Millimeter-wave polarization of
protoplanetary disks

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Akimasa Kataoka (NAOJ)

star formation process but have hitherto been observationally poorly between theoretical models of the magnetic fields in disks and the obconstrained. Field strengths have been inferred on T Tauri stars3 servations to date, requiring more sensitive observations of the dust
and possibly in the innermost part of their accretion disks4, but the polarization. The SMA recently detected the magnetic field morphostrength and morphology of the field in the bulk of a disk have not logy in the circumstellar disk of the Class 0 (that is, the earliest protobeen observed. Spatially unresolved measurements of polarized emis- stellar stage) protostar IRAS 16293–2422 B19, but since this disk is nearlysion (arising from elongated dust grains aligned perpendicularly to face-on, observations cannot detect the vertical component of the magthe field5) imply average fields aligned with the disks6,7. Theoretically, netic field. Moreover, this source is perhaps one of the youngest of the20
the fields are expected to be largely toroidal, poloidal or a mixture of known Class 0 sources , increasing the chances that the polarized flux
the two1,2,8–10, which imply different mechanisms for transporting an- could be from the natal environment. Nevertheless, since the disk is thegular momentum in the disks of actively accreting young stars such brightest component at the probed scale, polarization most probably
as HL Tau (ref. 11). Here we report resolved measurements of the comes from the disk, and the magnetic field morphology hints at toroi19
dalwrapping
polarized
1.25-millimetre
continuum
emission
from
the
disk
of
HL
No. 2, 2007
POLARIZED EMISSION FROM T TAURI DISKS .
1093
We obtained 1.25-mm CARMA polarimetric maps of HL Tau at 0.60
Tau. The magnetic field on a scale of 80 astronomical units is coincident with the major axis (about 210 astronomical units long12) of (84 AU) resolution and plot the magnetic field morphology in Fig. 1.
Non-detection
on HDdetection
163296,
Hya. three indeThis is a spatially resolved(with TW
approximately
the disk. From this we conclude that the magnetic field inside the disk
Radiative Torquebeams) of the magnetic field morphology in the circumstellar
at this scale cannot be dominated by a vertical component, thoughGMa pendent
Aur
and
DG
Tau
(Hughes
etfield
al.vector
2009,2013).
disk
of
a
T
Tauri
star.
The
centralmagnetichasameasured
purely toroidal field also does not fit the data well. The unexpected
Alignment
morphology suggests that the role of the magnetic field in the accre- position angle (PA, measured anticlockwise from north) of hB 5 143.6
inferred B vectors (rotated by 90 degrees)tion of a T Tauri star is more complex than our current theoretical
59.0″
understanding.
HL Tau0.00165
B- elds HL Tau is located 140 pc away13, in the Taurus molecular cloud. Al58.5″
though HL Tau is a T Tauri star, it is considered to be in an early stage
0.00150of development owing to its bipolar outflow14 and possible residual en0.00135
58.0″
velope15. Observations and modelling of this protostar assuming a thick,flared disk suggest a stellar mass of ,0.55 times the solar mass (M[)
0.00120
Ra
57.5″
and
a disk mass of 0.14M[ (ref. 12). A possible planet forming in the0.00105
disk of HL Tau has been observed16, though this detection was not
57.0″
confirmed12. However, the disk of HL Tau is gravitationally unstable,
0.00090
12,16
which could favour fragmentation into Jupiter-mass planets . HL Tau
0.00075
56.5″
has the brightest disk of any T Tauri star at millimetre wavelengths, allowing observations of the fractional polarization (P) to have the best
0.00060
Polarization
possible sensitivity. Previous observations of the polarization of the disk
56.0″
1%0.00045of HL Tau yielded marginally significant, spatially unresolved polarization detections with the James Clerk Maxwell Telescope (JCMT; polariza- +18° 13′ 55.5″ 100 AU
tion P 5 3.6 6 2.4% at 140 5 1,960 astronomical units (AU) resolution)638.55 s38.45 s4 h 31 min 38.5 s
RA (J2000)
and the Submillimetre Array (SMA; polarization P 5 0.86 6 0.4% at
20 5 280 AU resolution, archival observations released in this Letter). In Figure 1 | Detected magnetic field morphology of HL Tau at 0.60 resolution.
addition, observations
HL Tau with
the Combinedfor Millimetervectors(shortonly.
coloured
have been rotated
90u to show
Fig. of
11.—Simulated
observations.
Degree Arrayof polarization
is calculated forThethe radiationfrom thedisk interior
2polarization
sigma
detection
bylines)
CARMA
andbySMA
wave Astronomy(CARMA)
have shownthat the interferometric emis- the inferred magnetic field orientation. Red vectors are detections .3sP
e.g., Draine and Weingartner
1997,
Lazarian
2007,
blue vectors are detections
between 2sP and 3sP, where sP is the(Stephens
et al. 2014)
sioncomes entirely
fromwith nofromdisk symmetry
axis andthethelinediskof sight.
Wecontamination
plot the directionof large-scale while
Cho and Lazarian 2007…
12
envelope
emission
HL Tauwavelengths
is thereforeanda verypolarization
for three .different
twopromisingdifferent source to r.m.s. noise of P. We do not show vectors when the signal-to-noise ratio for
Stokes I is below 2. The sizes of the vector are proportional to the fractionalviewingfor
angles.
The lines
represent
the directiondetection.
of polarization.
searcha spatiallyresolved
polarization
polarization, P, with the red scale bar corresponding to P 5 1%. Stokes I
Since
wethroughassume thatmagnetic field
is azimuthal,direction
Onlyobservationsof polarized
dusttheemission
can the mor- contours are shown for [23, 3, 4, 6, 10, 20, 40, 60, 80, 100] 3 s , where

Before 2015 - what had been expected and achieved?
Observations

fi

Polarized intensity (Jy per beam)Dec. (J2000)

TheoryAfter 2015 - ALMA polarization and progress of theory
ALMA polarization (Class II disks)

Dramatic progress in 5 years
Downloaded from https://academic.oup.com/mnrasl/article-abstract/482/1/L29/5107365 by Unfi

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 al.
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 et al.
intensity, and this blob 4is signiﬁcantly brighter in 870 μm.
cal 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
et al.
HD 142527 4
IMHullLup
CWwellTau(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 the•polarization 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)is
(b)
0.0013 ± 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 theeft panel, the colorscale represents the polarized intensity in units
witha log scale,the grayThecontours
show
the continuum emission,edgeofofmJy
thebeamdetectedpolarized
emission).
P peaktowardtors show the polarization vectors. Note that the lengths of thethepolarization
are setbe the same.
The alevels
the (a)contours are (3, 10, 30,(b)northwestvectors
is 0.0077
±to0.0010.
Drawingline offromthe−1
I. Polarization
vectors theare center
plotted ofwhere
the polarized
intensity is larger than900, 1200, 1500, 1800)×σI(=185 μJy beam ) for Stokesnorthwest
peak throughthe disk,
at the same−1
y beam . In the right panel, the colorscale displays the polarization
fraction
overlaid withpolarization±
vectors.
TheP grayradius on
the southeastside,theP=0.0094
0.0010.
risescontours display theon 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
he difference in the grain size and its effects on asymmetries
power-lawsize distribution
a powerof −3.5 and theboth at 1.3
mm sizeand 870theyt efﬁciency; the radiative torque efﬁciency appearmaximum
grain
150μm
μm,suggests
which isthecould
most efﬁcient graina real feature. If we consider total polarization PT =h decreasing grain size if the grain size is smaller beContours:
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
ength. 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.
ing from grains smaller than the wavelengths, it Yangis etbasedon ashowed
previousof thethecontinuumat the sameal. (2017)that modelingasymmetry alongmajor
e 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
Gaussian(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
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
hal 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:
Grayscale
is
the
total
intensity
thermaldust
emission;
contoursarethepolarization
fractionP=
P/I,
plottedatlevels of⎛⎞⎤
ALMApolarimetricobservations
at
3.1
mm
(top,
Kataokaetal.
2percentage
regions indicatesthepoloidalmagneticﬁeld
0.005,
0.006,
0.007, 0.008,
0.009, 0.01.
The
coordinates and thegrayscale
are identicalThein the top
two bottom
panels.
The ALMA
data used
to intensity(andFigure1.
Sub-mmcontinuumpolarizationin
HD163296.
panels
show
(a)
the
total
(b)
the
polarization at band 7 in the centralqq)asymmetric
ifBacciotti
thedust disket
is al.
optically
thickDentand ⎜haseta al. d ⎟ ⎥Kataokaetwhereal.themake
2016,
Hull
et
2018,
2018,
figure areshow
availablethein theonlineal.
versionof this publication.
mm (middle), and870 μm (bottom),redthisvectors⎢
exp
Sangular
Swidth+ rings
S0,min-(c)marked
(S
)see
(d)
d = of
0,min
0,max
⎜
⎟
while
the radial
direction
on rotated).
the inner
ringareregion.
as ellipses
representations
the
three
in theillustration,
total
intensity
image,
1–3 in(b). The lower panels are (c) the polarized2
signiﬁcant(foracartoonFigure6zationmorphology(i.e., vectors
have
notSuperimposed
been
Vector
⎢⎣⎥⎦2fvectors⎝⎠dlinearly
proportional
to
P.
The
color
scale
shows
the
polarized
flux
intensity
and
(d)
the
polarization
angle,
both
with
the
polarization
vectors
superimposed.
In
(c),
the
are
shown at their actual angle, whereas in
2019,
Stephens
et
al.
2017,
cf.
Kataoka
et
al.
2017,
Ohashietal.
2018
toroidal magnetic ﬁeld. There has been no in Yang et al. 2017). HL Tau disk is known to be optically◦ is multipliedhich is masked to only show 3σ detections.
Stokes
I contours
in to the2. Linearlypolarized
P andpolarization
at truncated
870 µm in the disks around CW Tau (panels (a),(b)),(d)
thevectorrotation
relative
mean
of
44.1
by a factor
theintensity
relative
twist.
Polarization
fractionfraction
and anglep are
thick
at
870
μm
(Carrasco-González
al.emphasize2016), but
no2of⎞et3, to⎛Figurecally to rotate the direction of the magnetic ﬁeld

ALMA observations - many
polarimetric detections at 870,
1.3, and 3.1 mm wavelengths
Self-scattering - a new idea oforigin of polarization

Direction of the aligned
grains - grains may be aligned,
but not with the direction of Belds

1

1

I

1

P

1

00

00

I

P
frac

1

frac

ALMA polarization of smooth and inclined disks, around a low-mass stars, with scales less than 100 au

Azimuthal

Parallel to the minor axisl Letters, 844:L5 (5pp), 2017 July 20(0.9 mm)ngth dependenceHDof163296
the polarizationin the case of the grain alignment,
he case of the self-scattering because
polarization is efﬁcient only when theis around l 2p where λ is thet al. 2015).
ngth-dependent polarimetric images, we
k with the Atacama Large Millimeter/
LMA) using Band 3. HL Tau is a young
cular cloud with a distance of 140pc
The circumstellar disk is around int al. 2011). The disk has several ringtens of au scales (ALMA Partnershiped band corresponds to wavelengths ofently longer than the previous CARMA
ns at 1.3 mm (Stephens et al. 2014).
The Astrophysical Journal, 851:55 (6pp), 2017 December 10(a)Kataoka et al.

