SFN #361 65-81 (片岡, 2023/05/19)

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65. The HH 24 Complex: Jets, Multiple Star Formation, andOrphaned Protostars (Bo Reipurth et al.)
66. Searching for Molecular Jets from High-Mass Protostars (Tatiana
M. Rodriguez et al.)
67. Modelling the early mass-ejection in jet driven protostellar
out ows. Lessons from Cep E (P. R. Rivera-Ortiz et al.)
68. Grid-Based Simulations of Polar Circumbinary Disks: Polar
Alignment and Vortex Formation (Ian Rabago et al.)
69. A kinematically detected planet candidate in a transition disk
(Jochen Stadler et al.)70. The Gaia view of the Cepheus OB2 association (Máté Szilágyi etal.)
71. Evolution of the reservoirs of volatiles in the protosolar nebula(Antoine Schneeberger et al.)
72. Leaky dust traps: How fragmentation impacts dust ltering by
planets (Sebastian Markus Stammler et al.)73. Modelling grain-size distributions in C-type shocks using a
discrete power-law model (Rosie Sumpter and Sven Van Loo)
74. Probing Velocity Structures of Protostellar Envelopes: Infalling
and Rotating Envelopes within Turbulent Dense Cores (Jinshi Sai etal.)

75. A Uni ed Model for Bipolar Out ows from Young Stars:
Kinematic Signatures of Jets, Winds, and Their Magnetic Interplay
with the Ambient Toroids (Hsien Shang et al.)
76. A Uni ed Model for Bipolar Out ows from Young Stars:
Apparent Magnetic Jet Ac- celeration(Hsien Shang et al.)
77. Witnessing the fragmentation of a lament into prestellar cores inOrion B/NGC 2024 (Y. Shimajiri et al.)78. QUIJOTE scienti c results – V. The microwave intensity andpolarisation spectra of the Galactic regions W49, W51 and IC443 (D.
Tramonte et al.)79. Magnetic elds do not suppress global star formation in low
metallicity dwarf galaxies (David J. Whitworth et al. )80. A Naive Bayes Classi er for identifying Class II YSOs (Andrew
J. Wilson et al.)
81. ATOMS: ALMA Three-millimeter Observations of Massive Starforming regions -XIII. Ongoing triggered star formation withinclump-fed scenario found in the massive (∼ 1500 M⊙) clump (S.
Zhang et al.)

Leaky dust traps: How fragmentation impacts dust ltering by planets
Sebastian Markus Stammler1, Tim Lichtenberg2, Joanna Drą żkowska3,and Tilman Birnstiel1, 4January 24, 2023
ABSTRACTThe nucleosynthetic isotope dichotomy between carbonaceous (CC) andnon-carbonaceous (NC) meteorites has been interpreted as evidence forspatial separation and the coexistence of two distinct planet-forming
reservoirs for several million years in the solar protoplanetary disk. The
rapid formation of Jupiter’s core within one million years after theformation of calcium-aluminium-rich inclusions (CAIs) has beensuggested as a potential mechanism for spatial and temporal separation. In
this scenario, Jupiter’s core would open a gap in the disk and trap inwarddrifting dust grains in the pressure bump at the outer edge of the gap,
separating the inner and outer disk materials from each other. We
performed simulations of dust particles in a protoplanetary disk with a gap
opened by an early-formed Jupiter core, including dust growth andfragmentation as well as dust transport, using the dust evolution software
DustPy. Our numerical experiments indicate that particles trapped in theouter edge of the gap rapidly fragment and are transported through the gap,
contaminating the inner disk with outer disk material on a timescale that isinconsistent with the meteoritic record. This suggests that other processes
must have initiated or at least contributed to the isotopic separation
between the inner and outer Solar System.

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Keywords. Meteorites,meteors,meteoroids—Methods:numerical—
Protoplanetarydisks—Planetsandsatellites:formation— Planets andsatellites: composition• モチベーションとコンテクスト：炭
素質・非炭素質隕石の違い。木星コ
アができて、その内と外で物質をわけたことが定説となっている• 物質が分かれるのは木星ギャップの
圧力バンプをダストが通り抜けられないから→本当？

• DustPyを用いて木星コアギャップありでのダストの移流成長を説いた。

• 外から内側へダスト破片がたくさん輸送してしまった。ー＞これは、木星ギャップで物質が分けられないことを示唆• 参考：深井さん記事(遊星人2020)• Carbonaceous Chondrites (CC)とNonCC(NC)
グループに分けられる。e.g., Warren 2011

• Moの解析をすると、二分性があり、中間的な物
質が存在しない→木星コアを境に物質が互いに混
じり合わない領域があったはず。Kruijer et al.
(2017) and Desch et al. (2018)• Kruijer et al. (2017) argue that the twodust reservoirs have been separated fromabout 1Myr to 3 ­ 4 Myr after theformation of calcium-aluminium-rich inclusions (CAIs).

