星・惑星形成の命運を握る
原始惑星系円盤の研究の現状
高橋実道(工学院大学/国立天文台)

自己紹介
2015年
2015年-2017年
2017年-

京都大学 博士課程修了
東北大学
工学院大学/国立天文台

夏の学校歴
2010年-2013年 4回参加
2012年 ポスター賞 5位入賞
研究対象
星・惑星形成 原始惑星系円盤
他の天体周りの円盤も少し（初代星、BH…）
主に理論的研究（観測にも手を出し始めた）Outline• イントロ 原始惑星系円盤の形成・進化の概要!

• 円盤形成・進化の物理過程!

• 現在の課題 円盤の詳細構造形成の理解!

• 将来の展望、まとめOutline• イントロ 原始惑星系円盤の形成・進化の概要!

• 円盤形成・進化の物理過程!

• 現在の課題 円盤の詳細構造形成の理解!

• 将来の展望、まとめ原始惑星系円盤星形成の際に原始星周囲に形成、質量~0.01Msun
星・惑星形成に対して重要な役割を果たす。
星形成：星のガスは円盤を通して降着
惑星形成：円盤中で惑星が形成

星・原始惑星系円盤の形成・進化
分子雲コア（重いガス塊）が重力崩壊→星・円盤形成が開始~1Msun~104au星・原始惑星系円盤の形成・進化
分子雲コア（重いガス塊）が重力崩壊→星・円盤形成が開始

中心に原始星、周囲に原始惑星系円盤が形成
ガスは円盤を通して星に落下~102au星・原始惑星系円盤の形成・進化
分子雲コア（重いガス塊）が重力崩壊→星・円盤形成が開始

中心に原始星、周囲に原始惑星系円盤が形成
ガスは円盤を通して星に落下
分子雲コアの全てのガスが降着
円盤形成が終了

星・原始惑星系円盤の形成・進化
分子雲コア（重いガス塊）が重力崩壊→星・円盤形成が開始

中心に原始星、周囲に原始惑星系円盤が形成
ガスは円盤を通して星に落下
分子雲コアの全てのガスが降着
円盤形成が終了
円盤中で惑星が形成・円盤は散逸

Outline• イントロ 原始惑星系円盤の形成・進化の概要!

• 円盤形成・進化の物理過程!

• 現在の課題 円盤の詳細構造形成の理解!

• 将来の展望、まとめ

T = 150#
[K]
(131)
$
$
%
1
au
! r "−3/7
1
au
−1
$
−1 $
∂ α"
∂Ω
T = 150
[K]
10
(132)
α
"
(132)
−1
210
$ α$" 10
1 au (133)(
分子雲コアの重力崩壊の特徴的スケール
∝− α"
Σνr
−1
$
$
#
%
10 $ $∂r$$ $#$ $$% $ $%−1 (132)∂r∂ ∂ #
α " 10∂Ω∂Ω
2 $$2∂$ $%$$$#∂Ω$ (133)$%#
ここでは簡単のため球対称の場合を考える（磁場・回転無視）∝∝−∂− Σνr
(133)
2$
Σνr
$
$ ∂Ω $$
4 −$$∂Ω
∂
∝
Σνr
(
$
$
2
$
$
∂r
∂r
$
$
∂r ] 2+$∂r∂r
α=exp[−Qα∝−Σνr (134)
MRI
$
∂r
$ ∂r
$
∝ ρ−一定 Σνr $ $(133)
温度 T, 密度
∂r
∂r
∂r
4
4
4
4 (134)1α=exp[−Q]+αα=exp[−Q
]
+
α
MRI
MRI
α
=
exp[−Q] +(134)αMRIα=exp[−Q
]
+
α
(
MRI
√
t
∼
(135)
自由落下時間：崩壊したガスが中心に達する時間
ﬀ
4
1 (134)Gρ
α = exp[−Q ]1+1 αMRI 1
tﬀ ∼ √(135) (
√ √ tﬀ ∼ √
tﬀ t∼
(135)
Gρ
ﬀ ∼
Gρ
λJ ∼ cs t1Gρ
(136)
ﬀ Gρ
λJ ∼ c s t ﬀ
tﬀ ∼ √(135)
λJ ∼Gρ
cs tﬀλJ ∼ cs tﬀ
(136)
(
L
>
λ
J(137)
ジーンズ長：ガスが重力崩壊するために必要なサイズ
L>λJ

λJ ∼Lc>(136)(）
s tﬀλJ L > λJ で重力崩壊（tﬀ < L/cs (137)tﬀ < L/cs
(138)
t
<
L/cs
tﬀ < L/cﬀs3

ジーンズ質量 MJ ∼ ρλJ
3MJ ∼ ρλJ

MJ
c3s=
質量降着率 Ṁ ∼~ 10-6 Msun/yr
tﬀG(138) (

(139)

(139)
(140)

重力崩壊はいつまで続くか？
M

圧力勾配力~ P/R ∝ ργ/R ∝ R-3γ-1
重力~ GMρ/R2 ∝ R-5分子雲コア
質量M, 半径RRP∝ργρ∝M r-3

重力崩壊でRが小さくなる時、重力・圧力は増加
γ<4/3 →重力が圧力より増加率大γ>4/3 →圧力が重力より増加率大分子雲コアはT~10Kでほぼ等温 γ~1
重力崩壊が続く
等温進化が終わった時に崩壊が止まる。

原始星形成過程の1次元計算
分子雲コアの重力崩壊によりFirst
Coreを経て原始星が形成
PTEP 2012, 01A307
S. Inutsuka(Larson 1969, Masunaga et al. 1998, Masunaga Inutsuka 2000)

温度

Inutuka 2012
Effective Ratio of Specific Heatsγeff =1.1 < γeff =4/3

SecondCoreγeff = 7/5

Dissociation of H2

γeff = 5/3
First Collapse

Ebind = 4.48 eVFirst Core
Downloaded from http://ptep.oxfordjou

dense
core

Second Collapse

中心密度Fig. 1. Temperature evolution at the center of the gravitationally collapsing cloud obtained by Masunaga and(時間発展)
Inutsuka in their radiation hydrodynamical calculation of protostellar collapse in spherical symmetry [19]. The-2
first collapse phase corresponds to the formation of thefirst core, which
consists
mainlyof hydrogen molecules.
形成直後の質量：Fist
Core
~
10
Msun
The dissociation of hydrogen molecules triggers the second collapse, which eventually produces the second
core or a protostar. Each phase of the temperature evolution is characterized
by the effective ratio of specific-3 Msun原始星~
10heats, γ .
eff