HL Tau (3 mm)

4Harrison et al.

MixtureDG Tau (0.9 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
4 two P peaks along the major axis is
F. Bacciotti et al.
The AstrophysicalJournalsigniﬁcant.
Letters, 877:L2
0.0013 ± 0.0014, which
is not statistically
The (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] × sI ,asymmetry is detected along the minor axis. The lack ofwhere s is 44, 154, and 460 μJy bm−1 for 3.1 mm, 1.3 mm, and 870 μm,

aded from https://academic.oup.com/mnrasl/article-abstract/482/1/L29/5107365 by Univ

Motivation 1: polarization morphologies

Mori et al.

mm
continuum polarization in HD163296. The top panels show (a) the total intensity and (b) the percentage polarization at band 7 in the central. Observations
posed 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)onangle,2016both
Octoberded(d)by
the ALMA
polarization
with the12,
polarization vectors superimposed. In (c), the vectors are shown at their actual angle, whereas intion
PI:44.1
A.
◦Kataoka).
Figure2. Linearlypolarized
intensity P and polarizatio
Dent
al. 2019,
Stephens
et al. 2017,ation (2016.1.00115.S,
relative totheetmeanofis multiplied
by a factor of 3, to Kataokaemphasizetherelative
twist.
Polarization
fraction
and
angle
are
truncated
et al. 2017, Harrison et al. 2019…
Bacciotti et al. 2018, Mori et al. 2019…
onwasC40-6,
and41 antennas
Hullbeametal. (250µJy).
2018,
Bacciotti
etwereal.
andTau(panels(c),(d)). Contours as in Fig. 1. Pol
levelsof 5σ
perImagesare2018…
3 arcsec (315 au) across. Resolution is ∼0.2 arcsec (beams
areDG
shown
lower
left). Polarization(b)

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
the top-rightof the Stokes
F. O. toAlveset al.: Magnetic
fieldI in a circumbinary disk around a Class I YSO
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(e.g., Tazaki et al. 2017), StokesV has not been well
The transition of polarization morphologies from one
characterized
for
ALMA,
so
its
detection
couldbespuriousBand 3
Band 7
Band 6
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
870 μm,thethe positive regions almost completely disappear.
perpendicular to the major axis. We would expect
StokesUpolarization to be perfectly perpendicular to the majoraxis.shows two positive and two negative regions at
The negative blobs disappear at 1.3 mm, while the
The reason for this small 7° discrepancy is uncertain,3.1
butmm.
could
positive regions connect, and at 870 μm, the positive regions
indicate asymmetry in the disk.
turn into a single, large region.
The right panels of Figure 2 show P for each wavelength.
ForfortheP Stokes V images (Figure 2), 3.1 mm appears to be
For 1.3 mm and 870 μm, there is a slight asymmetry
purelymore
noise. For both 1.3 mm and 870 μm, StokesV has aalong the major axis of the disk, with the southeast
polarized than the northwest. For 1.3 mm, thenegative
absoluteﬂux blob offset to the top-right of the Stokes I
intensity,
difference between the two P peaks along the major
axis isand this blob is signiﬁcantly brighter in 870 μm.
Alves et can
al. 2018
Althoughpolarizationin principle be produced by
0.0013 ± 0.0014, which is not statisticallysigniﬁcant.
Thecircular
The AstrophysicalJournal,851:55(6pp),
2017
December
10 off non-spherical grains
scatteringoflinearlypolarizedlight
g. 1. Stokes I (left panel), polarized intensity (middle panel) and polarization fraction (right panel) ofasymmetry
our Bandfor
3 (upperpanels),Band
6(middle870 μm is more apparent, although the southeast
et al. 2017), StokesV has not beenThewelltransition oof the diskindoes
notband,peak (i.e.,
it is30,
still60,
increasingthenels) and Band 7 (lower panels) ALMA data. The contours indicate the intensity levels of the Stokespart
I emission
each
being
90,(e.g.,at Tazaki
characterized
for ALMA, so its detection could be wavelength
spurious to anoth
1
1
edge
of
the
detectedpolarized
emission).
The
P
peak
towardBand
70, 150,180 times the rms for bands of 3 and 6 (rms
⇠
0.012
mJy
beam
and
rms
⇠
0.15
mJy
beam
),
and
30,
60,
90,
120
times
Band
6
Band 3
Band 6willthenot be discussed in detail in this paper.
the northwest is 0.0077 ± 0.0010.
Drawinga lineandfromimages, as seen in
1
00
00
00
00
52 mJy beam , the rms for Band 7. The synthesized beams are 0.22 ⇥ 0.17 (position angle = 61.46
)
for
Band
3,
0.26
⇥
0.15
(position
Thesamecentral polarization vectors for 1.3 mm and 870
μm are image sho
northwest peak through the center of the disk, at the
StokesQ
00
00
55°. P
4 ±0°axis regions
gle = 85.65 ) for Band 6 and 0.21 ⇥ 0.18 (position angle = 72.79 ) for Band 7. The vector map radiusindicates
thesoutheast
orientation
the polarizationon theside, ofP=0.0094
± 0.0010.
rises. 96 and 55°. 3 ±0°. 41, respectively. The major
and positiveof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnershipet al.are much bhose length is proportional to the polarization fraction. The vectors are sampled as one vector every
two pixels.
two
to ∼0.0115
at the The
edge of
thestar-symbols
disk. Therefore, atthetheP asymmetry
regions
indicating the polarization vectors are ∼7° frommajor
for 870 μmpeakis ∼0.002–0.004.
These
870being
μm, the positiv
iddle-lower panel indicate the position of the two continuum peaks detected in the 34 GHz VLA data,along
beingtheVLA
5aaxisthe northernand VLA2015),
perpendicular
to
the
major
axis.
We
would
expectthe shows twasymmetries
arerelatively
moderate,
but
the
fact
that
they
StokesU
the southern one (see also Fig. 2).
polarization
axis.The negati
appear both at 1.3 mm and 870 μm suggests they
could to be perfectly perpendicular to the major
3.1 mm.
The reason
couldregions con
PT = for this small 7° discrepancy is uncertain, but
be a real feature. If we consider total polarization
positive
indicate asymmetry in the disk.
turn into a single, la
Q 2 + U 2 + V 2 I , the asymmetry is similar; for 1.3 mm, it is
The
right
panelsofFigure
2
show
P
for
each
wavelength.
of±
⇠10
AUwhileat thePipediso extended polarized emission is detected at scales larger than 12 (i.e. a spatial resolution
For the Stokes V
0.00120.0014,for 870μmnebula
it is ∼0.001–0.004.
For
1.3
mm
and
870
μm,
there
is
a
slightasymmetryfor noise.
P
100
1 asymmetry along the major
purely
For b
Yang
et
al.
(2017)
showedthat
7 , which corresponds to ⇠ 3 ⇥ of the primary beam in Band 7 tance). The rms noise of the map is 12 µJy beam .
along the major axis of the disk, with the southeast
more ﬂux blobnegative
axis
is
not
expectedforscattering-induced
polarizationinanhe smaller of the three bands).
polarized than the northwest. For 1.3 mm, the intensity,
absolute and thisaxisymmetric disk, so axisymmetry must be broken if thedifference between the two P peaks along the major
axis is circular po
Althoughpolarization is really due to scattering even though the total
0.0013 ± 0.0014, which is not statistically signiﬁcant.
The of linearlscattering
intensity(StokesI)ishighlyaxisymmetric.
On
the
other
hand,
Fig. 1. Stokes I (left panel), polarized intensity (middle panel) and polarization fraction (right panel) ofasymmetry
our Bandfor
3 (upperpanels),Band although
6 (middle
870 μm ismore apparent,the (e.g.,southeast
Tazaki et althepolarization
along
the
minor
axis
is
expected
tobeKataoka
et
al.
2017,
Stephens
et
al.
2017
Figure1.
ALMApolarimetricobservations
at
3.1
mm
(top,
Kataoka
et
al.
part
of
the
disk
does
not
peak
(i.e.,
itis
stillincreasingatthe
2. VLA
panels) and Band 7 (lower panels) ALMA
data.VLAThe contours
indicateiftheof the Stokes
I emissionin each band, being 30, 60, 90, characterized for AL
Previous
lowerasymmetricangularresolution
observations
theintensity
dust 1disklevels
is opticallythick(⇠andhas a2017), 1.3 mm (middle), and 870 μm (bottom), where the red vectors show the1edgeof beamthe detected
polarized
emission).
Thetimes
P peak00
120,
the (i.e.,
rmsvectors
for bands
3 rotated).
and 6 Vector(rmsBand 3signiﬁcant⇠ 0.012angular
mJy beam
rmsBandmJy), and30, 60,90, 120
andtoward
will not be disc6 ⇠ 0.15
width (foranda cartoon
illustration,
see Figure
6>3σ150,180
polarizationtimes
morphology
have notof
been

Motivation 2: wavelength dependence
0.87 mmBHB07-11(Class I)

HL Tau(Class I-II)

1.3 mm

3.1 mmWhat I would like to discuss today is …
• Introduction (~5 min., done)• Pre-ALMA era and ALMA discovery ofdiverse morphologies of polarization.