• しかし、木星ギャップは、大きなダストはせき止
めることができるが、小さなダストはすり抜けてしまうはず

核合成起源同位体二分性と初期太陽系の進化／深井

図1 : 隕石全岩のμ54Cr−μ50Tiデータを示す図(Cr: [9, 11‒15], Ti: [14, 16‒18])．全てのデータは同一の隕石から研究グループ(Cr: [9] ‒ Ti: [17]，またはCr‒Ti: [14])からデータが報告されている場合は，重複するデータがあの報告のみ採用している．Warren [10]では，国際会議のアブストラクトのデータも含めコンパイルしているが，μiM = ((Rmeteorites / Rterrestrial) ‒ 1) × 10^6), R = iM/jM を表す．プロットの誤差は，各論文に掲載され3. 同位体二分性
3.1

同位体二分性の発見

隕石全 岩に同位体 異常があることは，2000 年代

分 性は，単純な二成分混合など過程では達成されない．更に，のギャップがあり，中間的な同がないことが見てとれる．これら

C Cには形成時に時空間的な分の形成領域で異なる物質輸送がに質量分析計の分析精度向上に伴って，様々な元素られる．
図2: 隕 石全 岩のμ94Mo−μ95Moデータを示す図(EC (Enstatite Chondrites), OC (Ordinar y Chondrites): [21‒23],

22‒24], CAI: [25])．2本の直線は，NC・CCそれぞれのプロッ（計算には「ISOPLOT」
を用いたにおいて明らかになりつつあった[8,9など ]．炭素質 トから得られた回帰直線である
Wa r renの結果をもとに，更トの誤差は，各論文に掲載されている測定誤差を示す．

コンドライトは特に大きな同位体異常を示し，エンス

いたのが Budde et a l . [ 19]，K

タタイトコンドライトや 普 通コンドライトは 地 球に近である．著者達は Ti・Cr同位体

• Toy model:• 5 auに惑星があるとする(土星質量)。gapはKanagawa et al. (2017) の
pro le利用。ガスはr^-1, exp cuto あり(r̲c=30 au)。
Mdisk=0.05Msun。 ガスはviscous進化する。

• 初期ダストは1µmで、15auよりそとにおく。5 model やってみた（v̲frag=10m/s、1 m/s,の場合、fragmentationなしの場合、bouncingの場合、gapなしの場合）

ff

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•

Sebastian Markus Stammler et al.: Leaky dust traps: How fragmentation impacts dust filtering by planets

A&A proofs: manu

• Fiducialな場合(10m/s破壊速度):B• St=0.1くらい。cm。まで成長してトラップされる。

• St=0.01くらい、ミリダストは内側に漏れている。

• dust uxを見ると、惑星を入れると20000年くらい遅れてダス
トが内側に流入する。が、長時間内側へのmass uxがある。

• D：破壊なし。Kobayashi andTanaka 2021 とconsistent。

• E：1m/s破壊速度。ダスト小さすぎてトラップされない。

• F：bouncing。破壊がないから小さflfl

いダストがない（ダストを完全にせき止めるにはいい話）。だが、cm/s
くらいでbounceする設定だと、
St=0.001くらいにしかならない。ダスト小さい。あんまりせき止められない。

Fig. 2. Comparison of dust fluxes and the fraction of total accreted dus
mass in the toy model with and without planet. Top: Comparison othe dust flux in the inner disk (at 2 AU) and outer disk (at 15 AU) in th
toy model with a Saturn-mass planet at 5 AU (panel B in Figure 1) andmodel without a planet (panel C in Figure 1). The two green 15 AU line
overlap. Bottom: Total dust mass accreted through the inner disk ove
time in the model with (solid line) and without (dashed line) a planet.

sure bump at the outer edge of the gap, fragment down to smalle
sizes, and di↵use out of the pressure bump before the gas candrag them into the inner disk where they grow to larger parti
cles again. Due to this delayed processing, the maximum dus
flux is reduced by about one order of magnitude. The duration
however, is prolonged such that the total mass of dust flowing
through the inner disk is identical after 10 Myr, as can be seenin the bottom panel of Figure 2. The Saturn-mass planet did noFig. 1. Comparison of di↵erent toy models
with dust initiallyno only present outside of 15 AU. Panel A: Initial dust distribution. The white linesseparate the inner from the outer disk material, but only delayedcorrespond to Stokes numbers of St = 10 3 , 10 2 , 10 1 , 100 ; the bold white line corresponds to St = 1. All other panels show snapshots of models
the material transport.
at 1 Myr. Panel B: Fiducial toy model with a Saturn-mass planet at 5 AU and a fragmentation velocity of 10 m/s. Panel C: Model without a planet.
The vertical dashed lines are the location at which the dust flux is measured in Figure 2. Panel D: Model without fragmentation. Panel E: Model Panel D of Figure 1 shows a simulation without fragmen
tation. In this scenario, particles sizes are limited only by thewith a reduced fragmentation velocity of 1 m/s. Bottom right: Model with bouncing instead of fragmentation.
radial drift, consistent with the model presented by Kobayashi &Tanaka (2021). In the center of the pressure bump, the pressure
after 1 Myr. Particles trapped in the pressure bump outside the again grow to centimeter sizes and can contribute to phenomenagradient is zero and the growth is, in principle, unlimited unti

A&A proofs: manuscript no. dust_filtering• Full disk model。惑星の質量を変えてdust uxを比較。

• 30地球から１木星まで。
• 土星質量のときだけ、拡散パラメータδを変えた。

• 30地球質量ではせき止めが足りない。3e5年でおおよそ全部降着する。

• 200地球質量で随分delayはできる
が、せき止めには至らない。
Fig. 2. Comparison of dust fluxes and the fraction of total accreted dust
mass in the toy model with and without planet. Top: Comparison of
the dust flux in the inner disk (at 2 AU) and outer disk (at 15 AU) in the
toy model with a Saturn-mass planet at 5 AU (panel B in Figure 1) and amodel without a planet (panel C in Figure 1). The two green 15 AU lines
overlap. Bottom: Total dust mass accreted through the inner disk overtime in the model with (solid line) and without (dashed line) a planet.

