plots the unit of measuren(a)for theopacityais
per µmgramof adust
composite spheres made of astronomical sile.g., Miyake & Nakagawa 1993, D’Alessio et al. 2001
references to the optical constants). Left botto
dust opacity at 1 mm as function of β betwee
shown. In the plots the unit of measure for the-3

millimeter-wave opacity slope→grain size constraint

in the midplanein a protoplanetary
disk is muchhigherthanbein Natta etHowever,
low opacity
index
can
Opacity slope at mm wavelength the surface. At millimeter wavelengths, where the disk is mostly by the s
reproducedby thechemicalcomposition
optically
thin
to
its
own
radiation,
midplanetotalemission tral indechanges with grain grain size
orthatirregularshapedominates overof the surface(although the surface dust the M
in the midplane in a protoplanetary diskdu
plays a crucial role for the heating of the disk). As a conse- sible tothe surface. At millimeter wavelengths, w
quence, we can extract information from our analysis only on since it
optically thin to its own radiation, the m
the dust opacity of the midplane, and so when we consider the very fla
dominates over that of the surface (althdust opacity we will refer only to the midplane component for files. H
plays a crucial role for the heating of
the
rest
of
the
paper.
tions pe
Akimasa Kataoka
quence, we can extract information 4from

Grain size constraintof lopsided
Submm. index
α disks
Dust continuum (Band 7)

M. Fukagawa
al. α (Band 6&7)
Spectraletindex
optically thick (α<2)• Band6およびBand7連
続波から導出• ビームサイズ補正済み
Fukagawa
et al. 2013
• 0.7”x0.7”

T.Tsukagoshi

β= α-2 if optically thin

1. Dust continuum map at 336 GHz (890 !m) for the disk of142527. The color scale shows the brightness temperature on
garithmic scale. The black contours denote Tb = 5, 10, 15, andMillimeter-wave
slope
of optically thickK, while the white one denotesthe 5 " level. The size ofthe synthe166
d beam is shown at the leftregion
corner of theimagenowithinformationa white ellipse
have
on grain
Fig. 2. size
Moment 0 (left) and 1 (right) m:00 39 ! 0:00 34 (= 55 au ! 48 au) with a major-axis PA of 57ı .
J = 3–2 (lower). The contours in the lIn the right panels, the first moment ma
Akimasa Kataoka
5sion detected above 5 ". The contours

コントアは0.5毎

This study• We propose another way of constraining the grain size:
polarization due to dust scattering.
• The polarization requires two conditions:• Condition on grain size
• Condition on radiation field• Radiative transfer calculations of protoplanetary disk models

Akimasa Kataoka

6

Grain size and its opacity
Grain opacity

5

10

a=1µm
κabs

4

2

κabs,sca [cm /g]

10

3

10

102

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

100µm
κsca

κsca

1

10

0

10

κabs

-1

10

10-2
-3

10

10

0

1

10

2

10
λ [µm]

3

10

λ=1mm

4

10

n(a) ∝ a−3.5

Scattering opacity is larger for larger dust grains
Akimasa Kataoka

7

Grain size and its scattering opacity(x)
Albedoalbedo= κsca/(κabs+κsca)
1.2high albedo

1

omega

0.8
0.6
0.4

wavelengths
0.34 mm (Band 10)0.20.87 mm (Band 7)
3.1 mm (Band 3)
7 mm (Band 1)

0
0.1

1

10

(size parameter)
x=2πa/λ100(grain size) >~ λ →scattering is efficient
Akimasa Kataoka

8Polarization due to dust scattering(grain size) < λ：isotropic scatteringpolarization degree
for a single scattering
λ=870 µm (ALMA Band 7)
1
0.5-Z12 / Z11→ polarization degree is unity
for 90° scattering(grain size) > λ：forward scattering

010 µm
100 µm
1 mm
1 cm

-0.5
-1
0

→no polarization

λ=870µm

20 40 60 80 100 120 140 160 180
scattering angle [degree]

If (grain size) < λ, scattered emission is polarized
Akimasa Kataoka

9

Condition for polarization due to scattering
・For eﬃcient scattering

λ=870 µm (ALMA Band 7)
1.4(grain size) >~ λThere is a grain size which
contributes most to thepolarized emission

P(grain size) <~ λ

P
ω

1.2

・For eﬃcient polarization

1.4
1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0

-0.2
0.001

-0.2
0.01
0.1
Maximum grain size [cm]1(grain size)

If (grain size) ~ λ/2π, the polarized emission due
to dust scattering is strongest
Akimasa Kataoka