星形成の3次元シミュレーション
回転・磁場を含めた3次元シミュレーション
原始星形成後、First Core から円盤形成
Outﬂow,が形成
1100 磁場によって
INUTSUKA,&Jet
MATSUMOTO
No. 1, 2010
RMHD MACHIDA,SIMULATIONOF PROTO-STELLARCOLLAPSE

Vol. 676

L59

2. METHOD AND MODEL
We solve three-dimensional self-gravitational RMHD equations on nested-grids. Equations and quantities for the radiation
are defined in the comoving frame of the fluid. We treat only
the zeroth-order moment equations of radiation transfer using
the gray (i.e., equations are integrated over frequency assuming a blackbody spectrum of the local temperature) FLD approximation proposed by Levermore & Pomraning (1981) with
Levermore (1984) closure relations. We assume ideal MHD withno resistivity. The equation of state (EOS) of the gas is also assumed to be ideal, where the gas mainly consists of hydrogenmolecules and the adiabatic index γ is set to 7/5 throughout thesimulation, which is better to trace the realistic thermal evolution than γ = 5/3 (Stamatellos & Whitworth 2009). We assume
that the gas and the dust have the common local temperature.
Here, we do not describe the implementation of our codein detail but mention some points about the treatment ofradiation transfer. For the MHD and self-gravity parts, see
Machida et al. (2005a, 2005b). Our method for updatingradiation andgasenergysimilarthe
ZEUS-MP
code
Fig. 9.—Bird’s-eyeview ofismodel
MR at theto
same
epoch
as Figs. 6c and 7c,but with different
scales 1.
of 2:8AU (left) and 1:4 AUstructure(right). Theof
structureof thehigh-and outflow in level
FigureThree-dimensional
the first
core
and magnetic
field lines (black
are plotted in each panel. The structures of the high-velocity flow
region( ! > 0:1!
c ; red isodensity(Hayes (vdensity
et> al.
2006),
althoughthesurface)detailedtreatmentof andthewhite streamlines)
L = 10.
The left and bottom panels are density profiles and the right panel
7 km s#1 ) and low-velocity flow (v > 0:5 km s#1 ) are shown by purple and blue isovelocity surfaces, respectively. The density contours ( false color and contour
shows projected
the temperature
The cyan surface is a density isosurface.
MHD andparts(thinis arrows)
different
from theirs.
lines)radiationand velocity vectors
on the midplaneof x ¼ 0, y While¼ 0, and zour
¼ 0 are, respectively,in each walldistribution.
surface.
The fast outflowing region (vz > 0.3 km s−1 ) is also visualized with volume
MHD and self-gravity parts are advanced explicitly with a

Machida et al. 2008

Tomida et al. 2010

rendering. Red and yellow lines are the magnetic field lines.

原始惑星系円盤の形成・進化
分子雲コアのガスは一般に角運動量を持つ(Goodman et al.1993 Caselli et al. 2002)!

重力崩壊したガスは遠心力半径(重力＝遠心力)で円盤に降着
PTEP 2012, 01A307
分子雲コアのガスのほとんどは直接星に落ちず円盤を通して星に降着
outflow (low velocity)from second coreore
first caccretionaccretion

ro

ta

tio
n

circumstellar disk

tion

a
rot

内側のガスは角運動量を失う→星に降着
外側のガスは角運動量を得て広がる

from

円盤は角運動量輸送により拡散

jet (high velocity)

first core
protostar(second core)

Inutuka 2012

Fig. 5. Schematic picture proposed by Machida et al. [32] for the jet and outflow driven fro
the first core, respectively. Note that this is not to scale.

%&%&1/2 *

+
∆r/r
r
α 1/2
円盤中の角運動量輸送：重力不安定性
0M⊕
(123)
Toomre’s
0.1Q parameter
100 [AU]
10−4
cs:音速

4 Q UA S I - S T E A DY S T RU C T U R E S O FS E L F - G R AV I TAT I N G D I S C S W I T H R A D I AT I
TRANSFER
4.1 Simulation results

4.1.1 Overview of disc evolution

回転、圧力による安定化
tstop Ω
∼1

Ω:回転角速度
(124)

cs Ω
Q=
=が小さいほど不安定
3πGΣ
自己重力による不安定化

Σ:面密度

(125)

(Tsukamoto Takahashi et al. 2015)

6

若い円盤はΣが大きく不安定
Q>2：安定1<Q＜2：渦状腕形成→非軸対称な重力による角運動量輸送

Q<1：分裂We calculated the early evolution of the disc until about 10 0
after the formation of the protostar. Fig. 1 shows the evoluti
surface density at the centre of the cloud core for model 1 in Ta
In Figs 1(a) to (e), we can clearly see the bimodal structure, i.
central pressure-supported core (the first core) and the disc arit. The figure indicates that, before the second collapse, theforms around the central first core, and spiral arms develop. T
features are commonly seen in unmagnetized or weakly magne
molecular cloud cores (Bate 1998, 2011; Tsukamoto & Ma
2011; Machida, Inutsuka & Matsumoto 2010, 2011; Tsukam円盤中の角運動量輸送：MRI
磁気回転不安定性 (MRI) (Bulbus and Hawley 1991)
磁気張力で引き合う
前に引かれて角運動量を得る
より離れる

不安定化

磁力線
最終的に乱流状態

乱流粘性による角運動量輸送
非理想磁気流体力学の効果を考慮すると安定化される可能性(cf. Bai Stone 2013, Gressel et al 2015)(Sano et al. 2004)

円盤中の角運動量輸送：磁気制動
円盤が磁場を巻き込む 角運動量を上空に輸送

回転と逆向きの磁気張力

上空のガス：降着中の分子雲コア or 磁気駆動円盤風のガス
初期の円盤形成過程

円盤形成後の進化過程

若い円盤の半径、質量

MRIが安定化された場合を決めるの角運動量輸送として有望

cf. Li et al. 2011
Machida et al. 2011

cf. Suzuki et al. 2010
Bai 2013

円盤中のダストの運動
円盤中のダスト役割＊惑星形成の材料＊近年の詳細な観測の放射源（ダスト熱輻射）HL TauALMA partnership et al. 2015

ダストの運動はガスとの摩擦が重要

F IG . 2.— Panels (a), (b), and (c) show 2.9, 1.3, and 0.87 mm ALMA continuum ima
other panels, as well as an inset with an enlarged view of the inner 300 mas centered(f) show the image and spectral index maps resulting from the combination of the 1.3α/αerror < 4. The synthesized beams are shown in the lower left of each panel, also
corresponds to −2×rms to 0.9× the image peak, using the values in Table 1. The colorms and image peak corresponding to each respective wavelength in Table 1.