• 拡散係数変えたほうが結果は大きく
変わる。

fl

sure bump at the outer edge of the gap, fragment down to smaller

Fig. 3. Comparison of dust fluxes and the fraction of total accreted dust
mass in the full disk models for various planet masses and dust di↵usivities. Top: Dust flux through the planetary gap in models with di↵erent planet masses. The blue line is for a model without a planet. The
dashed, dotted, and dash-dotted red lines show additional simulations
with a Saturn-mass planet for di↵erent radial dust di↵usivity parameters r . Bottom: Total fraction of outer dust mass accreted through theplanetary gap.

this case, the particles cannot reach particles sizes large enoughA&A proofs: manuscript no. dust_filtering• 惑星質量が時間変化するモデルもやってみた。

• 結論は特に変わらず：leaky dust
trapping

Fig. 4. Comparison of models with fragmentation and bouncing with variable planet masses. Top left: Evolution of the planetary mass in thetime-dependent model. The solid line shows the default model where the planet reaches 20 M at 1 Myrs. The dashed line shows the evolution ina model with rapid early growth in which the planet reaches 40 M at 1 Myr. Bottom left: Fraction of outer disk dust mass accreted through thegap after 1 Myr in the default planetary mass evolution model for di↵erent values of dust di↵usivity r with fragmentation limited growth. Bottom
right: Solid lines show the fraction of outer disk material accreted through the gap after 1 Myr for bouncing limited growth for di↵erent values of
the i parameters in the default planetary growth model. The dashed green line shows a model of bouncing limited growth with i = 10 5 and rapid
early growth of the planet (dashed line in top left panel). The vertical lines indicate 4 Myr until which the two reservoirs needed to be separated.
Top right: Snapshot of the dust distribution at 4 Myr for the model with bouncing limited growth and i = 10 5 (dashed green line in bottom rightpanel). The inner disk is depleted in dust and only supplied with small amounts of outer disk material.

the outer disk material into the inner disk within 1 Myr. Lower
proto-Jupiter masses typically lead to complete homogenization
within ⇠ 105 to at most a few 106 yr. This presents a problem• 関係ないですが宣伝: DustPy講習会を6/19に実施します

60 % of the outer disk dust was accreted through the planetarygap after 4 Myr, as can be seen in Figure 4. However, increasing the core mass even more and earlier would enable Jupiter• Grid-based として始めて周連星円
盤のpolar alignmentのシミュレー
ションを行った。

• Polar alignmentは、周連星円盤とバイナリー軌道が90度のものを言う。Youtube動画参照。

• Athena++を使用。
• ポイントは、グリッドベースなので、低い粘性の場合のシミュレーシ
ョンができること。

• 低粘性円盤(α=1e-5)だと、高気圧渦が円盤の縁に確認された。この渦は、数千binary周期保存されて、密度の高い領域と、複数の渦状腕を作った。

• 渦はバイナリー軌道の３­４倍のところにできた。円盤の内縁。
https://www.youtube.com/watch?v=Ny-ggFHALMA• Polar disks•

周連星円盤は、バイナリー軌道に対して0度
または90度が安定。

al. 2019• HD 98800; Kennedy etLETTERSLETTERS

NATURE ASTRONOMY

2.0

1 AU

5 AU

–24° 46′ 38.5″

4°
To Earth
Sky north

0.5
AaAb

7.

170° 31′ 17.7″

170° 31′ 17.6″

170° 31′ 17.5″

170° 31′ 17.4″

Right ascension (J2000)

0°

31

′1

7.

4′
′

170° 31′ 17.8″

17

17

0°
17

0°

31

31

′1

′1

7.

8′
′

6′
′

–24° 46′ 40.5″

Right ascension (J2000)

Fig. 1 | ALMA 1.3!mm continuum image of the HD 98800 dust disk, showing a narrow dust ring 3.5!AU in radius that is 2!AU wide. White semi-transparent
lines show the orbits of the inner binary (BaBb) and the path of the outer binary (AaAb) with respect to BaBb, with dots at the star locations at the timeof the ALMA observation. The resolution of these ‘uniformly weighted’ images (32!×!25!milliarcsec2, or 1.4!×!1.1!AU2) is given by the ellipse in the lower left
corner. Left, entire system. Right, magnification of BaBb.

1412• 粒子数10^6個以上くらい

10

6
4

Velocity (km s–1)

Declination (J2000)82ているので、小さい粘性を取り扱うことがモ
チベーション

0–2

Right ascension (J2000)

𝛼

154°

16°

–24° 46′ 39.6″

1 AU• 原始惑星系円盤は乱流は小さいと言われてきFlux density (mJy beam–1)

Bb0• 過去のSPH計算と問題点• だが、実効粘性はどれも = 0.01 くらい。

1.0

Ba

–24° 46′ 39.5″–24° 46′ 39.5″–24° 46′ 40.0″

V773 Tau B (Kenworthy et al. 2022), IRS
43 system (Brinch et al. 2016)

al. 2019; Smallwood et al. 2019; Cuello& Giup- pone 2019; Martin et al. 2022).

Sky east–24° 46′ 39.0″• 観測：HD 98800 (Kennedy et al. 2019),• (e.g., Martin & Lubow 2017; Kennedy et

1.5–24° 46′ 39.4″

Declination (J2000)•

これは理論的及びSPHシミュレーションで調べられてきた（(Martin & Lubow 2017,2018; Lubow & Martin 2018; Zanazzi &Lai 2018; Smallwood et al. 2019).