10AA48CH07-Dullemond

ARI

16 July 2010

20:8

A light source of scattering?
1. INTRODUCTION

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

Hashimoto

The dust- and gas-rich disks surrounding many pre-main-sequence stars are of great interest for
gaining a better understanding of how planetary systems, like our own, are formed. Since the first
direct Hubble Space Telescope images of such objects in silhouette against the background light in
the Orion Nebula (McCaughrean & O’Dell 1996), the observational and theoretical study of theseplanetary birthplaces has experienced an enormous thrust, leading to a much better understandingof what they are, what they look like, how they evolve, how they are formed, and how they are
eventually dissipated. Although none of these aspects has yet been firmly understood in detail,there is a consensus on the big picture. It is clear that protoplanetary disks are the remnants ofthe star-formation process. Excess angular momentum of the original parent cloud has to be shed
before most matter can assemble into a “tiny” object such as a star. Protostellar accretion disks (seee.g., Hartmann 2009, for a review) are the most natural medium by which this angular momentum
can be extracted from the infalling material. When the star is mostly “finished” and makes its way
toward the main sequence, the remainder of this protostellar accretion disk is what constitutes a
protoplanetary disk: the cradle of a future planetary system.
Protoplanetary disks have a rich structure, with very different physics playing a role in different
regions of the disk. A pictographic representation is shown in Figure 1. One can see the strikingly
large dynamic range that is involved: the outer radius of a protoplanetary disk can be anywherefrom a few tens of astronomical units up to 1,000 AU or more, whereas the inner disk radius istypically just a few stellar radii, i.e., of the order of 0.02 AU. This spans a factor of 104 –105 in
spatial scale. For each orbit of the outer disk, we have up to ten million orbits of the inner edge

In the case of the infrared emission, the light source is the central starAU

-50 -100 -150 100

P3

P1
F
P2
G

ALMA

Mid-IR interferometry

Pure gas disk

0.03 AU

Dust inner rim

Planet-forming
region0.1 .. 1 AU
10 AU

Near-IR dust
continuumC

Near-IR continuum(origin unclear so far)+ atomic lines (Br–γ)+ occasional molecularlines (H2O, CO, OH)

0Outer disk
(mass reservoir)

Mid-IR:
dust continuum+ molecular lines(H2O, CO2, ... )

-0.5

-100

UV continuum,
H-recombination lines

Figure 1

B

Direct imaging (HST or 8-meter ground-based)

Near-IR interferometry

Magnetosphericaccretion

0.5
-0.5
-1
R.A. offset (arcsecond)Outer ring

-50

0

E

Inner ring

scattered light

A

AU
0

0.5

-0.5

Hashimoto et al. 2011 E

Ring gap-50 -100 -150

50

0
N

0

150 100

0.5

1
D

50
Annu. Rev. Astro. Astrophys. 2010.48:205-239. Downloaded from www.annualreviews.org
by Kyoto University - EBVC and BIOMED Multi-site on 04/25/11. For personal use only.

0

1

50

Dec. offset (arcsecond)
-0.5
0
0.5

100

(Sub)millimeter:
dust continuum+ molecular rot-lines

100 AU-1

Pictogram of the structure and spatial scales of a protoplanetary disk. Note that the radial scale on the x-axis is not linear. Above thepictogram shows which techniques can spatially resolve which scales. Below shows which kind of emission arises from which parts ofthe disk.

However, the central star is dark at mm· wavelengths.
206

100

(mJy/arcsec 2)

What can be a light source at mm wavelengths?
D

Total
intensityAkimasa Kataoka

G

F

Sur

2

Monnier100)
110 120

10Dullemond11Anisotropy of radiation and polarization
CMB E-mode & B-mode polarization
weakstronghttp://background.uchicago.edu/~whu/intermediate/Polarization/polar1.html

If radiation field has anisotropies,
the emission may be polarized
Akimasa Kataoka

12

A toy model
I [mJy/arcsec2]

dust model:
amax=100µm, λ=870µm

103

300
200

102

y[AU]

100

300

3.00

200

2.50

100

2.00

0

1.50

-100

1.00

-200

0.50

-300
-300 -200 -100

0.00

0
101

-100
-200
-300
-300 -200 -100

100
0 100 200 300
x[AU]

P[%]