小さなダストは摩擦によりガスと共に運動
reconcile with a simple disk/outflow scenario, suggesting thatblue-shifted outflow has broken out of the parental core
大きくなるとガスとは別に運動the(Monin et al. 1996), or that there is another – as yet unidenti12

fied – driving source. Unfortunately, the CO (1-0) data are
missing significant flux (due to a lack of short spacings), andhave insufficient sensitivity in the outer portions of the fieldof view to warrant deeper analysis of its properties. Figs. 1b,andYoudinc show zoomed
in views of our serendipitous detections of
Chiang and2010)
XZ Tau (A and B), and LkHα358; no other continuum sources
above the local 4σ level were detected.

円盤乱流 ダストの衝突合体・破壊(cf. Takeuchi and Lin 2005,

ダストの中心星落下(cf. Nakagawa et al. 1986)

等、惑星形成に影響大3.1. HL Tau

T
im
tio
ten
(co
AL
abs
by
04
ph
ap

円盤中のダストの落下問題
ガスとダストの回転速度は異なる
ダスト : (重力) = (遠心力)
ガス : (重力) = (遠心力) + (圧力)

ガス

回転速度
遠心力

重力

圧力

vrot,gas < vrot,dust
ダストは向かい風を受ける→角運動量を失い内側へ落下

ダスト
回転速度

重力

遠心力

ダストの落下は惑星形成の課題
円盤の圧力構造（温度・密度構造）の理解が不可欠原始惑星系円盤の形成・進化過程
分子雲コアが重力崩壊
降着率〜cs3/G~10-6Msun/yr

中心に星、円盤が形成
磁気制動・自己重力不安定性
で角運動量輸送分子雲コアの全てのガスが降着
MRI or 円盤風の磁気制動で進化
円盤中のダスト進化→惑星形成

Outline• イントロ 原始惑星系円盤の形成・進化の概要!

• 円盤形成・進化の物理過程!

• 現在の課題 円盤の詳細構造形成の理解!

• 将来の展望、まとめ円盤進化理論の課題：詳細構造形成
すばる望遠鏡・ALMA等の活躍により多様な円盤構造が発見
Muto et al.

渦状腕

三日月型

M. Fukagawa et al.

HD 135344B∆ Dec. (2000) [arcsec]

20.9-mm continuum

1.3

HD 142527

1.2

HL Tau

1.1
1

1
0.9

0

0.8

リング

log (Tb) [K]m and minimum baselines were 380 mly, and the latter corresponded to thef the detectable component of 10′′ . The
in this letter consisted of four scheduleriod from June to August 2012. The
ured to store dual polarizations in fourows with 469 MHz of bandwidth andoviding a channel spacing of 0.122 MHze that the effective spectral resolution
f around 2 (∼0.2 km s−1 ) because of
The central frequencies for these win9.331, 342.883, and 342.400 GHz, rebservations of molecular lines of 13 CO
3–2, and CS J = 7–6. The results ofill be Muto
reported etelsewhere.
The quasars
al. 2012
2 were targeted as bandpass calibrators,
and phase were monitored through obr J1427-4206. The absolute flux density
observations of Titan and Neptune.
rated and analyzed using the Common
Applications (CASA) package, version
errant data and applying calibrations ford flux scaling, the corrected visibilities
onvolved using the CLEAN algorithmwith a robust parameter of 0.5. In adsensitivity and image fidelity, the selfmed for the continuum for which the distected with a very high signal-to-noise
ration began with the CLEAN-ed imel of the source brightness distribution.

[Vol. ,

0.7

−1

0.6
−2

140 AU

0.5
0.4

2

1
0
−1
∆ R.A. (2000) [arcsec]−2

ALMA partnership et al. 2015

Fig. 1. DustFukagawa
continuum map atet
336al.
GHz2013(890 µm)
thePanels
disk ofF IG .for2.—(a), (b), and (c) show 2.9, 1.3, and 0.87 mm ALMA continuum images of H
HD 142527. The color-scale shows the brightness
in a as an inset with an enlarged view of the inner 300 mas centered on the pothertemperaturepanels, as welllogarithmic scale. The black contours denote T(f)5, 10,the15image
and 20and spectral index maps resulting from the combination of the 1.3 and 0.8
b =show
K while the white one does the 5σ level. The size
the <synthesized
α/αoferror
4. The synthesized beams are shown in the lower left of each panel, also see Tabcorresponds
to −2×rms
beam is shown at the left corner of the image with a white ellipseof to 0.9× the image peak, using the values in Table 1. The colorscales f′′′′◦
rms and PA
image
peak. corresponding to each respective wavelength in Table 1.
0. 39 × 0. 34 (= 55 AU × 48 AU) with the major-axis
of 57

これまでの基本的な円盤進化の理解では、
reconcile with a simple disk/outflow scenario, suggesting that2013). The northern region is brighter thansouthwestern
the theblue-shifted
outflow has broken out of the parental core
観測される多様な円盤構造を説明できない(SW) area, with an emission peak of 213(MoninmJy beamat the or that there is another – as yet unidentiet al. 1996),
′′

−1

12

projected distance of 1. 0 (140 AU) from fied
the star,and atsource.
a PA Unfortunately, the CO (1-0) data are– driving◦of 30 . When probed along the annular emission
ridge, bothflux (due to a lack of short spacings), andmissing significant
have insufficientsensitivity in the outer portions of the fieldends of the horseshoe appear to be connected
at the bright−1′′ of view to warrant deeper analysis of its properties. Figs. 1b,
ness minimum of 7 mJy beam at 1. 3 (180 AU) and PA =and c show
220◦ . The contrast in flux density thus reaches
to 30 zoomed
betweenin views of our serendipitous detections of

円盤進化の理解を進める（改める）必要がある

The fitimages itions aretent betw(consisten
ALMA pps/Rings
Resolved
with
ALMA
aps/Rings Resolved with ALMA

d visibility amplitudes in Figure
ge is 36 µJy/beam. All analyhe un-averaged two dimensional

Our 3 mm map of WL 17, shown in Figure 1, showsa well detected, compact source with a hole measuring⇠ 0.200 in diameter in the center. At the distance ofOphiuchus, which we assume to be 137 pc, the hole is(Akiyama et al. 2015; Rapson

原始惑星系円盤のリング構造の観測

on (Akiyama et al. 2015;
TW RapsonHya
2013,
from the2016).
Literature
WL 17
TW Hyaal.
2013,2016).
sent
andanalyzeobservations
shp+2015]
and spectral energy distribution[Andrews+2016]
present
andanalyzeershp+2015]
a thoroughWehesubstructurein theobservationsTW
Hya[Andrews+2016]
HLliterature
Tau search.
nsubstructure
in
theto
TW
Hya
e the
2. baselinesThe
data includes
Spitzerongof ALMA
meametry
as baselines
well as fluxes
the to meae long
offromALMAumemissionfrom
thiswavelengths (Wilking & Lada disk atinuum emission from this disk at
984;
Greene & Youngresolutionof ⇠11992;
AU.AnSection 2
tial
resolution
of
⇠1
AU.
Section 2
Stromet al. 1995;
Barsony et al.
ns,Section3 describes
a broad00;
AllenSection
et al. 2002;
et al. a broadtions,
3 Natta
describes
tinuumdata,
andSectionAlves de Oliveira& Casali
2008; 4 conontinuum
data,
and Section
4 conadgett
al. the2008;results
Wilking etationset ofinal.the conretations
ofal.theresultsin the conGutermuthet2009;
Barsonynd planet formation.
ne WISEand planet
formation.
photometry
because the
PRL 117, 251101 (2016)