• Theories/models (~20 min.)• Self-scattering polarization• Grain alignment in protoplanetary disks• Basic interpretations (~5 min.)• Implications to planet formation? What canbe and cannot be explained by the theories?
Recent progress? (~15 min.)Polarization mechanisms
Grain alignment

Self-scattering
IR scattered light

disk

Infraredradio scattered light(self-scattering)Linear polarization

Directions- B- elds- radiation- gas owe.g., Cho and Lazarian 2007, Tazaki et al. 2017,
Lazarian and Hoang 2007, Kataoka et al. 2019

millimeter

Note: dust grains at midplane do
not receive stellar photons
flfi

Kataoka et al. 2015

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

Vertical Polarization

Akimasa Kataoka (NAOJ)

Polarization due to scattering
Polarization is perpendicular
to a tube-like structure

Ring (face-on)

Lopsided (face-on)edge-on view

inclined disk

radialradialverticalparallel to minor axis

Akimasa Kataoka (NAOJ)

-2

0.50

[arcsec]

H. Yang et al.

[arcsec]

1.00

0

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 …

Parallel to thedisk minor axis
Figure 7. Scattering-induced polarization by large grains. As in Fig. 5,plotted are the polarized intensity (colour map) and polarization vectors

Akimasa Kataoka (NAOJ)

0.00

100

Kataoka, et al., 2015, Ohashi et al. 2020,…
2
01[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;

2802

Radiative transfer calculations

what can we learn from self-scattering?
Assumption: spherical dust grains

Albedo = ef ciency of scattering

a=λ/2πgrain size

Polarization at single scattering

a=λ/2πfi

Scattering-induced polarization is detectable only when a=λ/2πgrain size

-0.2

0.1
n size [cm]

1

-0.2
0.001

-0.2

what can we learn from self-scattering?
0.01
0.1
Maximum grain size [cm]1

Anisotropies ofcattering angle of 90 and the albedo ! = sca /(abs + sca ) as a function of maximum grain size.
radiation
eld
at
the
Polarization
Grain
size
=
3.5
ve power law of n(a) / a. The wavelengths are assumed to be 1.3 mm for the left panel andindicatethemaximum
grain
size
which
has
the
most
efficientpolarizationby
90
scattering.
observed wavelengths.
1.2

for observed

Prediction of polarization fraction

1

grain size amax

Pω

mm
0 µm
0 µm
0 µm

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

fi

r each wavelengthpolarization due to 90
gnificant only when theve a large albedo (§2.2)

0
0.001

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

(grain size) ~ λ/2π

Polarization mechanisms
Grain alignment

Self-scattering
IR scattered light

disk

Infraredradio scattered light(self-scattering)Linear polarization

Directions- B- elds- radiation- gas owe.g., Cho and Lazarian 2007, Tazaki et al. 2017,
Lazarian and Hoang 2007, Kataoka et al. 2019

millimeter

Note: dust grains at midplane do
not receive stellar photons
flfi

Kataoka et al. 2015

If grains are aligned with B- elds…
Toroidal magnetic elds

Synthetic polarimetric observations

Raviewing angles. The lines represent the direction of polarization.
Since we assume that magnetic field is azimuthal, the direction
calculateof polarization is predominantly radial (see Fig. 10, bottom).
Infor the dust polarization emission. Thefifi

and -II-low are shown. From left to right, theSuzuki
resultset
areal.shown
2014forensity surfaces.

Figure 1. The ring state: self-consistent radiative tr
Fig. 11.—Simulated observations. Degree andof polarization
is calculated
for the radiationdsimulated ALMA
observations(bottom fromrow; theCASA
Cho and Lazarian 2007
Bertrang et al. 2014
1 per cent, i.e. the 3σ level of ALMA) at three different
intensityof
which is overplotted by polarization vectors.T
disk symmetry axis and the line of sight. We plot the direction
magnetic field topology is traced by its characpolarization for three different wavelengths and two toroidal
differentDust alignment at disk midplane
Dominant alignment mechanisms
12et al.

Tazaki et al.

Ra
Figure 1. Definition of the coordinate system. aˆ1 is the short axis of thegrain, and aˆ2 and aˆ3 corresponds to the long axis of the grain. J is theangular momentum vector of the grain. B is the local magnetic field and k is
the direction of the anisotropic radiation field, or simply the direction of theradiative flux.

Figure 5. Timescales relevant to RAT alignment. Top and bottom panels show the alignment timescales and the precession timescales, respectively. Left and rightrotating suprathermally due to the effect known as thermal panels correspond to the two different locations in the disk, (R, z) = (50 au, 0 au), and (R, z) = (50 au, 10 au), respectively. For the top panels, black and red lines
Figure7. Polarizationis shown
the colortimescale
scale and the(tdirectionof For
E-vectorplotted as
the whiteand lineright panels
represent
mid-infrared
damping(tgas ) degree
and theRAT withalignment
the isbottom
panels,thebar.
redLeftsolid
indicates
the radiative
rad, align ).
flipping (Lazarian & Draine 1999; Hoang & Lazarian 2009b). represent the timescale of the gaseous
wavelength(λ lines= 12 µm)
and themillimeter
wavelength(λ = 870µm.), respectively.
The dust grains are
assumed to (bemagneticallypoorsuperparamagnetic( f p = 0.01 and φsp = 0).
precession
timescale
(t
).
Green
and
blue
show
Larmorprecession
timescale(t)
forparamagnetic
inclusions
f
=
10%)
and
L
p
rad,
p
Draine & Weingartner (1997) argued that dust grains can be
Polarization
are= 0.5, respectively.
The maximum3grain size is amax = 1000µm. Turbulent strength and the fhigh−J -parameterare assumed to bevectors
α = 10−3 and fhigh−J
spun up to suprathermal under an anisotropic radiation field. inclusions ( f p = 10%, φsp = 3%, Ncl = 2 × 10 ), respectively. The dashed line in the bottom panels represents the gaseous damping timescale.
In addition, they also found that in this case, RAT can drive
perpendicular to the radiation ux
are aligned with respect to the magnetic field. On the othergrain size does not strongly affect on the resultant polarization
external alignment even in the absence of paramagnetic dishand, atwithout
the inner disk,
micron-sized grains being aligned with
degree.
This result
implies that as
growth occurs,
superparamagnetic
5.1. Linear
degreeof polarization
ofthe
angrainellipsoid
sipation. However, calculations taking into account a more though sub-micron-sized grains
the radiativeflux are present
at the layer,
disk surface layer. Since
the degree of polarization can be small at all wavelengths, inaccurate treatment of crossover 4 showed that RAT under inclusions align with the radiation
directionatsurface
CL07wecalculated
absorption
cross
sectionalong
themicron-sized grains dominate the opacity at mid-infrared,
particularthe
for the(sub-)mm. The
expecteddegreeof polarizaan anisotropic radiation field often spin down the grain ro- those with superparamagnetic
inclusions
can becomealignedobservethe azimuthal
polarization
vector. As a result,
we seeshow ation ismuch
smalleraxes
than that
presented
in CL07, whocode
minor
axis and
the
major
using
the DDSCAT
tation to thermal or subthermal (Weingartner & Draine 2003;
result, in
mid-infrared
polarimewith
the radiation direction
at the innerdisk and36% 1994);
of degreetheof polarizationforamax = 100 µm
which drops
LH07). An important property of RAT alignment is that a with the magnetic field. As aalignment(Draine&
Flataudegreeofpolarizationisobtainedwiththe magnetic
at thehaving
outer disk.
increase
to 8% for amax = 1000 µm at λ = 850µm. This differencealignment
forfieldgrainssu- When wesystem of dust grains evolves into stable points in the pa- try, we expect magnetic fieldbyis mostly due to the fact that CL07 assumed perfect internalrameter space of the angular momentum and the alignment perparamagnetic inclusions.the number of magnetic inclusions, the boundary radius bealignment.
tween the radial and the azimuthal polarization vectors de-

Aligned with B- elds•

No alignment

flfi

Aligned with radiation

Tazaki et al. 2017

Mechanical alignment?

hysical Journal Letters, 874:L6 (5pp), 2019 March 20

Kataoka, Okuzumi, & Tazaki

8

Kataoka et al.
The Astrophysical Journal Letters, 874:L6 (5pp), 2019 March 20

Kataoka, Okuzumi,

hematic illustration of the direction of polarization with respect to the gas velocity against a dust grain. The left panel represents the Gold mechanism
where the polarization orientation (red) is parallel to the velocity vector (blue). The right panel represents the helical grain mechanism (Lazarian &b), where the polarization orientation (red) is perpendicular to the velocity ﬁelds (blue). Since the gas ﬂow in a protoplanetary disk is subsonic, the helicalnism would be realized in the disk.

8, in this letter, we assume that dust grains are aligned
ﬂow due to the mechanical alignment, and focus on
ological discussion of the polarization vectors in aetary disk.
1 shows the schematic illustration of the microscopic
ic direction of a mechanically aligned dust grain. The
dea has been proposed by Gold (1952), where an
n is aligned with the ambient gas for its major axis toto the direction of the gas velocity against the dust
his case, the polarization vector is parallel to the gas
gainst the dust grain as shown in Figure 1. However,& Hoang (2007b) proposed that a helical grain can beciently aligned with the velocity ﬁelds, where theain is aligned for the rotational axis parallel to theelds. In contrast to the Gold mechanism, as a result ofn, the polarization orientation is perpendicular to thef the ambient gas. The helical grain alignment works
ubsonic gas in contrast to the Gold mechanism. Since
y difference between gas and dust in a protoplanetary
bsonic, we take the helical grain alignment as a priorm at work in a disk.
e the relationship between helicity and polarity. The
n be either right-handed or left-handed. In both cases,

Kataoka et al.

Figure 3. Schematic illustration of velocity vectors of dust and gas. The left panel shows the location that we are considering. We assume that the disk gas
counterclockwise and the dust is feeling the headwind from the gas. The top right panel shows the azimuthal and radial components of the gas and dust veloc
is faster than gas in rotation as well as the radial drift. The bottom right panel shows the gas velocity on the rest frame of dust. The polarization is perpendicu
velocity vector, which is shown as a red line in the left panel.
Figure 2. Radial and azimuthal components of the velocity difference between
gas and dust, Equations (1) and (2), in a protoplanetary disk with
ηvK=53 m s−1 and set vgas,r=0.

Kataoka et al. 2019

Figure 5. Polarization vectors due to mechanical alignment in the cases of the Stokes number is 0, 0.01, 0.1, 1.0, 10, and muchgreater than unity. All disks are face-on viewed and rotating counterclockwise.

(See Gold 1952, Hoang 2018 for the microphysics of mechanical alignment)of polarization to investigate the grain growth in proto-Summary of polarization morphologiesalignment with B- elds
8alignment with radiation
Kataoka et al.

self-scattering• toroidal B- eld case8alignment with gas
ow
Kataoka
et al.

wavelength
independent
fl

fi

fi

Akimasa Kataoka (NAOJ)

wavelength
dependent
Kataoka et al. 2017, 2019, Ohashi et al. 2018

What I would like to discuss today is …
• Introduction (~5 min., done)• Pre-ALMA era and ALMA discovery ofdiverse morphologies of polarization.

• Theories/models (~20 min.,done)• Self-scattering polarization• Grain alignment in protoplanetary disks• Basic interpretations (~5 min.)• Implications to planet formation? What canbe and cannot be explained by the theories?
Recent progress? (~15 min.)aded from https://academic.oup.com/mnrasl/article-abstract/482/1/L29/5107365 by Univ

Motivation 1: the polarization morphologies
ALMA polarization of smooth and inclined disks, around a low-mass stars, with scales less than 100 au

Parallel to the minor axisl Letters, 844:L5 (5pp), 2017 July 20(0.9 mm)ngth dependenceHDof163296
the polarizationin the case of the grain alignment,
he case of the self-scattering because
polarization is efﬁcient only when theis around l 2p where λ is thet al. 2015).
ngth-dependent polarimetric images, we
k with the Atacama Large Millimeter/
LMA) using Band 3. HL Tau is a young
cular cloud with a distance of 140pc
The circumstellar disk is around int al. 2011). The disk has several ringtens of au scales (ALMA Partnershiped band corresponds to wavelengths ofently longer than the previous CARMA
ns at 1.3 mm (Stephens et al. 2014).
Dent et al. 2019

Azimuthal
HL Tau (3 mm)(a)Kataoka et al.

