Millimeter-wave polarization of
protoplanetary disks due to dust scattering
2

I [mJy/arcsec ]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.)

The Astrophysical Journal Letters, 783:L13 (6pp), 20

Akimasa Kataoka

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Planet formation in vortex?
1135

80

Akimasa Kataoka

3κabs [cm2/g](b) compact
510

a=0.1 µm, f=1

410103
102
101
100-1

10-21010-310-4 -41010-3

10-2

10-1100101

λ [cm]

Akimasa Kataoka

4Grain size constraint of lopsided disks
M. Fukagawa et al.

1. Dust continuum map at 336 GHz (890 !m) for the disk of142527. The color scale shows the brightness temperature ongarithmic scale. The black contours denote Tb = 5, 10, 15, andK, while the white one denotes the 5 " level. The size of the synthed beam is shown at the left corner of the image with a white ellipse:00 39 ! 0:00 34 (= 55 au ! 48 au) with a major-axis PA of 57ı .
Akimasa Kataoka

5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

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Grain size and its opacity
Grain opacity

510

a=1µm
κabs

42

κabs,sca [cm /g]

10310

102

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

100µm
κsca

κsca

110010κabs-11010-2-310100110210λ [µm]310λ=1mm410n(a) ∝ a−3.5

Scattering opacity is larger for larger dust grains
Akimasa Kataoka

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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)

00.1

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

8Polarization due to dust scattering(grain size) < λ：isotropic scattering

λ=870 µm (ALMA Band 7)
1-Z12 / Z110.5010 µm
100 µm
1 mm
1 cm-0.5-10Akimasa Kataoka

20 40 60 80 100 120 140 160 180
scattering angle [degree]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) <~ λPω

1.2・For eﬃcient polarization

1.41.2110.8

0.8

0.60.60.4

0.4

0.2

0.2

00-0.2
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A light source of scattering?

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

0-50 -100 -150 100

AOuter ring

B50Ring gap-50 -100 -150

EC

10

00.5
-0.5-1
R.A. offset (arcsecond)(mJy/arcsec 2)

Akimasa Kataoka

0-0.5-100-0.5-50

Inner ring

0P3P1FP2G00.5

110 1200150 100

1D500.5150

Dec. offset (arcsecond)
-0.5
00.5

100

Hashimoto

-1

100

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Anisotropy of radiation and polarization
CMB E-mode & B-mode polarization
weakstrong

http://background.uchicago.edu/~whu/intermediate/Polarization/polar1.html

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

12I [mJy/arcsec2]

Akimasa Kataoka

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Polarization mechanismP[%]y
A: at the peak

B: outside

y=0z・Akimasa Kataoka

x14

ring @ 170AU, d=140pc

I [mJy/arcsec2]

Akimasa Kataoka

2I [mJy/arcsec ]Akimasa Kataoka

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.

Akimasa Kataoka

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

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