M*
HL Tauを始めとするM*
数天体でリング構造が
観測

H
Y
S
II C
A
L
RE
EV
VringsI EEandW gapsLEinETthe
TTTprotoplanet
ERRSS
D.PPFedele
et
al.:
ALMA
unveils
H
Y
S
C
A
L
R
I
W
L
E
D. Fedele et al.: ALMA unveils rings and gaps in the protoplanetar

tt**

＜1Myr

PRL 117, 251101 (2016)
with the IRAC and MIPS fluxes.
AND
DATA
CALIBRATION
ALMA
partnershipet al. 2015
Sheehan et al. 2017ESbeamis larger
than
the Spitzer
AND
DATA
CALIBRATION
confusion
with nearby
sources.Novemd
by
ALMA
on
2015
rved
by ALMA
onalso2015
flux
measurements
werein- NovemFigure 1. ALMA 3 mm map of WL 17 showing a clear ring(c)
show
2.9,
1.3,
and
0.87
mm
ALMA
continuum
images of HL Tau. Panel (d) shows the 1.3 mm psf forthe same FOV as thendDecember
1.
The
array
inTW
Hya
likeinstructure.
The163296
synthesized beam size is 0.06” by 0.05” HD 169142
HDd,t withbytwodi↵erentgroupsusing
andDecember
1.
The
array
an enlarged view of the inner 300 mas
centeredon
the psf’s
peak (theotheratbands
show
similar patterns). Panels (e) and
with
a
P.A.
of
81.9
.
Contours
begin
4
and
subsequentns
et al.maps
2009;
Gutermuth
etconfigured
al.configured
tennas,respectively,l antennas,
index
resultingfrom thecombinationof the are
1.3 and0.87
mm data.2 The
spectral(α) map
respectively,
contours
every
additional, with1 =index
36 µJy.
The has been masked whereare shown in
the
lower
left of eachemission
panel, also
see to
Table
The
range
thetocolorbar
shown
sebeams
measurements
tobereliable.
interior
the 1.
ring
does
not ofdrop
zero, butratherfor panel (b), at 1.3 mm,
from
20
m
to
14
km.
The
correhs
from
20
m
to
14
km.
The
corre×theSL,
image
the values in Tablefalls
1. The(a), (c)and ring.
(e) areexcept using the values of
to a colorscales
4 level at forthe panels
inner edgeof theAtthethesamecentertheSH,peak,
andusing
LH calibrated
ding
towindows
eachwindows
respective
wavelength
inat
Table
1.the ring the
Figure1.1risesimage
theemissiontral
centered
at344.5,
ofemission
tosynthesizeda 6 level. This
mayof
indicate
Figure.AAsynthesized
imageof
the 870
870µmµm continuum
continuum emission
pectralcentered
344.5,
om theCASSIS databasein our
from
the
disk
with
mas
circularthe presenceofmaterial
remaining
the cleared
region.
from
theTW
TWHya
Hyain
disk
with aouta 30
30
mas FWHM
FWHM (1.6(1.6 AU)AU) circular
2011,2015).
Webandwidths
find that weof ofGHzwithbandwidths
1875,
.1
GHz
with
1875,
1
beam.
level
isis⇠35
beam
inset showsshowsbeam.The
TheRMS
RMSnoisenoiseleveland⇠35µJyµJybeam 1. The inset
3.1.1.
Position
ProperMotionisk/outflow scenario, suggesting that
00
00
Hz,
a a0.20.2-wide
resolutionMHz,
respectively.
Theobservaobserva-wide(10.8(10.8AU)AU)zoomzoomusingusing anan image
image with
with finer resolution
has respectively.
brokenout of theTheparental
core
(24
⇥⇥
1818
mas,
(24
mas,oror1.3
1.3⇥⇥1.0
1.0AU,
AU,FWHM
FWHM beam).
beam).
targetJ1103-3251
withthetargetandJ1103-3251
witha a
hat
there
isand
another– as yet unidenti-

Maps of 190GHz Continuum and Spectral index~10Myr

The fitted position for HL Tau in each of the ALMA
nfortunately,theCO(1-0) datawereareional visits
to toJ1107-3043
dditional
visitsJ1107-3043
were images is given in Table 1. The phase calibrator posidue
toa lack of shortspacings), andareaccurate
toThe< combined
1combinedmas and thepositionsintegration
are consis- time
0.5–1
mm. Theon-target
ofof0.5–1mm.
on-targettime
es.
J1037-2934,
J1058+0133,
and tions
J1037-2934,
J1058+0133,
andity in the outer portions of the field
tentwasbetweenthe three The
observedbands
to better than 2 describedmas95
minutes.
basic
calibration
was95
minutes.
The
basic
calibration
wasasdescribed
yobservedascalibrators.
The
preas
calibrators.
The
predbserved
continuum
imagesofofHL
HLTau.
Tau.
Panel(d)showsshows
the 1.3
1.3 mmmm
psf for the
87
mmmm
ALMA
continuum
Panel
(d)
the
same FOV
FOV asasthe
ther 0.87analysisof ALMA
its properties.
Figs.images
1b,(consistentwithdedicated
LBC astrometry
experiments,
see same
100au
50au
above.
Asa(thea(thecheck,
wecomparedthe
100au
50au(e)above.
As
check,
wecomparedtheamplitudes
from
(PWV)
levels
were
⇠1.0
mmof
ononthe
w
of
the
inner
300
mas
centered
the
psf’s
peak
other
bands
show
similarpatterns).
PanelsPWV)levels
were
⇠1.0
mm
onon
ws
of ourserendipitous
detections
partnership
etotheral.
2015);
thus,show
we assume
2 mas
as the from
of
the
inner
300
mas
centered
psf’s
peak
bands
similarpatterns).
Panels(e) andand30
au ALMA
each
individual
dataseton overlapping
overlapping
spatialnoothercontinuum
sourcesabsolute
ALMA
position
uncertainty.
The(α)
position
reported
gkHα358;
fromthe
combinationof
the1.31.3and
and
0.87
mm
data.
The
spectral
index
(α)
map
has frequenbeen
mm
on
the
lattertwo
each
individual
datasetonfrequenom
combination
ofexecutions.
the
0.87
mm
data.
The
spectralindex
been masked
masked where
where
m
onthe
the
lattertwo
executions.
weredetected.
Kwon
etThe
al.
(2011)
from
1.3
CARMA
observationsis (b),
Fedele+2017
ciesandandfound
exceptional
consistency.
the
lower
left
each
panel,also
alsosee
seeby
Table
1.
The
range
themm
colorbarshown
for panel
Tsukagoshi+2016
tegration
was⇠2
hours.
Isella
+2016
cies
found
exceptional
consistency.
lower
lefttimeof of
each
panel,
Table
1.
range
ofofthecolorbar
shown
for
panel
(b), at
at 1.3
1.3 mm,mm,
12

alstructures?
structures?