0 100 200 300
x[AU]What is the mechanism of the polarization?
Akimasa Kataoka

13

Polarization mechanism
P[%]
300

3.00

200

2.50

100

2.00

0

1.50

-100

1.00

-200

0.50

-300
-300 -200 -100

0.00
0 100 200 300x[AU]y
A: at the peak

B: outside

y=0

z・

x

Strong peak or strong gradient make theemission polarized
Akimasa Kataoka

14

The adopted values are x0 = y0 = 27 AU and ⇢0 =rows), they are polarized in th
10 13 g cm 2 . Radiative transfer calculations are perarrow). If the photons are informed with RADMC-3D1 .
blue arrows), they are polariz
Figure 5 shows that the intensity, polarized intensity,
thin blue arrow). The former
and polarization
overlaid with polarization vecring @ degree
170AU, d=140pc
latter because
tors. The observerin the z-direction. The intensities
Stokes Iis(continuum)
Polarization
degree point A is at
2
Hence,
are shown in theI [mJy/arcsec
unit of [mJy/arcsec].
2
P[%] the radiation is partial]
tion. The polarization
degreeThe map of the polarization degree 10
shows
it has peak3
3.00
incident radiation anisotropy
area on y = 0, which is at the peak of the surface density.
2 tubemoment.
2
The polarization
degree has two dips around the
2.50
Next, we consider the last s
at y ⇠ 60 AU and y ⇠ 60 AU, then it goes up to a1
1 value in the outside. In addition,ure 6, where is the2.00
outside th102
constant
polarization
dent photons of the last scatte
vectors are directed in y direction at the peak of theThus, the radiation1.50
from poisurface0 density, y = 0, but it is in x-direction 0in the
direction.
outer side, y & 70 AU.
1
-1
10
-1
Note that the 1.00
polarizatio
anisotropic radiation
field has
0.50
-2
-2 y
text ofλ=870µm
E-mode polarization
λ=870µm
0
background radiation
0.00 (e.g.,
10
A: at the peak
B: outside-2-1 Kamionkowski
01
2 et al. 1997).
-2
-1
0
1
2
[arcsec][arcsec]

Polarization of a ring-like disk

[arcsec][arcsec]

3. IMPLICATIONS FOR POLAOF PROTOPLA

y=0

Anisotropy → net polarizationz・

The polarization
degreeIn this section,
we apply theof polarization to two protop
is as high section
as 2.5%
3.1, we discuss a possizationof anALMA
axisymmetric ri→detectable
with

Akimasa Kataoka

3.2, we use lopsided disks to cx

15

The adopted values are x0 = y0 = 27 AU and ⇢0 =rows), they are polarized in th
10 13 g cm 2 . Radiative transfer calculations are perarrow). If the photons are informed with RADMC-3D1 .
blue arrows), they are polariz
Figure 5 shows that the intensity, polarized intensity,
thin blue arrow). The former
and polarization degree overlaid with polarization veclatter because
tors. The observerin the z-direction. The intensities
Stokes Iis(continuum)
Polarization
degree point A is at
2
Hence,
2are shown in theI unitof[mJy/arcsec].
P[%] the radiation is partial[mJy/arcsec ]tion. The polarization
degreeThe map of the polarization degree 10
shows
it has peak3
3.00
incident radiation anisotropy
area on y = 0, which is at the peak of the surface density.
2 tube2
moment.
The polarization
degree has two dips around the
2.50
Next, we consider the last s
at y ⇠ 60 AU and y ⇠ 60 AU, then it goes up to a1
1 value in the outside. In addition,ure 6, where is the2.00
outside th102
constant
polarization
dent photons of the last scatte
vectors are directed in y direction at the peak of theThus, the radiation1.50
from poisurface0 density, y = 0, but it is in x-direction 0in the
direction.
outer side, y & 70 AU.
1
10
-1
-1
Note that the 1.00
polarizatio
anisotropic radiation
field has
0.50
-2 y
-2
text ofλ=870µm
E-mode polarization
λ=870µm
0
background radiation
0.00 (e.g.,
10
A: at the peak
B: outside
-2
-1
0
1
2
-2
-1 Kamionkowski
01
2 et al. 1997).
[arcsec][arcsec]

Polarization of a lopsided disk

[arcsec][arcsec]

3. IMPLICATIONS FOR POLAOF PROTOPLA

y=0

Anisotropy → net polarizationz・

In this section, we apply the
The polarizationis alsoto two protop
of polarization
section 3.1, we discuss a poss
expected fromlopsideddisks ri
izationof an axisymmetric
3.2, we use lopsided disks to cx

Akimasa Kataoka

16

d the albedo ! = sca /(abs + sca ) as a function of maximum grain size.
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)
).

Grain size dependence of polarization(polarization degree for 90° scattering) × (albedo)
1.2

1

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

Multi-wave polarization → strong constraint on grain size
Fig. 4.— The polarizationAkimasa
times
the albedo P ! against the maxKataoka

17

Conclusions• We derived the conditions for polarization due to dust scattering• If the grain size is comparable to the wavelength, a~λ/2π, thepolarization is most eﬃcient• Anisotropy of radiation field make the emission polarized due todust scattering.

• We performed radiative transfer calculations of lopsided
protoplanetary disks to investigate the polarization• The polarization degree is as high as 2.5% in lopsided disks• To detect the polarization, both high spatial resolution and highsensitivity are required.

Akimasa Kataoka

18