Fig. 2 | Carbon monoxide gas velocity map. Colours show the intensityweighted carbon monoxide velocity, and contours the dust. The gas velocity
structure is consistent with that expected if the carbon monoxide disk has thedust and carbon monoxide are at 2.5 ± 0.02 and 1.6 ± 0.3 au, respectively, while the outer edges are at 4.6 ± 0.01 and 6.4 ± 0.5 au (seeMethods). These models show that the disk is largely axisymmetrical, although a small asymmetry in the dust distribution at the inneredge may be a sign of interaction with the binary. The dust andcarbon monoxide components are consistent with having the sameorientation; the disk has a position angle of 16 ± 1° (measured anticlockwise from north) and is inclined by either 26 or 154° (±1°)
from the sky plane. While the Doppler shifts seen in carbon monoxide show that the north side of the disk is rotating towards us(Fig. 2), thus constraining the ascending node to be north of thestar, the inclination remains ambiguous because the disk could be
rotating either clockwise or anti-clockwise as projected on the sky.
That is, these observations do not distinguish whether the east or
west side of the disk is closer to Earth.
Of the two possible disk orientations, the 154° case is only 4° awayfrom the polar configuration (that is, it is perpendicular to both the
BaBb orbital plane and the BaBb pericentre direction), while the 26°
case is inclined 48° from the BaBb binary plane (which we refer to as
the ‘moderately’ misaligned case). The uncertainty on these relative
angles is about 4°, so the polar orientation is consistent with being
perfectly polar. Given the small chance that a randomly chosen orientation should appear to be in the polar configuration, which is• SPH法と粘性

Fig. 3 | Three-dimensional sketch of the polar configuration. Grey ellipses
show the orbit of the BaBb binary, and the torus shows the surrounding
disk. The axes are indicated by the three labelled arrows. The two triangularplanes show the plane of the sky (grey) and disk (red), which intersect
at an angle of 16° from south (that is, the disk position angle). The angle
between these planes is the disk inclination of 154°. Grey lines show
the angular momentum vector of the disk Lc (dotted), and the binary
pericentre direction ωb (solid), both of which point away from Earth. These
vectors are aligned within 4°, meaning that for this orientation, the disk
plane is almost perfectly perpendicular to both the binary orbital plane andthe pericentre direction.

Independent of the disk orientation, we therefore conclude that the
dust observed with ALMA is embedded within a more massive gas
disk, which acts to stabilize the disk against both interior and exterior stellar perturbations. Our estimates of the gas and dust massin the disk are consistent with this picture, but do not confirm it
because they have large systematic uncertainties (see Methods).
The n-body dynamics, in concert with the detection of carbon
monoxide, oxygen and hydrogen gas, therefore suggest that HD
988000BaBb almost certainly harbours a long-lived gas-rich protoplanetary disk.
Our fluid-based simulations find that torques from the innerbinary reorient a gas disk in the moderately misaligned configuration to the polar configuration in several hundred years. In contrast,
the polar configuration is stable and remains in the observed state
for at least 500 BaBb orbits (430 years). While the timescale for thisevolution depends on the specific assumptions made for the simulations (for example, the disk scale height and viscosity) and may belonger than found by our simulations, theory suggests that disks will
typically become aligned within a few million years5,10. The reorientation time is therefore expected to be shorter than the system ageof about 10 Myr, and we conclude that the most probable interpretation is that the disk is in the polar configuration.
While we cannot currently detect planets within the HD 98800
disk (the high optical depth and small angular scale hamper imaging, and radial velocity precision is limited for young binaries), ourdata do show evidence of dust growth. Specifically, our models find

• 粒子法。密度のコントラストが強いときに得意。実効粘性が大きくなりやすい

sizes ladistanc
effectssame eequivaHow
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commrelativeto affeformlyshouldInformboth cpolar obrethreical ev
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2•

I. Rabago et al

et al. 2016) have found an edge-on circumbinary disk with the binary
セットアップstar components orbiting outside of the circumbinary disk plane.
Both components of the binary are also surrounded by circumstellar
disks, each at a different angle to the circumbinary disk, suggesting
Athena++ (Stone etcomplex
al. 2020)
accretion from the circumbinary disk onto the central stars.
To date, all simulations of polar disks have been performed using smoothed-particle hydrodynamics (SPH) (e.g., Martin & Lubow
spherical-polar coordinates
2017; Kennedy et(r,θ,φ)al. 2019; Smallwood et al. 2019; Cuello & Giuppone 2019; Martin et al. 2022). These simulations typically makeuse of over 106 particles and are able to capture the global dynamical
binary軌道がxz平面内。e=0.5の軌道。軌道固定。
evolution of the disk. However, the range of viscosities that can be
included in SPH simulations is limited by the number of particles
in a given region. The minimum disk effective viscosity (Shakura &円盤はスムーズなべき分布。z方向は初期に静水圧平衡。温Sunyaev 1973) is roughly U = 0.01 for most simulations (Price et al.
2018). Protoplanetary disks around single stars have been found with
度は初期べき乗で手で与える。simulation開始後はviscosities of U . 10 4 (Pinte et al. 2016; Villenave et al. 2022), andt̲cool=0.01Ω̲K。 so the study of how polar disks behave at lower viscosities is important but has been unexplored.
In this paper we work to expand on previous results using a gridbased hydrodynamic code to simulatealignment
the circumbinary する
disk. This
この設定だと、38度以内の傾きならpolar
allows us to extend the results of previous works to lower viscosiと期待される(Faragotiesand
Laskar2010)。i<180-38。
than havepreviously been
examined using SPH simulations. Our
paper is organized as follows. In Section 2, we outline our computational setup. Our results are presented in Section 3. We discuss
初期i=120度で設定し、手をはなす。
the implications to circumbinary disk evolution in Section 4, andconclude in Section 5.