MixtureDG Tau (0.9 mm)

See the talk by Francesca Bacciotti
for DG Tau and CW Tau

Kataoka et al. 2017

Bacciotti et al. 2018

Center:self-scatteringmmcontinuum polarization in HD163296. The top panels show (a) the total
intensity and (b) thepercentage polarization at band 7 in the central. Observations
Alignmentwith(c)posed as ellipses areSelf-scattering
representations of the three rings in the total intensity image, marked 1–3 in (b). The lower panelsouterare (c) thepart:polarizedself-scattering?
onangle,2016both
Octoberradiation?
gasded(d)by
the ALMA
polarization
with the12,
polarization vectors superimposed.
In (c), thevectors ow?
are shown at their actual angle, whereas intion
PI:44.1
A.◦Kataoka).
Alignment?
Figure2. andLinearly
intensity P and polarizati
ation (2016.1.00115.S,
relative to the mean ofis multiplied by a factor of 3, to emphasize the relative twist. Polarization
fractionangle arepolarized
truncated
fl

on
was
C40-6,
and(250µJy).
41 antennas
were
DG Tau(panels(c),(d)). Contours as in Fig. 1. Po
levelsof 5σper beam
Imagesare 3 arcsec (315 au) across. Resolution is ∼0.2 arcsec (beamsand
are shown
lowerleft). Polarization

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
the top-rightof the Stokes
F. O. toAlveset al.: Magnetic
fieldI in a circumbinary disk around a Class I YSO
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(e.g., Tazaki et al. 2017), StokesV has not been well
The transition of polarization morphologies from one
characterized
for
ALMA,
so
its
detection
couldbespuriousBand 3
Band 7
Band 6
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
870 μm,thethe positive regions almost completely disappear.
perpendicular to the major axis. We would expect
StokesUpolarization to be perfectly perpendicular to the majoraxis.shows two positive and two negative regions at
The negative blobs disappear at 1.3 mm, while the
The reason for this small 7° discrepancy is uncertain,3.1
butmm.
could
positive regions connect, and at 870 μm, the positive regions
indicate asymmetry in the disk.
turn into a single, large region.
The right panels of Figure 2 show P for each wavelength.
ForfortheP Stokes V images (Figure 2), 3.1 mm appears to be
For 1.3 mm and 870 μm, there is a slight asymmetry
purelymore
noise. For both 1.3 mm and 870 μm, StokesV has aalong the major axis of the disk, with the southeast
polarized than the northwest. For 1.3 mm, thenegative
absoluteﬂux blob offset to the top-right of the Stokes I
intensity,
difference between the two P peaks along the major
axis isand this blob is signiﬁcantly brighter in 870 μm.
Alves et can
al. 2018
Althoughpolarizationin principle be produced by
0.0013 ± 0.0014, which is not statisticallysigniﬁcant.
Thecircular
The AstrophysicalJournal,851:55(6pp),
2017
December
10 off non-spherical grains
scatteringoflinearlypolarizedlight
1. Stokes I (left panel), polarized intensity (middle panel) and polarization fraction (right panel) ofasymmetry
our Bandfor
3 (upperpanels),Band
6(middle870 μm is more apparent, although the southeast
et al. 2017), StokesV has not beenThewelltransition ofof the diskindoes
notband,peak (i.e.,
it is30,
still60,
increasingtheels) and Band 7 (lower panels) ALMA data. The contours indicate the intensity levels of the Stokespart
I emission
each
being
90,(e.g.,at Tazaki
characterized
for ALMA, so its detection could be wavelength
spurious to another
1
1
edge
of
the
detectedpolarized
emission).
The
P
peak
towardBand
7150,180 times the rms for bands of 3 and 6 (rms
⇠
0.012
mJy
beam
and
rms
⇠
0.15
mJy
beam
),
and
30,
60,
90,
120
times
Band 3
Band 6 Band 6
willthenot be discussed in detail in this paper.
the northwest is 0.0077 ± 0.0010.
Drawinga lineandfromimages, as seen in F
1
00
00
00
00
mJy beam , the rms for Band 7. The synthesized beams are 0.22 ⇥ 0.17 (position angle = 61.46
)
for
Band
3,
0.26
⇥
0.15
(position
Thesamecentral polarization vectors for 1.3 mm and 870
μm are image shows
northwest peak through the center of the disk, at the
StokesQ
00
00
55°. P
4 ±0°axis regions fro
e = 85.65 ) for Band 6 and 0.21 ⇥ 0.18 (position angle = 72.79 ) for Band 7. The vector map radiusindicates
thesoutheast
orientation
the polarizationon theside, ofP=0.0094
± 0.0010.
rises. 96 and 55°. 3 ±0°. 41, respectively. The major
and positiveof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnershipet al.are much brig
se length is proportional to the polarization fraction. The vectors are sampled as one vector every
two pixels.
two
to ∼0.0115
at the The
edge of
thestar-symbols
disk. Therefore, atthetheP asymmetry
regions
indicating the polarization vectors are ∼7° frommajor
for 870 μmpeakis ∼0.002–0.004.
These
870being
μm, the positive
dle-lower panel indicate the position of the two continuum peaks detected in the 34 GHz VLA data,along
beingtheVLA
5aaxisthe northernand VLA2015),
to the major axis. We would expect
the shows two
asymmetries are relatively moderate, but the factperpendicularthat they
StokesU
he southern one (see also Fig. 2).
polarization
axis.The negative
appear both at 1.3 mm and 870 μm suggests they
could to be perfectly perpendicular to the major
3.1 mm.
The reason
couldregions conne
PT = for this small 7° discrepancy is uncertain, but
be a real feature. If we consider total polarization
positive
indicate asymmetry in the disk.
turn into a single, large
Q 2 + U 2 + V 2 I , the asymmetry is similar; for 1.3 mm, it is
The
right
panelsofFigure
2
show
P
for
each
wavelength.
of±
⇠10
AUwhileat thePipedisextended polarized emission is detected at scales larger than 12 (i.e. a spatial resolution
For the Stokes V im
0.00120.0014,for 870μmnebula
it is ∼0.001–0.004.
For 1.3 mm and 870 μm, there is a slight asymmetry
for noise.
P0purelyFor bothal. 12(2017)
the major, which corresponds to ⇠ 13 ⇥ of the primary beam in Band 7 tance). The rms noise of theYang
mapet isµJyshowed
beamthat1 .asymmetry alongalong
the major axis of the disk, with the southeast
more
negative ﬂux blob ofaxis is not expected for scattering-induced polarization in an
smaller of the three bands).
polarized than the northwest. For 1.3 mm, the intensity,
absolute and this blo
axisymmetric disk, so axisymmetry must be broken if thedifference between the two P peaks along the major
axis is circular polar
Althoughpolarization is really due to scattering even though the total
0.0013 ± 0.0014, which is not statistically signiﬁcant.
The of linearly p
scattering
intensity(StokesI)ishighlyaxisymmetric.
On
the
other
hand,
et al.
2017,
Stephens
al. 2017
Fig. 1. Stokes I (left panel), polarized intensity (middle panel) and polarization fraction (right Kataoka
panel) ofasymmetryourBand
3 (upperpanels),Band
6 (middle
for
870
μm is
more etapparent,
althoughthe (e.g.,southeast
Tazaki et al.
thepolarization
along
the
minor
axis
is
expected
tobe
Figure1.
ALMApolarimetricobservations
at
3.1
mm
(top,
Kataoka
et
al.
part
of
the
disk
does
not
peak
(i.e.,
itis
stillincreasing
at
the
VLA
panels) and Band 7 (lower panels) ALMA
data.VLAThe contours
indicateiftheof the Stokes
I emissionin each band, being 30, 60, 90, characterized for ALM
Previous
lowerasymmetricangularresolution
observations
theintensity
dust 1disklevels
is opticallythick(⇠andhas a2017), 1.3 mm (middle), and 870 μm (bottom), where the red vectors show the1edgeof beamthe detected
polarized
emission).
Thetimes
P peaktoward00
120,
150,180
times
the
rms
for
bands
of
3
and
6
(rms
⇠
0.012
mJy
beam
and
rms
⇠
0.15
mJy
),
and
30,
60,
90,
120
and
will not be discuss
Band
3
Band
6
signiﬁcantangular
width
(for
a
cartoonillustration,
see
Figure6>3σ polarization morphology (i.e., vectors3 havenot beenrotated).
Vector)at
3.6cm
detectedthesource
VLA
5
near
the
cenBand7
thenorthwestis0.0077±0.0010.
Drawing
a
line
from
1
00 Tau disk is known to be optically
00
00
Thethecentral polarizat
lengths
are beam
linearly proportional
to for
P. Thecolor 7.
scaleTheshows
the polarized beams
in Yang
etal. 002017).
HL
0.52
mJy
,
the
rms
Band
synthesized
are
0.22
⇥
0.17
(position
angle
=
61.46
)
for
Band
3,
0.26
⇥
0.15
(positionused the Karl G. Jansky Very Large Array(VLA)
toobserve
ter
of
the
disk
of
BHB07-11
(Dzib
et
al.
2013).
The
newnorthwest peak through the center of the disk, at the same
intensity, which is masked to only show 3σ detections. Stokes I contours in

Motivation 2: wavelength dependence
0.87 mmBHB07-11(Class I)

3.1 mmAlignment (with B- elds? with gas ow?)flSelf-scatteringfifl

HL Tau(Class I-II)

1.3 mmAlignment with radiation?
gas ow?

What I would like to discuss today is …
• Introduction (~5 min., done)• Pre-ALMA era and ALMA discovery ofdiverse morphologies of polarization.