thegaps/rings?
gaps/rings?
fof
theration time was ⇠2 hours.

h

m

s

◦

′

′′

惑星形成理論との関係
HL Tauギャップに惑星？
形成時間に制限（<1Myr）

リングにダスト濃集？
微惑星形成を促進

リング・ギャップ形成メカニズムの解明がc) show 2.9, 1.3, and 0.87 mm ALMA continuum images of HL Tau. Panel (d) shows the 1.3 mm psf f
惑星形成過程の理解のヒントになるwith an enlarged viewof the inner 300 mas centered on the psf’s peak (the other bands show similar pndex maps resulting from the combination of the 1.3 and 0.87 mm data. The spectral index (α) map hbeams are shown in the lower left of each panel, also see Table 1. The range of the colorbar shown fo

リング・ギャップ形成メカニズム
多重リング
惑星 (cf. Kanagawa et al. 2015, 2016, Dong et al. 2015, 2017, Jin et al. 2016)
ダスト進化 (成長:Zhang et al. 2015 Sintering:Okuzumi et al. 2015)
永年重力不安定性 (cf. Takahahsi inutsuka 2014, 2016)
ダスト沈殿に伴う不安定性 (Loren-Aguilar & Bate 2015)
MRI (dead zone, zonal ﬂow)(cf. Uribe et al. 2011, Flock et al. 2014)
単一リング
円盤散逸（Photoevaporation, 円盤風）
ダスト成長（内側で早い成長）リング・ギャップ形成メカニズム
多重リング
惑星 (cf. Kanagawa et al. 2015, 2016, Dong et al. 2015, 2017, Jin et al. 2016)
ダスト進化 (成長:Zhang et al. 2015 Sintering:Okuzumi et al. 2015)
永年重力不安定性 (cf. Takahahsi inutsuka 2014, 2016)
ダスト沈殿に伴う不安定性 (Loren-Aguilar & Bate 2015)
MRI (dead zone, zonal ﬂow)(cf. Uribe et al. 2011, Flock et al. 2014)
単一リング
円盤散逸（Photoevaporation, 円盤風）
ダスト成長（内側で早い成長）

惑星によるギャップ構造形成
The Astrophysical Journal Letters, 806:L15 (6pp), 2015 Jun

惑星と円盤ガスとの重力相互作用でギャップを形成& Sunyaev 1973), we write O  Bh 2R 28, where h 
惑星がガスに与えるトルク
denotes the disk aspectratio and c is the sound spee
(Lin and Papaloizou 1979)(δvare)r,vθ2
dependent on the disk temperature.
Because of a strong
gravitational
exerted by
惑星重力δvtorqueron the disk, a gap opens along the planet–orbit. We a
運動エネルギー保存
sufﬁciently wide gap so that the torque is exerted main22
2
a ﬂat gap bottom withvθ2a constant+ δvr = surfacevθ1 density 4
using the WKB torque formula with a cutoff, the o
回転速度の減少 vθ2 < vθ1
Lindblad torque, TLB, which is exerted by the plane
outer disk, is approximately
given by (see Lin &惑星周囲にギャップ形成
zou
1979,
and
K15)
ガス粒子
トルク
4
2
(0,vθ1)d
 Mp ¬ 3 2  R p ¬­
­

­­ dR
TLB 
­­ R p 8 p 4 p 
0.80Q  M ­®
­
Rp %

R
R

­®
p

*

∝

¨

(2)

Figure 3 shows ∆!gap against
the dimensionless parame
"
−3/7
r
′
[K]
(
K defined T
by= 150

ギャップの構造#"!
planet and the1
au$−3of the parameter K. The solid line denotes
Figure 1. Gap depth 2as a function−1
hpαcircles,p crosses,−1 triangles represent the gap depth′ (5). M
Equation
The
and
"
10
((
α
.
K
=
粘性との釣り合いで決定
notes
the values
obtained by hydrodynamic
done$ by Duffell$% & MacFadyen (2013),
M∗
Rsimulationsp #$ ∂Ω $ respectively. (Entire runs ofFung et al. (2014), and Varnière
et al.2(2004),∂
he torque cutoff
$ $
∝
−
Σνr
(g
are
shown
in
these
papers.)K , 8000
粘性による正味のトルク
and
there
are
also
recoded
in
Table
1.
It
is
clear
that
the
$
$
torque with the∂r∂rwidth is well scaled by the parameter K ′ . We find an empiric
anet interaction
4 . If K is appreciably
Equation
(5)
would
be
valid
for
K
1
10
2002;
Muto &
密度勾配負
角運動量増加ギャップを埋める
formula for the gap
width aslarge, the gap becomes eccentric and non-steady, which breaks
t the planetary
#
$
−3/4
!
"
1/2 (Kley &down
oursimpleestimate
Dirksen 2006). In the
Mp
hp
∆gap
validΣ
when the
−1/4
′1/4
=
0.41
α
=
0.41K
. (
eccentric
state,
thegapisshallowerthanthepredictionbyh.
Rp (5) (FungM
Rp∗
Equationetal.
2014).
2 the 1.4
andangular 1.6
As
seen
in
Equation(5),
itisrelatedtotheplanet
mass,
the
As
seen
from
Equation
(4),
the
gap
width
depends
weaklanetary torque.
viscosity,
andtheaspectratio.
Solving
Equation(5)
forside of the gap,ontheplanetmass
andtheviscosity,which
isconsistentw,
weobtainMMp*omentum ﬂux atrprevious studies (Varnière et al. 2004;
Duffell & MacFady
12
eraged surface density
52
12
¬


¬
M
h

¬
2013)
. We also
find
that
the
disk
aspectratio
affects the g
p
p
B
1
­

4

­

­
­­ 

presented in Figure 1.



q
5
10
1
. (7)
­
­
−3/4
­

(3)
­

3
­­®  0.1
深さ® ∗ , we obtain4 p 40 Equation
M* as hp
width
. Solving(4)­®forM
10p /M#$2 #$3/2 !
"
the unperturbed
1/2
∆
h
α
M
gap
Figurep 2 displays themass given pby Equation (7) as a
−3 planet= 2.1 × 10
. (n Rp though 幅
the−3function
the disk
aspect10ratio forM∗ of the gap depth R
4p 40 and0.05R
p
en,(Kanagawa
we can set
et al. 15,several
16) cases of α. The dependence of the planet mass on hp isThis equation allows us to estimate the planet mass from the oandthereforeTable 2. Measured gap properties and estimated planet

観測との比較
masses.
10AU gap
30AU gap
80AU gap

Rin

Rout

(AU)
7
28.5
70

(AU)
16.5
36
94

∆gap
Rp

0.81
0.23
0.29

hp
Rp

Mp (MJ )

0.05
0.07
0.1

(from the width)
1.4
0.2
0.5

We set α = 10−3 , β = 1.5 and M∗ = 1M⊙ at the evaluation in thistable.