•
•
•
•

•
•

• binary軌道で1000周シミュレーションした。
2 METHODS• α=0.1, 0.05, 0.01, 0.001, 0.00001にふった。

We simulate a circumbinary disk using the grid-based hydrodynamical code ATHENA++ (Stone et al. 2020), using spherical-polar coordinates (A, \, q) for the simulations. Figure 1 shows a visualizationof our simulation setup. A disk that begins with an inclination in

Figure 1. Visualization of the U = 10 2 simulation setup at C = 1000 binary
orbits. The disk starts inclined at C = 0 by rotating the disk along the x-ôaxis, keeping ! disk in the yz-plane, and undergoes nodal precession about

the z-axis due to the binary torque. Colors show a slice of density along thexz-plane, with red contour showing a 3D isosurface. The orbits of the binarystars are visible in the center. The simulation grid is shown at half resolution
on the right half of the simulation domain. Regions close to the binary andthe z-axis are not in the computational domain. An animation of the disk
evolution is available in the online material associated with this paper andcan be downloaded at https://youtu.be/Ny-ggFHALMA.

at '. The disk temperature is initialized using the power-law profile
✓ ◆ @
A

6

I. Rabago et al4= 0.05= 0.01= 10 5= 0.001120

i (Deg.)= 0.1

I. Rabago et al
1.0

100
80
60

0.8
0

200

400

600

800

1000

=0
=0
=0
=0
=1

10 2

10 1

100

/ 0
Figure 6. Face-on density profiles of the disk at C = 675 binary orbits.

that binary accretion rates show no periodicity and are roughly con• メインの結果：αを変化させたときの結果
stant in time for a polar disk with U = 0.01. The high viscosity inthese simulations means they do not form vortices, even during theの違い
passage of the outer AaAb binary.

relatively quick, and all vortices are combined into a single vortex
within a few hundred orbits of their creation (middle). The remaining
vortex persists until the end of the simulation (right). A comparison
with the disk density (far right) shows the coincident overdensity andspiral arm features as in Figure 7.
The orbital motion of the vortex is shown in Figure 9. We locate
cells of density d > 0.5d <0G within the vortex and calculate theaverage of their locations as the vortex radius and azimuthal positionin the local disk coordinates. We also use the radial and azimuthal
extent of these cells to calculate the aspect ratio of the vortex j =A q/ A. After the initial vortices merge, the resulting single vortex
orbits at roughly 3 times the binary separation at Keplerian speed.
The vortex aspect ratio is somewhat more variable even after thevortices have finished merging, but is generally around a value ofj ⇠ 5.

The vortex in our U = 10 5 simulation exhibits similar variablebehavior on both short and long timescales. Figure 10 shows theshell-averaged radial mass flux over roughly 10 binary orbits. Longterm flows are present at distances of 3 40 1 , oscillating with aperiod of roughly 5)1 . This low frequency mass flux is due to theorbital motion of the vortex around the binary, carrying the overdense
region on an eccentric orbit at its local orbital period (Figures 5, 9).
Closer to the binary, at roughly 20 1 , short-term outflows are visible
with a periodicity of roughly )1 . These outflows are caused by small
streams of material pulled from the inner edge of the disk and flung
outwards by the binary torque, similar in nature to those seen by
Shi et al. (2012). Since our inner binary is eccentric, these streams
do not pile up and form an overdense lump (Miranda et al. 2017).
Overall the vortex in our polar circumbinary disks is different fromthe lump in coplanar circumbinary disks in two ways: 1) the vortex
only forms when U is very low, while the lump can form in diskswith a much higher U (even in MHD simulations with U ⇠ 0.1, Shi
et al. 2012); 2) the vortex exists in polar circumbinary disks with an
eccentric binary, while the lump is only found when the binary isnearly circular (4 b . 0.05, Miranda et al. 2017).
The overdensity created by the vortex changes the local pressure gradient on the neighboring gas, producing regions of superKeplerian and sub-Keplerian velocity just inside and outside of thevortex orbital radius, respectively (Kuznetsova et al. 2022). These
deviations from Keplerian rotation may be observable as a kinematic
signature (Boehler et al. 2021), which are inverted but similar instrength to the signatures formed in the gaps of protoplanetary disks• αが大きい(0.1とか)だと、inclinationはすぐdampされて90度になる• アルファが小さいと、inclinationは90度を中心に振動する

4 DISCUSSION

4.1 The effect of vortices vs. lumps in the disk

• Polar alignment timescaleはα=0.1で300

The overdensity feature observed in the U = 10 5 simulation isnoticeably different than similar features created in coplanar circumbinary disks. Several coplanar disks have been found to exhibit
horseshoe features, but these features have been explained as a density “lump”, created by eccentric gas at the inner edge of the diskinteracting with inflow streams created by the action of the binary
torque (Shi et al. 2012; Miranda et al. 2017; Ragusa et al. 2017,2020). In contrast, the overdensity feature in the polar disk corresponds to the vorticity minimum in the disk, and is closer in nature
to vortex-induced clumps caused at the edges of gaps opened bybinary orbits, α=0.05で500 orbits, これ
は以前の解析解？とおおよそ一致(220Tb,
455Tb; Lubow and Martin 2018)

80
60

polar (Deg.)

10 3

0

200

400

600

800

1000

0.4

20

0.2
0

polar (Deg.)

10 4

0.6

0

200

400

600

800

1000

100

0.0

0
100

0.4
0

200

400

600

800

1000

1.00

M/M0

10 5

100

i sin /

(Deg.)