• Theories/models (~20 min.,done)• Self-scattering polarization• Grain alignment in protoplanetary disks• Basic interpretations (~5 min., done)• Implications to planet formation? Whatcan be and cannot be explained by thetheories? Recent progress? (~15 min.)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 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 are
ALMA Band 7
StokesQ
image
shows
negative
regions
from
north
to
south
55°Astrophysical. 4 ±0°. 96 and 55°. 3Journal
±0°. 41, respectively.
major(5pp),
axis 2017 July 20
The
Letters, The
844:L5
Kataoka et al.
andpositive
regions
from
east
to
west.
At
1.3
mm,
the
negativeof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnership et al.
ALMA Band 6
regionsaremuchbrighterthanthepositive
regions,andat2015), indicating the polarization vectors are ∼7° from being
870
μm,thethepositive regions
However,cannotoutwould
the expect
grainalignment
withalmost
the completely disappear.
perpendicularweto themajor ruleaxis. We
StokesUshows two positive and two negative regions atpolarizationmagnetic
to be perfectly
perpendicular
to themajor
axis.thepoloidalﬁelds.
In
the
case
of
1.3 mmThe negative
blobs image,disappear at 1.3 mm, while the
The reason for this small 7° discrepancy is uncertain,3.1
butmm.
could
regions connect, and of
at 870μm, the positive regions
however,
we interpretthe self-scatteringtheindicate asymmetry
in the disk. it with (c) positive
turn into a single, large region.
The right
panelsof Figure 2 whichshow P foreach wavelength.
thermaldust
emission,providesthepolarization vectors
For
For 1.3 mm and 870 μm, there is a slight asymmetry
fortheP Stokes V images (Figure 2), 3.1 mm appears to be
purelynoise.
For bothmmsomeand 870 μm, StokesV has aparallelthe axis
minor
However,
there
could
be 1.3also
along thetomajorof theaxis.
disk, withthe southeast
more
negative
ﬂux blob offset to the top-right of the Stokes I
polarized than the
For 1.3 mm, theabsolute
contributionsof northwest.
(b) the alignment
withtheradiationﬁelds
to brighter in 870 μm.
intensity,
and
this
blob
is
signiﬁcantly
difference between the two P peaks along the major axis is
Althoughcircular polarizationcaninprinciple be produced by
the0.0013
polarization,
which
the
polarization
vectorsatthe± 0.0014, which
is notenhances
statisticallysigniﬁcant.
The
The AstrophysicalJournal, of
851:55(6pp), polarized2017 December
10 off non-spherical grains
Stephens et al.
scattering
linearly
lightasymmetry
for
870
μm
is
more
apparent,
althoughthesoutheast
north–west and south–east regions (along
the majoraxis) StokesVwhile has not been well(e.g.,at Tazaki
et al. 2017),
part of the disk does not peak (i.e., it is still increasingthe
The transition of polarization morphologies from one
characterized
for
ALMA,
so
its
detection
couldbespurious
decreasing
the polarizedpolarization
at the north–east andedge of the detected
emission). fraction
The P peak toward
wavelength to another is also apparent in the StokesQ and U
willthenot be discussed in detail in this paper.
the northwest regions
is 0.0077 ±0.0010. Drawing
a lineandfromimages, as seen in Figure 2. Speciﬁcally, at 3.1 mm thesouth–west(alongthe minoraxis).
Thesamecentral polarization 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
StokesQ
55°. P
4polarization
±0°±0°. 41, respectively.
The major
axis regions from east to west. At 1.3 mm, the negative
The onwavelength
dependence
theinradiusthe southeast side,P=0.0094 ±in
0.0010.
rises. 96 and 55°. 3fraction
and positiveof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnershipet al.are much brighter than the positive regions, and at∼0.0115ofat theof the disk. Therefore,
P asymmetry
regions
theto casetheedgeself-scatteringis thestrong(Kataokaetal.
2015),
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.
perpendicular
to
the
major
axis.
We
would
expectthe shows two positive and two negative regions at
while
it is weakerin thecasebutofthe
thefactgrainalignment. Therefore,
asymmetries
are relatively
moderate,that they
StokesUpolarization
to be perfectly perpendicular to the majoraxis.The negative blobs disappear at 1.3 mm, while theat 1.3 mm
and 870 μm suggests
they
couldalignment
3.1 mm.
theappear
mostbothnaturalinterpretationis that
the
with
the
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
positive
indicate asymmetry in the disk.
radiation
axisymmetric
turn into a single, large region.
Q 2 + U 2 ﬁelds+ V 2 I ,provides
the asymmetrythe
is similar;
for 1.3 mm, it isazimuthal polarizaThe right panels of Figure 2 show P for eachFigure
wavelength.
Total
polarization
fractionfunction
wavelengths.
Band 3For4.theStokesV images (Figure2), as3.1ammappearsoftothe
be observedALMA
0.0012
± 0.0014,
for 870
μm it is ∼0.001–0.004.
tion
vectors
onwhilebothwavelengths,
while
the
self-scattering
For 1.3 mm and 870 μm, there is a slight asymmetryforP
Thepurely
total polarization
fraction
derivedbyStokesVintegrating
noise. For both
1.3 mm isand
870 μm,has aeach Stokes I, Q, and U
Yang et al. (2017) showed that asymmetry along the major
along
the
major
axis
of
the
disk,
with
the
southeast
more
dominates
at 1.3formm.
negative ﬂux
offsetrepresent
to the top-rightof the Stokes
axis is not expected
scattering-induced polarization in an
Theblobcurvesthe predictionof theI HL Tau disk with thepolarized than the northwest. For 1.3 mm, component.
the intensity,
absolute andthis blobis signiﬁcantly
brighterin 870μm.are aaxisymmetric disk, so axisymmetry must be broken if theself-scattering
model
where
the
maximumgrain
sizes
max = 50, 70, 100 ,difference between the two P peaks along the major
axis is circular polarization can in principle be produced by
Althoughpolarization is really due to scattering even though the total
0.0013 ± 0.0014, which is not statistically signiﬁcant.
(Kataoka
et al. 2016a)
with the radiativeand scattering
150 Them m oflinearly polarized
light andoff non-sphericalgrains alignment model. The(StokesI)ishighlyaxisymmetric.
On
the
other
hand,
show 2.9, 1.3, and 0.87 mm ALMA continuum images of HL intensity
Tau. Panel
(d)
shows
the
1.3
mm
PSF
for
the
same
FOV
as
the
other
4.2.along
Modeling
the
Scattered
Components
asymmetryfor 870 μm is more apparent, althoughdashed,
the (e.g.,southeast
solid,
lines
representwith the local alignment
Tazakiandet dotted
al. 2017),
StokesV
has thenot models
been wellthepolarization
the
minor
axis
is
expectedtobeenlarged
view
of
the
inner
300
mas
centered
on
the
PSF’s
peak
(the
other
bands
show
similarpatterns).
Panels
(e)
and
(f)
show
the
1. ALMA polarimetric observations at 3.1 mm (top, Kataoka et al.
part of the disk does not peak (i.e., it is still increasingat thecharacterized
ALMA,
so its3.6%
detection
could be spurious, respectively.
efﬁciencyof p for
= 0%,
1.8%,
asymmetric
if
the
dust
disk
is
optically
thick
and
has
a
α
α
<
4
.
The
sultingfromthecombination
of
the
1.3
and
0.87
mm
data.
The
spectral
index
(α)
map
has
been
maskedwhere.3 mm (middle), and 870 μm (bottom), where the red vectors show theedgeerrorof thedetectedpolarized emission). The P peaktowardBymodeling
thescatteredcomponentsofthepolarization,
will not be discussed in detail in this paper.
angularfor
width
(for
a cartoon
illustration,
see Figure
larization(i.e.,
vectorshavebeen 1.
rotated).
Vector of thesigniﬁcantto 0.0077 ± 0.0010. Drawing a line andhelowermorphology
left of eachpanel;
also
seenotTable
The range
color bar shown
panel
(b)
at 1.3 mmcorresponds
tonorthwest−2×6rms is
the
from
the
The
central polarization vectors for 1.3 mm and 870 μm arearelinearly
proportional
to
P.
The
color
scale
shows
the
polarized
in
Yang
et
al.
2017).
HL
Tau
disk
is
known
to
be
optically
wecanconstrain
the
grain
size
in
the
HL
Tau
disk.
To
model
values 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
55°. 4 ±0°. 96 and 55°. 3 ±0°. 41, respectively. The major axis
thick at 870 μm (Carrasco-González et al. 2016), but nowavelengthin[3,Table
el are shown for
10, 25,1.50, 100, 200, 325, 500, 750, 1000] × sI , the scattering components in polarization,
radius onwe
the consider
southeast side,P=0.0094
±
0.0010.
PHLrises
the totalof
Tau’s disk
is 138°. 02 ±is
0°. 07(ALMA
al. it is diluted by the−1asymmetryisdetected
along
the
minor
axis.
The
lack
of
the spatial
resolution
betterorPartnership
smalleret if
is 44, 154, and 460 μJy bm for 3.1 mm, 1.3 mm, and 870 μm,
to ∼0.0115 at the edge of the disk. Therefore, theif
P asymmetry~100 µm sized grains?

fi

ALMA Partnership 2015, Stephens et al. 2017

Kataoka et al. 2017, modi ed

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 e
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. Bacciottintensity, 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
as shown
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,
0.8,
0.9
⇥
the
peak
of
1.37
mJy
beam
.
Bottompolarization ⎡ along
the minor = axis
is expected ⎛to be
Grayscaleis the total
intensity thermal dust emission; contours are
the polarization fraction P
P/I, plotted at levels of⎞⎤
1. ALMA
polarimetricobservations
atpoloidal
3.1 mmright:(top,
Kataokaetal.
2percentage
in theFigure
outerregions
indicates
the Figure
magneticﬁeld
0.005,
0.006,
0.007,
0.008,
0.009,
0.01.
The
coordinates
andthegrayscaleareidentical
in
the
two
bottompanels.
The
ALMAdata used
to intensity(and1.
Sub-mmcontinuumpolarizationin
HD163296.
The
top
panels
show
(a)
the
total
(b)
the
polarization at band 7 iqq)
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⎢S0,min + (S0,max - S0,min ) exp ⎜⎜ -(c)
⎥
⎟
S
=
d
⎟ ⎥(b). The lower panels are (c) t
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 2f 21–3 in>3σ polarization
morphology(i.e., vectors
have
notSuperimposed
been
Vector⎢⎝⎠ are⎣ the HL
⎦ shown at their actual angledlengthsthe
are linearly
proportional
to P. The
color
scale
shows
the(d)
polarized
flux intensity
andthepolarization
angle,etbothpolarization
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(d) theof
vectorrotation
relativemeanatof 870
44.1μmby a factor
theintensity
relative
twist.
Polarization
fractionfraction
and anglep a
thick(Carrasco-González
al.emphasize2016), but
no2of⎞et3, to⎛Figuremechanism
locallytorotatethedirectionthemagneticﬁeldeach panel are shown for [3, 10, 25, 50, 100, 200, 325, 500, 750, 1000] × sI ,rr()
cminorDG
Tau(panels
as in(beams
Fig.
1. Polarizationang
polarized
flux and5σ per beam
(250µJy).
are⎜and3-arcsec
au)
across.
Resolution
isof∼0.2 arcsec
areshown lower left).
asymmetryis Images
detectedalongthe(315
axis.(c),(d)).
The lackContours
,
1
´ exp
(
)
sI is 44, 154,atandleast
460 μJyat
bm−1
for at3.1
mm, 1.3 mm,
870of
μm,
where
⎟
by 90°.
Therefore,that
position,thelevelsmechanism
2 thick
indicatethejetDisk near-side lies towards the receding jeasymmetryfor P alongtheoptically
minor axis implies
vectors have 1/2 beam spacing, withlengths proportional
to thepolarization
fraction.
respectively.
2r⎠ orientation.
⎝w
should be different from the grain alignment.
−1
total intensity is I > 10 mJy beam
for CW Tau and I > 30 mJy be(c)~100 µm sized grains?
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

Many disks show self-scattering at 0.9 mm→ Do disks have dust grains with size of ~ 100 µm?
fracFigure 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.