惑星の観測/惑星最大質量の制限からモデルを検証可能

10
Dong, Li, Chiang, & Li
similar. That is, it is assumed that
dust particles are reasonably
 




どうやって惑星を形成？
coupled to the disk gas and thus the dust filtration 0is 2weak.
4
6 If8
0
0.02 0.04 0.06 0.08
全てのギャップを惑星で説明？
thedust filtration is strong, the dust surface density is enhanced
40
at the outer edge of the gap by orders of magnitude
and
sig20
一つの惑星で複数のリングを
nificantly
reduced at the inner part of the disk (e.g.,Zhu
et al.
0
2012;
Dong et al. 2015; Picogna & Kley 2015).
In the case-20
説明可能かもしれないof relatively weak filtration, on the other hand, -40the gap widths 

(Dong
et
al.
2017)
-40 Zhu-20 0et 20of the dust disk is not altered much (see Figure 3 ofal. 40 -40 -20 0 20 40  
2012). Because no significant pile–up of dust is found at the  





 



リング・ギャップ形成メカニズム
多重リング
惑星 (cf. Kanagawa et al. 2015, 2016, Dong et al. 2015, 2017, Jin et al. 2016)
ダスト進化 (成長:Zhang et al. 2015 Sintering:Okuzumi et al. 2015)
永年重力不安定性 (cf. Takahahsi inutsuka 2014, 2016)
ダスト沈殿に伴う不安定性 (Loren-Aguilar & Bate 2015)
MRI (dead zone, zonal ﬂow)(cf. Uribe et al. 2011, Flock et al. 2014)
単一リング
円盤散逸（Photoevaporation, 円盤風）
ダスト成長（内側で早い成長）

ダスト進化によるリング・ギャップ形成
観測で見えているのはダストの熱放射
ガスが滑らかな分布でも、ダスト放射に構造があれば良い
ダストの焼結による構造形成（Okuzumi et al. 2015）
円盤温度 各分子の昇華温度で焼結が起こる
モノマーの結合部部が太くなる
衝突時にエネルギーを逃がしにくくなり、壊れやすくなる

Pino et al. 2014

ダスト焼結によるリング構造形成
Sintering-induced Multiple Ring Formation in Protoplanetary Disks

Formation in Protoplanetary Disks

T

昇華温度でダスト破壊
落下速度減少面密度上昇
11 リング構造
焼結する分子の種類で多重リング構造を形成!

温度構造によってリングの位置・幅が決定

観測との比較

Figure 18. Same as the right panels of Figure 11 but for runs Sa0-tuned (left panels) and La0-tuned (right panels

ｔ〜0.26Myr で観測を再現するようなリング構造が形成
その後、ダスト落下と共にリング構造も消える
Figure 18. Same as the right panels of Figure 11 but for runs Sa0-tuned (left panels) and La0-tuned (right panels)
リング構造は若い円盤の特徴

リング・ギャップ形成メカニズム
多重リング
惑星 (cf. Kanagawa et al. 2015, 2016, Dong et al. 2015, 2017, Jin et al. 2016)
ダスト進化 (成長:Zhang et al. 2015 Sintering:Okuzumi et al. 2015)
永年重力不安定性 (cf. Takahahsi inutsuka 2014, 2016)
ダスト沈殿に伴う不安定性 (Loren-Aguilar & Bate 2015)
MRI (dead zone, zonal ﬂow)(cf. Uribe et al. 2011, Flock et al. 2014)
単一リング
円盤散逸（Photoevaporation, 円盤風）
ダスト成長（内側で早い成長）

Secular GIのメカニズム

0色の濃淡：ダスト面密度

Secular GIのメカニズム
速度
重力

コリオリ力

0

色の濃淡：ダスト面密度
長波長の揺らぎはコリオリ力で安定化される。

Secular GIのメカニズム
速度
重力

x

x コリオリ力0

色の濃淡：ダスト面密度
長波長の揺らぎはコリオリ力で安定化される。
ガス・ダスト摩擦でダストの速度揺らぎが減少
長波長の揺らぎが不安定化→Secular GIが成長

永年重力不安定性によるリング形成
Takahashi and Inutsuka 2014
永年重力不安定性(Secular GI)
ダスト­ガスの摩擦が引き起こす重力不安定性
成長時間が長い リングとして観測可能
半径100AUに13AU間隔のリング構造が形成「ダスト 多 」と「乱流 弱 」が必要
リング構造がダスト/ガス>0.01と弱い乱流（α 10-3）を表す指標になる
Secular GI によるリング構造形成シナリオと整合的
実際にHL TauはSecular GI に対して不安定か？

ERRATUM: “AN ORIGIN OF MULTIPLE RING STRUCTURE AND HIDDEN PLANETS IN HL TAU: A
UNIFIED PICTURE BY SECULAR GRAVITATIONAL INSTABILITY” (2016, APJ, 152, 184)

HL Tau でのSecular GI

Sanemichi Z. Takahashi1 , Shu-ichiro Inutsuka2

100au での分散関係

「ダスト
多
」と「乱流
弱
」が
n our paper (Takahashi & Inutsuka 2016), there areographical errors in Equation (13) and (17). The cor観測から示唆
t equations
are

d

"
(Kwon et2πG
al. !2015,
Pinte
et
δΣ
δΣd al. 2015)δΦ = −|k|

1 + kH

+

1 + kHd,(1)

Secular GI が不安定

+ (5/4)(tstop Ω)3 2
αcs ,
2
2
[1 + (tstop Ω) ]1 + 2(tstop Ω)
c2d =

2

(2)