120

= 0.1

0.10

0

200

= 0.05400= 0.01= 0.001

600

800= 10 5

1000

Time (Binary Orbits)

Figure 3. Time evolution of the disk for different values of U, showing largechanges in orientation. Top: Disk inclination 8. Top Middle: Longitude ofascending node ⌦. Middle: Angle between the disk and the binary eccentricity
vector \polar . Bottom Middle: Longitude of ascending node in the xy-plane⌦polar . Bottom: Disk mass as a fraction of the initial mass. All angularquantities are measured in reference to the binary orbital plane at a distanceof ' = 301 .

with a higher U-viscosity settle towards a polar alignment quicker,

Figure 4. Trajectories
Each trajectory starts a
towards the point (0.0binary orbits marked breference to the binary
3. Gray paths show theanimation of the test pphase space, is availab
downloaded at https:

the same Shakura-Su
Martin & Lubow (20periods of roughly 3
80 .
The settling behav
Figure 4, which plot
phase space, along w
initial damping phas

= 0.1= 0.05= 0.01= 0.001= 10

be createinteracti
unclear i
HD 1425• α=1e-5の低粘性円盤のみで見えた渦に

4.2 Proついて詳しく見る• Coplanarなシステムで見えていた
horseshoeは、密度の塊(lump)として理解されてきた(Shi et al. 2012; Miranda
4
et al.102017;
Ragusa10et3 al. 2017, 10 2
/ 0
2020)

10 1

100

Figure 6. Face-on density profiles of the disk at C = 675 binary orbits.

• それに対して本研究のpolar diskは、渦度の極小値に対応している。惑星によっck, and all vortices are combined into a single vortex
that binary accretion rates show no periodicity and are roughly conhundred orbitsof their creation (middle). The remaining
stant in time for a polar disk with U = 0.01. The high viscosity inて空いたギャップの縁にできるvortexs until the end of the simulation (right). A comparison
these simulations means they do not form vortices, even during theinduced
Val-Borroetthe outer AaAb binary.
density (farright) showsclumpに近い(dethe coincident overdensity andpassage ofatures as in
7.
The vortex
al.Figure2007;
Zhu et al. 2014; Hammer
et in our U = 10 5 simulation exhibits similar variable
l motion of the vortex is shown in Figure 9. We locate
behavior on both short and long timescales. Figure 10 shows theal. <0G
2017).
ity d > 0.5d
within the vortex and calculate theshell-averaged radial mass flux over roughly 10 binary orbits. Long-eir locations as the vortex radius and azimuthal position
isk coordinates. We also use the radial and azimuthal
se cells to calculate the aspect ratio of the vortex j =er the initial vortices merge, the resulting single vortex
ghly 3 times the binary separation at Keplerian speed.

•

Figure 7.aCloseup of the vortex in the U = 10 simulation at C = 692
term flows are present at distances of 3 40 1 , oscillating withbinary orbits. Top left: Gas midplane density. The local overdensity and spiralpairs
are clearly visible. Top right: Local vorticity. Strong anticyclonicperiod of roughly 5)1 . This low frequency mass flux is due arm
totheregions are indicated in blue. Spiral arms are visible as red diagonal lines inthe vicinity of the vortex. In both plots, black curves show contours of density.
orbital motion of the vortex around the binary, carrying the overdense
Middle: Azimuthal density across the vortex center. Bottom: Radial density
the vortex center.
region on an eccentric orbit at its local orbital period (Figuresacross5, 9).
Closer to the binary, at roughly 20 1 , short-term outflows are visible
5

It is unk
disks. Cu
binaries,
detection
current
with musystems.
variation
Inclineddue to th& Triau
methods
special t
circumb
are in csingle-st
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its orbit2005). O
particles
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in-situ fo
the sharp
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planet fo
close tofi

fi

Probing Velocity Structures of Protostellar Envelopes: Infalling and Rotating
Envelopes within Turbulent Dense Cores
Jinshi Sai, Nagayoshi Ohashi, Hsi-Wei Yen, Anaëlle J. Maury, Sébastien
Maret ⋆ We have observed the three low-mass protostars, IRAS 15398−3359,
L1527 IRS and TMC-1A, with the ALMA 12-m array, the ACA 7-m array,and the IRAM-30m and APEX telescopes in the C18O J = 2-1 emission.
Overall, the C18O emission shows clear velocity gradients at radii of∼100-1000 au, which likely originate from rotation of envelopes, while
velocity gradients are less clear and velocity structures are more perturbed onscales of ∼1000-10,000 au. IRAS 15398−3359 and L1527 IRS show a breakat radii of ∼1200 and ∼1700 au in the radial pro le of the peak velocity,respectively. The peak velocity is proportional to r−1.38 or r−1.7 within the
break radius, which can be interpreted as indicating a rotational motion of theenvelope with a degree of contamination of gas motions on larger spatial
scales. The peak velocity follows vpeak ∝ r0.68 or vpeak ∝ r0.46 outside thebreak radius, which is similar to the J/M-R relation of dense cores. TMC-1A
exhibits the radial pro le of the peak velocity not consistent with therotational motion of the envelope nor the J/M -R relation. The origin of therelation of vpeak ∝ r0.46 - 0.68 is investigated by examining correlations of
the velocity deviation (δv) and the spatial scale (τ) in the two sources.
Obtained spatial correlations, δv ∝ τ∼0.6, are consistent with the scaling law
predicted by turbulence models, which may suggest the large-scale velocity
structures originate from turbulence.