The polarization fraction in the south region is as high as
sub-mm observations found an upper
limit rofand
1 per
centthetoetradial
the
total
on-source
20,max
h,
where
θ are
andTheazimuthalcoordinates,◦ although some 15 m
Piétual. (2014)
andthetimeoneof jet, ijetwas=S49
reportedof
13.9±0.7%,
whichishigherthan
thepredicted
value(e.g.,
Kataoka et al. 2016, Hull et al. 2018, Bacciotti et
al.
2018,
Dent
et
al.
2019,
Stephens
et
al.
2017,
Kataoka
et
al.
2017,
polarization
fractionin a 1 arcsec beam
(Hughesetal.
2009).
Pinte
were
flaggedinthesecondsessionwhile
thetargettran
2. LinearlypolarizedP
andapolarizationand S0,min are Figure
theHartigan
maximumand(2004).
minimum
surfaceat posi- fraction
et al.
Theintensity
same
fit density
gives
disk
in
ijet
Cho & Lazarian 2007). The high fractionofpolarizationmeans
11
et al. (2018) and Teague et
have
also
recently
found
to
the
zenith.
3 al. (2018)
andDG(c),(d)).
inFig. 1.with
Polarization◦◦ center andthe center of the
ring,
θTau
fd represent
theContours
width
d and
tion
angle,
PA(panels= 60.7±1.9, in goodasagreement
hig
that
the
alignment
efﬁciency
maybe
higherthan
expected
or
the
disk
dynamical
evidenceof massive planets in the system. indicate the jet
Ohashi long-to-short
et al. 2018,
Sadavoy
et
al.
2019
The
system
was
set
up
to
observecontinuuminborientation.
Disknear-sidelies
towards
thereceding◦ direction,◦of the vortex inPA
thedisk
azimuthalandrc andr
represent
w
=
62
±
3
(Piétuetal.
2014),
andalmostper201
axis ratio of elongated dust
grainsislargerthan−1
In this paper, we present ALMA observations of polarized
dust
of
343.5
total intensity
is Imean> 10frequency
mJy beam
forGHz,
CW withTau spectral
and I >windows
30 mJy◦thecenter
and
width
of
the
vortexintheradialdirection.
The
et
al.
2004).
pendicular
to
the
jet
PA
=-29
(Hartiganalm
the assumed value (Cho & Lazarian emission2007). of
Alternatively,theHD163296 at 870 µm with a resolution of ∼0.2arcsec –338.432,jet
348.494, and 350.494
Akimasa Kataoka (NAOJ)−2 GHz,◦ each having 31.25
values are Piétu
taken
toTau,
bethe andΣ0,maxcm
Σ0,high polarization fraction observed in the southwest region(2014)
the=0.6
oneflux
ofgjet,ijet, =±49
For etDGal.
integrated
is 880.2
9.4reported
mJy,
199

Spectral index vs. grain size
M. Tazzari et al.

8

L. Ricci et al.: Protoplanetary disks in Taurus-Auriga

Ricci
2010a
Fig. 3. Millimeter dust opacity for the adopted dust model.
Leftettopal.
panel:
dust opacity at 1 mm as a function of amax for a grain size Tazzari
distributionet al. 2020a
Figure 5. (Left) Spectral index between 1 and 3 mm as a function of integrated 1 mm flux for Lup−qn(a) ∝ a between amin = 0.1 µm and(cf.aMiyake
curves are for different values of q, aslabelled. The dust grains adopted here are porous
max . Different
and Nakagawa 1993, Pollack etl. 1994…)
Lupus TDs are marked with an additional red circle. The dark shaded region represents the sensitivi
composite spheres made of astronomical silicates (≈10% in volume), carbonaceous materials(≈20%)
waterThe
icedashed(≈30%;
forU the of the optically thin emission of
are notsensitiveandanymore.
line issee
the text
typical
1 3 mmreferences to the optical constants). Left bottom panel: β between 1 and 3 mm as a function of
amax index
for thesame grainshown
distributions.
Right panel:
spectralmeasurementsin the left panel.
dust opacity at 1 mm as function of β between 1 and 3 mm for the same grain distributions; different iso-amax curves for amax = 0.1, 1, 10 cm areshown. In the plots the unit of measure for the dust opacity is cm2 per gram of dust.
5

Akimasa Kataoka (NAOJ)DISCUSSION(0 max 1mm
size distribut

Prediction
from
grain
growththeoryA&A 593, A12 (2016)

A&A
A12 (2016)
Investigating dust trapping in
A.transition
Pohl et al.:disks
Investigatingwith millimeter-wave
dust trapping
polarization
in593,
transition
disks with millimete

Pohl et al. 2016

Fig.
11. Polarization
maps
withwith
overplottedpolarization
vectors
after
0.1 Myr,
1 Myr,
and 3 Myr massof dust
sity
PI,
and
polarization
degreePoverlaid
polarization
vectorsforthereference
model(planet-to-star
rated
Fig.
dust
2. Snapshotsdensity distributionof the hasverticallyforevolutionary
integrated
times
dust density
ofP[%]
0.1,is1distribution
andweak
3 Myr.
forThe
evolutionary
planet is locatedtimesatof60
0.1,
au 1a
If
grainsradialsize
distribution,
too
to
be
detected
40 evolution,. The images
producedau, 1 Myr ofof
dust
dustareopacity
mixture,= 0.87 mm, and face-on disk).
3 at 0.87 mm.

he horizontal
the planet-to-stardashed lines
mass represent
ratio is 10the. particle
The horizontal
sizes corresponding
dashed lines represent
to a size parameterthe particle
ofsizesx = 2⇡a/corresp⇠
Akimasa Kataoka (NAOJ)

One idea: at gas surface density
HL Tau Band 7

The Astrophysical Journal, 878:132 (12pp), 2019 June 20

model

Okuzumi & Tazaki•

How can we achieve 100 µm grain sizefor the entire region?
•

Non-sticky (=fragile) dust grains, suchas covered by CO2 mantle•

Radially at gas surface density, thatmakes radially at grain size

Ra

June 20

Okuzumi & Tazaki

mn: ALMA polarimetric image of the HL Tau disk at λ=0.87 mm (Stephens et al. 2017). The color scale is the polarized intensity, and the red
the direction and degree of polarization. Contours are the total intensity, with the contour intervals taken to be the same as in Figure 1 of Stephense and right columns: synthetic polarimetric images at λ=0.87 mm from four dust evolution models. The model images are after convolution withkernel of 0 44×0 35, the beam size for the corresponding observation.

4. Discussion

fl

fl

fl

correspond to the dust rings in the sintering zones. For
comparison, we also show in the left panel of Figure 6 theations for the Ring–Gap Substructure andradial brightness temperature proﬁles of the HL Tau disk
ter Spectral Slope of the HL Tau Disk
derived from the ALMA high-resolution images (ALMAve focused on the polarized emission of the HL
Partnership et al. 2015). O16 produced these proﬁles by
00 au scale. It is also interesting to see what our
azimuthally averaging the observed maps (see Section 2.1
for the ring–gap intensity proﬁles observed inof O16 for more details).
MA observations (ALMA Partnership et al.
The most prominent feature in the intensity proﬁles caused
iddle and right panels of Figure 6, we plot theby CO2 ice mantles is a deep gap at r≈10 au. Interestingly,of the Planck brightness temperatures TB at
theoflocationof diskthisatdeep
gapmm
coincidesthat ofTheHL
Tau’s
Figure 4. Left column:
ALMA
polarimetricthe HL Tauλ=0.87(Stephenswith
et al. 2017).
color
scale is the polarized intensity, and the redand 2.9 mm (corresponding
to ALMA
Bands
7, image
innermost Contours
gap (ALMA2015).
Intakenthese
line segments show the direction and degree of polarization.
are the totalPartnershipintensity, withet
the al.
contourintervals
to be the same as in Figure 1 of Stephens
ned from our dust
evolutionmodels.
Heretheet al. (2017). Middle and right columns: synthetic
polarimetricλ=0.87
from fourmodels. The
model images are after convolution withmodels,theimages
deepat gap
is mm
causedby dustthe evolution
rapid growthandAkimasa
Kataoka (NAOJ)
ghtness temperatures
are calculatedusing 35, the beam size for the corresponding observation.
an elliptic Gaussian
kernel of 0 44×0

Okuzumi and Tazaki 2019

Another idea: optically thick diskberThe
1 Astrophysical Journal, 900:81 (17pp), 2020 September 1

Observations

Observations

Ohashi et al.

OhashiObservations•

IRS 48 - lopsided disk•

How can we explain bothpolarization at 0.9mm brightemission at 8.8 mm (VLA)?

•Best model: very opticallythick dust (τ ~ 7.3) at 0.9 mm
Ohashi et al. 2020

Akimasa Kataoka (NAOJ)

Polarization and substructures

High definition study of the HD 163296 disk

3

Dust self-scattering in HD 163296

HD 163296

175

W. R. F. Dent et al.

Ra

(b)
(b)

DSHARP; Isella et al. 2018
Figure 1. Map of the HD 163296 disk recorded in the 1.25 mm continuum. The angular resolution of the observations is0.03800 ⇥0.04800 and is indicated by the white ellipse in the bottom left corner of the left panel. At the source distance of 101
pc, the spatial resolution is 3.8au⇥4.8au. Inset (a) and (b) show zoom-in view of two asymmetric features revealed by theobservations. The rms noise is 0.023 mJy beam 1 . The horizontal segments indicate a spatial scale of 10 au.

tude self-calibration on both short and long baseline
data. The self-calibration procedure resulted in an improvement of 43% in the peak signal-to-noise ratio in
the dust continuum image. A complete description of
the DSHARP data calibration procedure is presented
in Andrews et al. (2018), while the CASA script used
to calibrate and image HD 163296 data, including themanual flagging and flux rescaling, is available online athttps://almascience.org/alma-data/lp/DSHARP. The
1.25 mm dust continuum emission was imaged using the
CASA task tclean and a robust parameter of -0.5 resulting in a synthesized beam FWHM of 0.03800 ⇥0.04800 ,corresponding to a spatial resolution of 3.8⇥4.8 au at
the distance of the source. The rms noise is 0.023 mJy
beam 1 , and the peak signal to noise ratio is 185.
The complex gain solutions of the self-calibration of
the continuum emission were then applied to the 12 CO
data. The line was observed at the same angular resolution of the continuum (⇠0.0400 ), but we imaged it using
Briggs robust=0.5 (no uv-tapering) to achieve higher