最大成長波長11AU
成長のタイムスケール9x10 年≈ 観測されたリング間隔
HL Tau の年齢

Wavelength [AU]Fig. 1.— Same as Figure 1 in the original paper but α = 2×1
pectively. Since we used the correct equations in ourculations, these typographical errors do not change
dispersion relation in our original paper.
4
3
Apart from the above typographical errors, we used10
incorrect equation for the dust diﬀusion by the turence to calculate the dispersion relations. We undermated (overestimated) the diﬀusion of dust particles
102
h small (large) Stoke number. The secular GI is stabid when we use the corrected equation with the expontial cutoﬀ surface density model with the parameters
1
10
en in the original paper. Thus, we show the alternae results whose strength of the turbulence α are 2/3
es smaller than that used in the original paper. The
Tominaga, 0Takahashi, Inutsuka 2017
10 1
ucial value of α in the original paper is observationally2
10
10
gested by Pinte et al. (2016). Since this alpha value

不安定モードの成長でリング構造形成を説明可能

リングにダストが濃集→その後の惑星形成につながる可能性
大局的非線形計算が必要

モデルの比較
ガス構造
温度分布
ダストサイズ惑星

焼結

Secular GI

有

無

ほぼ無

ギャップ構造 リング位置/幅

安定条件

リングで大

リングで大

リングで小
温度分布

リング間隔

惑星の軌道

年齢との関係

若いと困難

古いと困難

古いと困難

惑星形成

結果

ー

原因

分子種

モデルの検証/複数天体を説明可能か？

不安定波長

リング・ギャップ形成メカニズム
多重リング
惑星 (cf. Kanagawa et al. 2015, 2016, Dong et al. 2015, 2017, Jin et al. 2016)
ダスト進化 (成長:Zhang et al. 2015 Sintering:Okuzumi et al. 2015)
永年重力不安定性 (cf. Takahahsi inutsuka 2014, 2016)
ダスト沈殿に伴う不安定性 (Loren-Aguilar & Bate 2015)
MRI (dead zone, zonal ﬂow)(cf. Uribe et al. 2011, Flock et al. 2014)
単一リング
円盤散逸（Photoevaporation, 円盤風）
ダスト成長（内側で早い成長）3.1.2.
円盤円盤
3.1.2.
磁気駆動円盤風によるリング形成
4 4
内縁半径
11
au,au,
外側境界
10 10au.au.
角運動量輸送とし
内縁半径
外側境界
角運動量輸送磁気流体シミュレーション
上空
α
α粘性モデルを用いる。温度分布
粘性モデルを用いる。温度分布
円盤から上下方向にガスが流出! ! "−3/7"
Suzukiet al. 2010
−3/7
r r
T 磁気回転不安定性による乱流=
150
T = 1501 [au]円盤
1 [au]SUZUKI, MUTO, & INUTSUKA−4
磁場を曲げエネルギーを上空へ
α = exp[−Q ] + α

α = exp[−Q

−4

MRI

] + αMRI

円盤風による mass ガスの上下方向の速度に転換
loss
上空
円盤風による mass#loss# 0 (Minf < Mcl )0 (Minf < Mcl )Mass loss rateΣ̇wind =M-5cl-10) -3
CW >Σ̇wind = Cw ΣΩ (Minf~10

Cw ΣΩ (Minf > Mcl )CWここで一定なら円盤内側ほど効率的
Mcl は分子雲コアから降着した総質量。ダス

ここでStM
運動は固定で計算。
cl は分子雲コアから降着した総質量。

円盤風で内側に穴をあけるとリング構造が説明できるか？
運動は St 固定で計算。

観測との比較
原始惑星系円盤の形成・進化モデルで円盤風の強さ等をパラメータとして多数のモデル計算(Takahashi and Muto submitted)
ALMAによる観測

WL 17

モデルの模擬観測

計算結果を使って模擬観測
ダスト放射の輝度分布
コントアは同じ輝度に対応(Sheehan and Eisner 2017)

磁気駆動円盤風によるリング構造形成シナリオでWL 17 の観測結果を整合的に説明可能

その他の構造：三日月型構造
非軸対称にダストが集中した構造も発見[Vol. ,

wa et al.

0.9-mm continuum

1.3
1.2

(Fukagawa et al. 2013)

1.1
1

1
0.9

0

0.8

log (Tb) [K]∆ Dec. (2000) [arcsec]

2

HD 142527

0.7−1

Oph IRS 48

0.6−2

定性 [RWI]
2

1
0−1∆ R.A. (2000) [arcsec]

140 AU

0.5(van der Maler et al. 2013)

0.4−2

るシアー不安定性
Fig. 1. Dust continuum map at 336 GHz (890 µm) for the disk of
強い変化がある時、不安定
HD 142527. The color-scale shows the brightness temperature in a

ロスビー波不安定性で説明可能か？

logarithmic scale. The black contours denote Tb = 5, 10, 15 and 20
K while 軸対称密度バンプ
the white one does the 5σ level.
The size@r=1
of the synthesized
800回転
beam is shown at the left corner of the image with a white ellipse of0.′′ 39 × 0.′′ 34 (= 55 AU × 48 AU) with the major-axis PA of 57◦ .

二次元計算、高密度の渦が形成

2013). The northern region is brighter than the southwesternSW) area, with an emission peak of 213 mJy beam−1 at the
projected distance of 1.′′ 0 (140 AU) from the star, and at a PAof 30◦ . When probed along the annular emission ridge, both
成ends of the horseshoe appear to be connected at the brightness minimum of 7 mJy beam−1 at 1.′′ 3 (180 AU) and PA =220◦ . The contrast in flux density thus reaches to 30 between
he northern peak and the SW minimum. The peak flux density
s expressed by a brightness temperature (Tb ) of 24 K withり
out the Rayleigh-Jeans approximation. This Tb is much higher
han those beyond 100 AU in other disks. Unless the emitting
grains are significantly warmer than 24 K, the region should be
optically thick to the submillimeter radiation due to the highcolumn density.

渦にダストを集められると観測を説明
惑星形成にもつながる

小野さんのスライドより

その他の構造：渦状腕構造
惑星か重力不安定か？
惑星が円盤に立てた波による腕構造 Muto et al. 2012
惑星の位置を仮定
惑星が作る波の形状
HD 135344B

reen points indicate the locations of the maxima of radial profiles for S1 (top) and S2 (bottom). The green ones are used for the fitting byDashed lines indicate circles with r = 0.′′ 39 (top) and r = 0.′′ 3 (bottom). Right: the spiral shape given by Equation (1) with the best-fit
d S2 (bottom). Crosses show the locations of (rc , θ0 ).

重力不安定による腕構造と観測の比較 Tomida et al. 2017

1 (8pp), 2017 January 20

5シミュレーション

Tomida et al.
観測(Perez et al 2016)

Elias 2-27

回転対称な2本の腕構造は重力不安定性で説明しやすいOutline• イントロ 原始惑星系円盤の形成・進化の概要!