• ３つの低質量原始星をACA, IRAM,
APEX でC18Oのラインで観測し、速度構造を調べた。

• 100-1000au: infalling envelope• 1,000-10,000au: あまりクリアな速度構造ではない。

• 速度の動径方向の構造のturnoverの起源を議論。

• large scale turbulenceとconsisitent

IRAS 15398 3359
L1527 IRS
TMC-1A
TMC-1A (SW side only)

0.013 ± 0.001
0.069 ± 0.003
0.068 ± 0.005
0.099 ± 0.007

1180 ± 90
1700 ± 50
760 ± 10900 ± 30

1.7 ± 0.3
1.38 ± 0.03
4.1 ± 0.1
2.33 ± 0.09

0.68 ± 0.05
0.46 ± 0.05
0.30 ± 0.06
0.60 ± 0.07

The first three rows show results of the fitting to the averaged peak velocities, and the last row shows a result of the fitting to
the peak velocities measured on the southwest side of TMC-1A.

16

Sai et al.
(a) IRAS 15398–3359

NW

S

SE

N

(b) L1527 IRS(c) TMC-1A

Figure 4. ACFs calculated from the one-dimensional slices of the large-scale moment 1 maps.
SWNE(a) IRAS 15398–3359
γ2D=0.6±0.2

Figure 3. Radial profiles of the peak velocities measured with the PV diagrams. Green and purple circles show the data points
measured on opposite sides of the protostars and the black circles represent the averaged value at each radius. The dashed lines
are the extrapolated best-fit power-law functions measured at ⇠100 au in previous works (Aso et al. 2015, 2017; Yen et al. 2017).
The black, solid lines show the double power-law functions with the best-fit parameters for the averaged peak velocities in thiswork. The green, solid line shows the double-power law function with the best-fit parameter for the peak velocity measured on
the southwest side of TMC-1A.

(b) L1527 IRS
γ2D=0.65±0.08(c) TMC-1A
γ2D=0.93±0.08

Figure 5. Spatial correlations of the velocity deviation around the three protostars. Red solid lines indicate the best-fit
power-law relations. Vertical dashed lines show ⌧0 , within which the fitting was performed.

is because density fluctuation causes additional smallscale fluctuation in the centroid velocity through intensity weighting and the projection-smoothing e↵ect iscanceled out. The coefficient , on the other hand,decreases to zero when injection of turbulent energy isturned o↵ and turbulence is decaying (decaying turbulence). We, therefore, estimate the possible 2D values
for the both cases of driven turbulence (  ⇠ 1.5–0.5) and decaying turbulence (  = 0) with Equationand L1527 IRS are consistent with this range. A simulation work suggests that outflows associated with lowmass protostars can drive and maintain turbulence inan isolated core over an entire lifetime of Class 0 protostars of ⇠105 yrs (O↵ner & Arce 2014; O↵ner & Chaban2017). Hence, it could be possible that turbulence is being driven around these protostars.
TMC-1A shows a spatial correlation of the velocity
deviation with a steeper slope than the other two pro-

78. QUIJOTE scienti c results – V. The microwave
intensity and polarisation spectra of the Galactic
regions W49, W51 and IC443 (D. Tramonte et al.)
ABSTRACT

𝜇

fi

𝛼

𝜈

𝜈

fi

𝜇

fl

𝜎

𝛼

we combine QUIJOTE maps with ancillary data at frequencies ranging
from 0.4 to 3000 GHz, reconstruct the spectral energy distribution andmodel it with a combination of known foregrounds. We detect
anomalous microwave emission (AME) in total intensity towards W49 at
4.7 and W51 at 4.0 with peak frequencies AME = (20.0 ± 1.4) GHz
and AME = (17.7 ± 3.6) GHz respectively; this is the rst detection of
AME towards W51. The contamination from ultra-compact HII regions
to the residual AME ux density is estimated at 10% in W49 and 5% in
W51, and does not rule out the AME detection. The polarised SEDs
reveal a synchrotron contribution with spectral indices s = −0.67 ± 0.10
in W49 and s = −0.51 ± 0.07 in W51, ascribed to the diffuse Galactic
emission and to the local supernova remnant respectively. Towards
IC443 in total intensity we measure a broken power-law synchrotron
spectrum with cut-off frequency 0,s = (114 ± 73) GHz, in agreementwith previous studies; our analysis, however, rules out any AME
contribution which had been previously claimed towards IC443. No
evidence of polarised AME emission is detected in this study.

𝜈• 低周波の銀河系のforegroundは以下のものが知られている

We present new intensity and polarisation maps obtained with theQUIJOTE experiment towards the Galactic regions W49, W51 andIC443, covering the frequency range from 10 to 20 GHz at ∼ 1 deg
angular resolution, with a sensitivity in the range 35–79 K beam−1 fortotal intensity and 13–23 K beam−1 for polarisation. For each region,

𝜎

• 文脈

• 銀河磁場に巻き込まれていく高エネルギー電子からのシンクロトロン• フリーフリー放射• ISMの熱放射• anomalous microwave emis- sion (AME,
Planck Collaboration et al. 2016c);• 特にAMEの素質がよくわかっていない。10-60GHzく
らいにあるダストに関連したsignalで、spinning dust
grainsという説がある(Draine & Lazarian 1998 )。

• amorphous dust grainsという説もある(Nashimoto
et al. 2020 )• AMEの偏光特性も知りたいContext of the research:QUIJOTE: a polarimetric CMB experiment for the characterization of
the low frequency galactic foregrounds
●
●
●