Dent et al. 2019signal-to-noise ratio (see Andrews et al. 2018 for moredetails about CO imaging). The FWHM of the synthesized beam of the presented CO maps is 0.10400 ⇥0.09500 ,which is about half the beam of the CO observations
published in Isella et al. (2016), and about 7 times
smaller than the resolution of the ALMA science verification data (Rosenfeld et al. 2013; de Gregorio-Monsalvo
et al. 2013). Channels are spaced in velocity by 0.32 km
s 1 , but, due to Hanning smoothing, the velocity resolution is 0.64 km s 1 . The velocity grid for HD 163296
slightly di↵ers from the fiducial channel spacing of 0.35
km s 1 adopted for the other DSHARP sources. The
rms noise per channel is 0.84 mJy beam 1 .
3. DUST CONTINUUM EMISSION

The map of the 1.25 mm continuum emission (Figure 1) features two bright elliptical rings previously reported by Isella et al. (2016), as well as three new morphological features: an arc of emission inside the firstring (inset a), an inner dark gap and bright ring at about•

Even if assuming100 µm grains, beam convolution of
optically thick rings (α~2) and thin gaps (α~4) can
explain both spectral index and polarization.
Lin et al. 2020
(See also Ohashi and Kataoka 2019)

Downloaded from https://academic.oup.com/mnras/

10 au

Downloaded from https://academic.oup.com/mnrasl/article-abstract/482/1/L29/5107365

(a)
(a)

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
Akimasa Kataoka (NAOJ)
Superimposed as ellipses are representations of the three rings in the total intensity image, marked 1–3 in (b). The Figure
lower panels5.are Panel(c) the polarized(a): The 0.043 resolution Band 6 Stokes I image in mJy per beam. The unScattering makes disk continuum fainter← no scattering← with scattering•

Miyake and Nakagawa 1993
Akimasa Kataoka (NAOJ)

If the emission is very optically thick,the continuum emission becomes
fainter due to dust scattering (Miyake
and Nakagawa 1993, Birnstiel et al.
2018, Liu 2019, Zhu et al. 2019, Sierra
and Lizano 2020)

Full modeling on radial pro le - HL Tau
The Astrophysical Journal, 883:71 (21pp), 2019 September 20

Carrasco-González et al.

The Astrophysical Journal, 883:71 (21pp), 2019 September 20•

Carrasco-González et al.

Optical depth is > 10 (!) at rings and ~5 at
gaps at 870 micron
Carrasco-Gonzalez et al. 2019
(See Ueda et al. 2020 for TW Hya)

Figure 2. Final images of the HLTau disk used in the analysis (see Section 2.3 for details). All images are convolved to the same angular resolution of 50 mas(∼7.35 au), and all panels show the same spatial extent (2″×2″, centered on the disk peak intensity). Color scales in the four panels are between twice the rms ofeach map and the maximum intensity (see Table 2). The VLA image at 8.0 mm was made by combining data in the Ka and Q bands after subtraction of the free–freeemission (see Appendix A for details).

See the talks by Anibal Sierra for the similar analysis on several∼49 mas and an rms noise of ∼14 μJy beam (for a robust 0
targets with MAPS data and Enriqueweighted image). Macias for TW Hya−1

Telescope

Band

Wavelength(mm)

Rms Noise(μJy beam−1)

Maximum Intensity(mJy beam−1)

ALMA

B7

0.9

15

33

2.2. VLA Observations

Akimasa Kataoka (NAOJ)
fi

Table 2
Final ALMA and VLA Images of HL Tau Used in the Analysis

870 μm,thethe positive regions almost completely disa
perpendicular to the major axis. We would expect
StokesUpolarization to be perfectly perpendicular to the majoraxis.shows two positive and two negative regi
The negative blobs disappear at 1.3 mm, wh
The reason for this small 7° discrepancy is uncertain,3.1
butmm.
could
positive regions connect, and at 870 μm, the positive r
indicate asymmetry in the disk.
turn into a single, large region.
The right panels of Figure 2 show P for each wavelength.
ForfortheP Stokes V images (Figure 2), 3.1 mm appears
For 1.3 mm and 870 μm, there is a slight asymmetry
purelymore
noise. For both 1.3 mm and 870 μm, StokesValong the major axis of the disk, with the southeast
polarized than the northwest. For 1.3 mm, thenegative
absoluteﬂux blob offset to the top-right of the St
intensity,
difference between the two P peaks along the major
axis isand this blob is signiﬁcantly brighter in 87
Althoughcircular polarization can in principle be produ
0.0013 ± 0.0014, which is not statisticallysigniﬁcant.
The
The AstrophysicalJournal, of
851:55(6pp), polarized2017 December
10 off non-sphericalscattering
linearly
lightasymmetry for 870 μm is more apparent, although the southeast(e.g.,at Tazaki
et al. 2017), StokesV has not beenpart of the disk does not peak (i.e., it is still increasing
thecharacterized
spedge of the detected polarized emission). The P peaktoward for ALMA, so its detection could be wa
willthenot be discussed in detail in this paper.
the northwest is 0.0077 ± 0.0010. Drawing a lineandfromimThesamecentral polarization vectors for 1.3 mm and 870
northwest peak through the center of the disk, at theStoμ55°. P
4 ±0°radius on the southeast side, P=0.0094 ± 0.0010.
rises. 96 and 55°. 3 ±0°. 41, respectively. The majoandof HL Tau’s disk is 138°. 02 ± 0°. 07 (ALMA Partnershi
to ∼0.0115 at the edge of the disk. Therefore, the P asymmetry
reg2015),
indicating the polarization vectors are ∼7° fromalong the major axis for 870 μm is ∼0.002–0.004.
These87
to the major axis. We would expe
asymmetries are relatively moderate, but the factperpendicularthat theyStopolarization
appear both at 1.3 mm and 870 μm suggests they
could to be perfectly perpendicular to the majo
3.1
The reason
PT = for this small 7° discrepancy is uncertain, but
be a real feature. If we consider total polarizationpoindicate asymmetry in the disk.
2
2
2
tur
Q + U + V I , the asymmetry is similar; for 1.3 mm, it is
The right panels of Figure 2 show P for each wave
0.0012 ± 0.0014, while for 870 μm it is ∼0.001–0.004.
For 1.3 mm and 870 μm, there is a slight asymmetrypu
Yang et al. (2017) showed that asymmetry along the majoralong the major axis of the disk, with the southeastnegaxis is not expected for scattering-induced polarization in anpolarized than the northwest. For 1.3 mm, the int
abaxisymmetric disk, so axisymmetry must be broken if thedifference between the two P peaks along the majorAl
polarization is really due to scattering even though the total
0.0013 ± 0.0014, which is not statistically signiﬁcansca
intensity (Stokes I ) is highly axisymmetric. On the other hand,asymmetry for 870 μm is more apparent, although the (e.
southe polarization along the minor axis is expected to bepart of the disk does not peak (i.e., it is still increasingcha
asymmetric if the dust disk is optically thick and has aedge of the detected polarized emission). The P peaktandsigniﬁcant angular width (for a cartoon illustration, see Figure 6
the northwest is 0.0077 ± 0.0010. Drawing a line froin Yang et al. 2017). HL Tau disk is known to be opticallynorthwest peak through the center of the disk, at the55
thick at 870 μm (Carrasco-González et al. 2016), but noradius on the southeast side, P=0.0094 ± 0.0010.of P
asymmetry is detected along the minor axis. The lack ofto ∼0.0115 at the edge of the disk. Therefore, the P asym
20
asymmetry for P along the optically thick minor axis implies
along the major axis for 870 μm is ∼0.002–0.004.
perasymmetries are relatively moderate, but the fact thapo
Akimasa Kataoka (NAOJ)

Is the alignment-induced polarization
wavelength dependent?

Self-scattering

Figure 1. ALMA polarimetric observations at 3.1 mm (top, Kataoka et al.
2017), 1.3 mm (middle), and 870 μm (bottom), where the red vectors show the>3σ polarization morphology (i.e., vectors have not been rotated). Vector
lengths are linearly proportional to P. The color scale shows the polarized
intensity, which is masked to only show 3σ detections. Stokes I contours ineach panel are shown for [3, 10, 25, 50, 100, 200, 325, 500, 750, 1000] × sI ,where sI is 44, 154, and 460 μJy bm−1 for 3.1 mm, 1.3 mm, and 870 μm,
respectively.

Alignment with radiation?

Wavelength dependence in alignment
If size << wavelength

If size ~ wavelength

If size >> wavelengthRano polarization

See next page for more details.

Band 6

Band 3

Wavelength dependence in alignment

emission in the Mie regime

F. O. Alves et al.: Magnetic field in a circumbinary disk aroun

1.3 mm0.87 mm
Band 7

3.1 mmBand 3

Band 6

Alves et al. 2018

Ra

Fig. 1. Stokes I (left panel), polarized intensity (middle panel) and polarization fraction (right panel) of our Band 3 (upper panels), Band 6 (middle
panels) and Band 7 (lower panels) ALMA data. The contours indicate the intensity levels of the Stokes I emission in each band, being 30, 60, 90,
1Band120, 150,180 times the rms for bands of 3 and 6 (rmsand rmsBand 6 Band
⇠ 0.156 mJy beam 1 ), and 30, 60, 90, 120 times
Band 37⇠ 0.012 mJy beam
0.52 mJy beam 1 , the rms for Band 7. The synthesized beams are 0.2200 ⇥ 0.1700 (position angle = 61.46 ) for Band 3, 0.2600 ⇥ 0.1500 (position
angle = 85.65 ) for Band 6 and 0.2100 ⇥ 0.1800 (position angle = 72.79 ) for Band 7. The vector map indicates the orientation of the polarization
whose length is proportional to the polarization fraction. The vectors are sampled as one vector every two pixels. The two star-symbols at the
middle-lower panel indicate the position of the two continuum peaks detected in the 34 GHz VLA data, being VLA 5a the northern peak and VLA
5b the southern one (see also Fig. 2).

•

If a<λ : polarization parallel to the major axis

no extended polarized emission is detected at scales larger than
5.700 , which corresponds to ⇠ 13 ⇥ of the primary beam in Band 7(the smaller of the three bands).

12 (i.e. a spatial resolution of ⇠10 AU at the Pipe nebula distance). The rms noise of the map is 12 µJy beam 1 .