• 円盤形成・進化の物理過程!

• 現在の課題 円盤の詳細構造形成の理解!

• 将来の展望、まとめ今後の展望１：観測との関係
ALMAによる詳細な円盤観測が続く
新たな構造の発見、統計的な特徴
観測が理論をリードする時代が続く✦新しい観測を説明する円盤構造形成モデル✦構造形成の統計的特徴の研究✦乱立する理論モデルの淘汰（だと良いな。。。）

円盤観測を惑星形成シナリオの解明につなげる✦ダストの光学特性の理解✦構造形成から惑星形成への応用（ダスト進化計算の組込）

観測的にもガス分布の理解は今後の課題✦化学進化計算により、line観測から重要な情報を引き出す

今後の展望2：星形成理論との関係
星・円盤形成過程は主にシミュレーションで研究が進展
3次元で磁場、輻射が実装されている。
No. 1, 2010

L59
Tomida et al. 2010

RMHD SIMULATION OF PROTO-STELLAR COLLAPSE

2. METHOD AND MODEL

We solve three-dimensional self-gravitational RMHD equations on nested-grids. Equations and quantities for the radiation
are defined in the comoving frame of the fluid. We treat only
the zeroth-order moment equations of radiation transfer using
the gray (i.e., equations are integrated over frequency assuming a blackbody spectrum of the local temperature) FLD approximation proposed by Levermore & Pomraning (1981) with
Levermore (1984) closure relations. We assume ideal MHD withno resistivity. The equation of state (EOS) of the gas is also assumed to be ideal, where the gas mainly consists of hydrogenmolecules and the adiabatic index γ is set to 7/5 throughout thesimulation, which is better to trace the realistic thermal evolution than γ = 5/3 (Stamatellos & Whitworth 2009). We assume
that the gas and the dust have the common local temperature.
Here, we do not describe the implementation of our codein detail but mention some points about the treatment ofradiation transfer. For the MHD and self-gravity parts, see
Machida et al. (2005a, 2005b). Our method for updating
André et al.: The Herschel Go
radiation and gas energy is similar to the ZEUS-MP code
Figure 1. Three-dimensional structure of the first core and outflow in level(Hayes et al. 2006), although the detailed treatment of the
L = 10. The left and bottom panels are density profiles and the right panel
shows the temperature distribution. The cyan surface is a density isosurface.
MHD and radiation parts is different from theirs. While our
The fast outflowing region (vz > 0.3 km s−1 ) is also visualized with volume
MHD and self-gravity parts are advanced explicitly with arendering. Red and yellow lines are the magnetic field lines.
second-order scheme, the radiation part is advanced implicitlywith the first-order backward Euler method for stable timesize of the finer grid is half of the coarser grid, and the finer grid
integration. Newton–Raphson iteration is used to solve theis placed around the center of the simulation box self-similarly.
resulting nonlinear equations. The sparse matrix appearing
The simulation starts with five levels of nested-grids, and finer
here is very large and not diagonally dominant because ofgrids are generated adaptively to resolve the local Jeans length
the strong nonlinearity of the system; hence, a fast and robustwith 32 meshes not to induce artificial fragmentation (Truelove
iterative solver is required. We use a stabilized biconjugate
et al. 1997). This is also because insufficient resolution causes
gradient solver with a multi-color modified incomplete LU
the gas entropy to be overestimated near the center of the core. At
decomposition preconditioner, which is stable and efficient.
the end of the simulation, 18 levels of nested-grids are generated
We determine the timestep by the Courant–Friedrich–Levy
and finest resolution is ∆x ∼ 0.009 AU. We stop the simulation(CFL) criterion derived for the MHD part. All the grids
when the gas temperature of the central region reaches 2000 K
have this common timestep and are advanced synchronously,
at which temperature hydrogen molecule starts to dissociate andalthough individual (asynchronous) timesteps are generally
the second collapse begins.
used in AMR simulations. In usual MHD simulations using
3. RESULTS
individual timesteps, boundary values in the finer level areconstructed by time-interpolation of the values in the coarser
3.1. Overview
level. However, if we use an implicit time-integrator and a farlarger timestep than that determined by the CFL condition for
Figure 1 is a typical bird’s-eye view of the first adiabatic core
radiation transfer (i.e., ∆t ≫ ∆tRT = ∆x/c, where c is the speed
and the outflow ∼500 yr after the first core formation. Therecoexist two components of outflow: well-collimated fast outflow
of light), then this time-interpolation is not adequate, at least in(associated with red magnetic field lines) and slow outflow
principle.
with a large opening angle (associated with yellow magnetic
We use a compiled table of opacity adopted from Ferguson
field lines). The former is driven by magnetic pressure andet al. (2005) and Semenov et al. (2003). We use Semenovthe latter by magneto-centrifugal force (Blandford & Payne
et al. (2003) for the Rosseland mean opacity, and we smoothly
1. Column1982).
densitymaps of(2002)
two subfields
in Aquila(left) andPolari
Tomisaka
showed thatthe magnetic
pressure
combine the two for the Planck mean; Ferguson et Fig.
al. (2005)
filaments
withtypicallyrespectappears
to the innon-filamentary
has b
mode
the case of weakbackgroundmagnetic fields,in high temperature (T ! 1000 K) and Semenov etof
al. the(2003)

新規参入で最先端の計算コードを作ることが困難に

Athena ++ など高性能な公開コードが存在

No. 1 よりOnly 1のシミュレーション、新たな発想が求められるよりsmall scale に行くか

（高分解能、惑星形成との関係）!

large scale に行くか

（分子雲コア、フィラメントとの関係）(Andre et al. 2010)

今後の展望3：惑星形成理論との関係
観測の情報をフル活用（展望１）
赤道面の乱流等これまで分からなかった物理量が定量的に分かるようになってきた (Pinte et al. 2015)

個別と全体
個別
✦惑星形成理論ではファクターの違いでも結果に大きく影響✦各素過程の詳細なシミュレーションは今後も必要（ダストの進化、MRIなど。。。）

全体✦増え続ける惑星系の観測結果✦惑星の多様性の起源を探る✦円盤の多様性との関係

まとめ•

原始惑星系円盤は原始星の周囲に形成•ガスは円盤を通して星に降着し、惑星は円盤中で形成されるため、星・惑星形成の理解のために重要•

分子雲コアの重力崩壊によって形成され、重力不安定性
やMRIなどの角運動量輸送により進化していく•

近年円盤に多様な構造が観測されている。リング構造形
成に関して、惑星や焼結、永年重力不安定性など複数の理論モデルが提唱されるが起源は未だに解明されていない。

•

今後も詳細な観測・統計的観測が進むため、観測にリードされる形で円盤の研究が進んでいくと思われる