●

CMB polarization experiments are searching for the polarization pattern
imprinted by primordial gravitational waves: the “B-modes”.
QUIJOTE is a polarimetric CMB experiment installed at the Teide
observatory since 2012.
QUIJOTE extends the Planck and WMAP coverage to low frequency, with
two instruments:○ Multi Frequency Instrument (MFI):
11, 13, 17, 19 GHz;
○ Thirty and Forty GHz Instrument (TFGI):
Q
Q
J
30-40 GHz.
JTTQUIJOTE tests the low frequency
galactic foregrounds to provide aTMF
precise separation between the galactic
FG
I
and cosmological microwave emission.
I

XIV.0 Reunión Científica

Q
J
T
M
F
I

Q
J
T
T
F
G
I

13-15 julio 2020

Description of the experiment:

QUIJOTE and the wide-survey
QT1 & MFI

QT2 & TFGI(Multi Frequency Instrument)➢ 4 Horns, 32 channels,
4 frequency bands:(11, 13, 17, 19) GHz➢ Angular resolution: 0.92°-0.63°➢ Sensitivity per channel:
500-600 µK ٠sqrt(s)➢ Stepping polar modulator(HWP)➢ Operative since Nov 2012

(Thirty and Forty GHz Instrument)➢ 14 pixels at 30 GHz, 15
pixels at 40 GHz➢ Angular resolution: 0.32°-0.26°➢
Sensitivity of the full array:
85-71 µK ٠sqrt(s)➢ Observations started in
2018. Now delayed, fixing aproblem in the cryostat

QUIJOTE-MFI observations:○ Galactic regions: W49, W51 and IC443 SNRs (Tramonte et.
al (in prep)), Taurus (Poidevin et al. (2018)), Perseus(Génova-Santos et al. (2015)), Fan (Ruiz-Granados et al. (inprep.)), Cygnus, W43 W44 W47 (Génova-Santos et al.
(2017)), Haze (Guidi et. al (in prep)).
○ Cosmological fields 3.000 deg² in three regions○ Wide survey 20.000 deg²
XIV.0 Reunión Científica

Wide survey
20.000 deg²
∼1 year in nominal mode
Sensitivities in Q,U:
≈55 μK/1ºbeam @ 11, 13 GHz≈40 μK/1ºbeam @ 17, 19 GHz

13-15 julio 2020

16

D. Tramonte et al.

• ３領域のSEDを ttingした。
• anomalous microwave emission (AME) が見つかった： W49 at 4.7 and W51 at 4.0 withpeak frequencies AME = (20.0
and AME = (17.7

1.4) GHz

3.6) GHz respectively• The polarised SEDs reveal a synchrotron
contribution with spectral indices s = ­0.67
0.10 in W49 and s = ­0.51

0.07 in W51,

ascribed to the di use Galactic emission andto the local supernova remnant respectively• IC443 ではAMEは検出されなかった。

𝜎

𝛼

𝜎

𝛼

𝜈

ff

fi

𝜈

Figure 8. SEDs for W49, W51 and IC443, obtained from the combination of QUÒOTE and ancillary data, for the total intensity (left panels) and the total
polarised intensity % (right panels). The flux densities have been obtained via aperture photometry in a 1-degree radius aperture centred in the source, asdetailed in Section 5, considering all maps smoothed at a 1 deg resolution. QUÒOTE points are the only available data for these regions covering the range
between 10 and 20 GHz. Overplotted to the data point we show the best-fit models discussed in Section 6.2; the foregrounds considered for each fit are quoted
in the plot legends. In total intensity the model plotted here for W49 is the one including a synchrotron component with a fixed spectral index (third column inTable 8), the model for W51 is the one with no synchrotron component (second column in Table 9), and for IC443 we show the model with a broken power-law
synchrotron spectrum (last column of Table 10). When fitting for a dust component in the polarised SEDs, the dust temperature is always fixed to the value
obtained in total intensity; for W51, the DRAO point was not included in the polarisation fit.

QUÒOTE study o

The thermal emission
in the FIR intensity SEDs
this emission as a modified
regime the dust blackbody
dust optical depth gdust :(dust (a) = gdust (a)⌫ a ()dus⇣a= g2501200 GHzIn the second equality wedust opacity as a power law(or 250 `m). In this case w
sivity Vdust and optical dep
The AME emission
parabola in the log-log plan(

• 偏光角の周波数依存性はFaraday
rotationでよく説明できそう(破線)(AME (a) = AME · exp

In this case we fit for the pe
AME and the width of th
the AME fitting function, aparameters, was proposedin the previous QUÒOTE
has the drawback of coupof the parabola (meaning
value of ,AME ). The func
disentagles the parameters
varied independently.
Finally, we fit for a CM
ential of the flux density w
CMB temperature fluctutat• AMEの偏光へのcontribution はないこととconsistent。アッパーリミットはそれぞれ 1.2% for W49 at 44.1 GHz
and 6.0% for W51 at 22.8 GHz.

(CMB (a) =•Figure 9. Polarisation angle W as a function of frequency, towards the three
regions. We also overplot to the data points the best-fit Faraday rotation
model from equation (9), and report the resulting parameter estimates ineach panel.

is found to be more accurate than the conventional one (Wilson⌘2 a 422: B)CMB
22s

where ⌘ is the Planck’s cotemperature )CMB = 2.725
the value of )CMB .
The SED modelling issquare fit (Markwardt 2009
the chosen foreground mod
Language (IDL) MPFITFU
tion 5, the model is used tofor all frequencies above 1
the original flux densities a
fit is repeated, until converg
both the intensity and polarmodel that best reproduces
different foreground combi