If
a~λ
:
polarization
reversalFig. 1. Stokes I (left panel), polarized intensity (middle panel) and polarization fraction (right panel) of our Band 3 (upper panels), Band 6 (mi•2.2. VLA

panels) and Band 7 (lower panels) ALMA
data.VLAThe contours
indicate theintensity levelsof the Stokes
Previous
lower angularresolution
observations(⇠ I emission in each band, being 30, 60
100
120, 150,180 times the rms for3bands
of3.6
3 and
6 (rms0.012
mJy beam
andrmsBand0.15 mJy beam 1 ), and 30, 60, 90, 120 ti
Band 3 7⇠the
6 ⇠cen)atcm
detectedsource
VLA
5
near
the
Band
00
00
mJy(VLA)beam 1to, the
rms for Band
7. Thesynthesized
beams are 0.22
⇥ 0.17(position
angle=
61.46 ) for Band 3, 0.2600 ⇥ 0.1500 (pos
We used the Karl G. Jansky Very Large0.52
Arrayobserveter ofthediskof
BHB07-11
(Dzib
et
al.
2013).
The
new= 85.65 ) for Band 6 and 0.2100 ⇥ 0.1800 (position angle = 72.79 ) for Band 7. The vector map indicates the orientation of the polariza
the continuum emission at 34.5 GHz ( angle⇠ 8.7mm, Ka band) in observations resolved VLA 5 in a binary system, VLA 5awhose length is proportional to the polarization fraction. The vectors are sampled as one vector every two pixels. The two star-symbols a
its most extended configuration. The observations
were indicate
carried the(RA= 17:11:23.1057,
DECpeaks= detected
27:24:32.818)
5b, being VLA 5a the northern peak and V
middle-lower panel
positionof the two continuum
in the 34 andGHz VLAVLA data,
out on December 4 and 10, 2016. The 5b
total
time
(17:11:23.1017,
27:24:32.985). The uncertainties in the potheon-source
southern one(seewasalso Fig.
2).

•

If a>λ : no polarization

77 minutes. The calibration was performed using the standard sitions are '4 mas. Their flux densities are 0.32 ± 0.03 and
CASA VLA pipeline. The maps were obtained from the cali- 0.23 ± 0.03 mJy, respectively. The two radio sources appear inbrated visibilities using a robust weightingof 0, which
providedside isthedetected
disk, slightly
the dust
continuum
12 millimeter(i.e. a spatial
resolution of ⇠10 AU at the Pipe nebula
no extended
polarized
emission
at scaleso↵setlargerofthan
00
00
1
00
a synthesized beam of 0.10 ⇥ 0.04 5.7
with, which
a position
angle ofto ⇠peaks(Fig. 2).
corresponds
tance). The rms noise of the map is 12 µJy beam 1 .
3 ⇥ of the primary beam in Band 7(the smaller of the three bands).

Guillet et al. 2020

Article number, page 3 of 8

2.2. VLA(See
also
Brunngräber
and
Wolf
2019,
Fig. 1. Stokes I (left panel), polarized
intensityVLA(middlepanel)angularand polarization
fraction(right pa
Previous
lower
resolution
observations
panels) and Band 7 (lower panels)
data. The contours indicate the intensity levels of the300 ) ALMAat 3.6cm
the source VLA 5 near the cKirchschlager
etal.detected
2019)
120, 150,180 times the rms for bands of 3 and 6 (rms
⇠ 0.012 mJy beam and rms

We used the Karl G. Jansky Very Large Array (VLA) 1to observe

Band 3

1

Band 6ter of the disk of BHB07-11 (Dzib
00 et al.00 2013). The

azimuthal polarization: mechanical alignment?

, 2017 July 20

HL Tau (3 mm)

the polarization
grain alignment,
scattering because
ent only when thewhere λ is the

Kataoka et al.

imetric images, we
Large Millimeter/
HL Tau is a young
distance of 140pc
disk is around ink has several ring
ALMA Partnership Mori et al.
to wavelengths ofprevious CARMA
ns et al. 2014).

Kataoka et al. 20172016 October 12,
S, PI: A. Kataoka).
41 antennas were
spectral windows
z with a bandwidthe, and phase wereJ0423-0120, andon calibration was
The raw data were

• HL Tau Band 3 shows elliptical pattern, which is inconsistent

ways to improve the model predictions. Additional challenges ofwith alignment with radiative ux but with gas ow. But italigned grain models in explaining the multiwavelength observa2.2
requiressupersonic
ow.
tions
of the HL
Tau disc arebriefly discussed. Our main results arepolasummarized in Section 5.
Besi
Yang et al. 2019
dyna
2021Iforradiative transfer simulations)
2 P O L A R I (SeeZ ATMoriI O NandOKataoka
R I E N TAT
ON
Laza
Akimasa Kataoka (NAOJ)
gas

Figure 1. ALMA Band 3 observations of the HL Tau disk. The wavelength is
3.1 mm. The top panel shows the polarized intensity in colorscale, thepolarization direction as red vectors, and the continuum intensity as the solid
contour. The vectors are shown where the polarized intensity is larger than
5sPI . The contours correspond to (10, 20, 40, 80, 160, 320, 640, 1280)´ therms of 9.6 μJy. The bottom panel shows that the polarization fraction incolorscale, polarization vectors in blue, and the same continuum intensity
flMori et al. 2019flarized intensity in,9 and the contour

AS 209 (0.9 mm)flAN deconvolution
image quality. We
t parameter of 0.5
ters of 0, 0.3, andct is 0. 45 ´ 0. 29,
e of 140 pc to the, 6.9, and 6.9 μJy,

Figure 2. Elliptical versus circular polarization pattern. The red solid line
If grainsaligned withradiation•segments
are arefor polarization
orientations,andgradients,
green dashedpolarizationline segments
forpattern
the directionoftherequiredradiative
flux
projected
into
the
sky
plane
would be circular.
in the case of radiative alignment.

alon
ular
as il
of F
lariz
thin
com
lipti
prod
see
such
gree
thus
axis

non-spherical grains?
5

Symmetry axis perpendicular
f = 1.00
f = 0.10
f = 0.01

ω Psca [%]P ! e↵ , P !

0.8
0.6
0.4

100

100

80

80

80

60

60

60

40

40

40

20
0
λ = 0.87 mm (ALMA B7)
λ = 1.3 mm (ALMA B6)
λ = 1.5 mm (ALMA B5)
λ = 2.1 mm (ALMA B4)
λ = 3.1 mm (ALMA B3)
λ = 4.0 mm (ALMA B2)
λ = 7.0 mm (ALMA B1)

−20
−40

0.2

102

0
10 3

−60
−80
10

10 2

10 1
100
amax (cm)

101

102

Tazaki et al. 2019and compact dust aggregates (f = 0.1, 0.01) at = 1 mm. (Left) Solidthe results for the volume filling factor of f = 1, 0.1, and 0.01, respectively.
ering albedo ! anddegreeareof linear
polarization
P at scattering
angle of
• Ifthegrainsporous,polarization
can beosition of amax f = 160 µm. (Right) Solid and dashed lines indicate results
detectable in a wider size range, but theate P ! e↵ at amax f = 160 µm. The P ! e↵ -values at x > 1 is significantly
ing albedo.
fraction gets smaller.

x > 1.
f ⌧ 1
acuum,

Symm

100

100
amax [µm]ω Psca [%]1

Sphereω Psca [%]ate Structure in Protoplanetary Disks

F. Kirchschlager and G. H.-M. Bertrang: Self-scattering of non-spherical dust grains

20
0

20
0

−20

−20

−40

−40

−60

−60

−80
1000 10−801000 10100
amax [µm]Fig. 6. Albedo ! times scattering polarisation Psca for a grain size distribution dn / aeff3.5 daeff as a function of t
This figure represents the grain sizethat contributes mostandto theBertrang
polarised intensity.
Left:2020
scattering on oblate grai
Kirchschlager
etal.
the grain’s symmetry axis (⇥sca,2 = 90 ). Centre: scattering on spherical grains (c/b = 1.0) . Right: scattering on oblat
symmetry axis is coplanar to the scattering plane (⇥sca,2 = 0 ).

If grainsareupnon-spherical,
evenincreasinglarge grain size. Following thedegree of•⇠29%
at grain sizes
to 1 mm. The peak polarisation of the scattering plane coplanar to S (⇥sca,2 = 0 ) even (2015) for spherical grains, the prodgrains canemit
at 870
micron! Psca , defines a win
ing polarisation,
drops to approximately
70% foramax =polarization
120 µm and converges
to approximately 21% for larger grain sizes, and the peak polar- sizes that contribute to the scatterin
wavelengths.
isation is flippedin orientation by 90 for all size distributions size distributions with maximum radwith amax & 110 µm.
a significant scattering polarisation an(See also
andsignal
Wolfat 2017)
We also calculated the scattering polarisation
for a Bertrang
size polarisation(sub-)millimetre
distribution of spherical dust grains using DDA (Fig. 5). The functions of non-spherical (Fig. 6, leflu↵y aggregates. In this section, we use df = 2.0 andSee
the talks
by RyoFlorianKirchschlager
polarisation
degreesof the spherical grains are larger than that of (Fig. 6, centre) dust grains are very
k0 = 1.0 in order to attain clear
physicalinsights
intoTazaki andscattering along the short axis (coplanar scattering) and smaller maximum sizes smaller than or com
their optical properties.
than that of scattering along the long axis (perpendicular to ing that grains of at least ⇠ /2⇡ in sLine polarization
Line Polarization toward HD 142527 and IM Lup

•

•

13

Non-detection of CN circular polarization•

TW Hya (Vlemmings et al. 2019)•

See Mazzei et al. 2020 for radiative transfer
for Zeeman effectFigure 14. HD 142527 IQU V moment 0 maps over the velocity range shown in the bottom left of the panel, which is the pinkshaded area shown in Figure 12. The spectra in Figure 12 is the average spectra taken at the location of the white circle.

Non-detection (?) of CO linear polarization•

HD 142527 and IM Lup (Stephens et al.
2020)

See the talks by Rachel Harrison for upper limit on
AS 209 and Boy Lankhaar for more prediction

Figure 15. IM Lup IQU V moment 0 maps over the velocity range shown in the bottom left of the panel, which is the pinkshaded area shown in Figure 13. The spectra in Figure 13 is the average spectra taken at the location of the white circle.

the QU V moment 0 maps is = 0.78 mJy bm 1 km s 1 ,anything that is red-colored is above 2 and whitecolored is above 3 . While the >2 pixels are blotchy
rather than a smooth cohesive structure, we note thatfor an image that is purely noise, only 2.3% of the area is
Akimasa Kataoka (NAOJ)
expected to be above the 2 value. Since the Stokes Q

Stokes Q is expected to be pure noise. We tried circular apertures with integer radii sizes between 1 and27 pixels (0.00 11 ⇥ 300 ). For every circular aperture, we
looked for the highest SNRQ possible for 2 to 32 consecutive channels (i.e., a window of sizes between ⇠0.16
and 2.5 km s 1 ), restricting the search for a signal within

Stephens et al. 2020

Summary•

Millimeter polarization of protoplanetary disks• Disks show combination/superposition of self-scatteringand alignment-induced polarization.
•

Grain size inconsistency• Many disks show self-scattering polarization at 0.9 mm,

which indicates 100 µm grains.
• Radiallyat gas surface density and fragile grains? Opticallythick disks? Optically thick substructures?

•

Grain microphysics• Porosity? Mie regime? Fundamental discussion onalignment physics is missing.
Line polarization - no robust detection so far
fl•