Star Formation Newsletter
No. 298 16-20
高橋実道（工学院大学）

１. Signatures of broken protoplanetary discs in scattered light and in sub-millimetre observations

Stefano Facchini1 , Attila Juhász2 and Giuseppe Lodato3
1

Max-Planck-Institutfür Extraterrestrische
Physik,Giessenbachstrasse 1, 85748 Garching, Germany
Circumbinary
disk：inner
disk
がwarp
する
2
Institute of Astronomy, Madingley Road, Cambridge CB3 OHA, UK
3
Dipartimento di Fisica, Universitá degliStudi di Milano, process）で
via Celoria, 16, Milano, I-20133, Italy
SPHシミュレーション＋radiationtransfer（post
E-mail contact: facchini
at mpe.mpg.de
散乱光とsub-mmの模擬観測

Figure6. Leftevolutionof theangle
the inner and outer discs,
Spatially resolved observations of protoplanetary discs are revealing
that
theirpanel:
inner
regions
caninclination
be warped
orofbroken
angular momentum to the z-axis. Right panel: evolution of the cosine of the angle
from the outer disc. A few mechanisms are known to lead toangularsuch
3D structures;
among
them,
the Oneinteraction
シミュレーション：初期の連星と円盤のなす角60
momentumunit
vectoraroundthez-axis.
period in cos indicates a w
inner
disk
が歳差運動
Observational signatures of broken discs 3
with a stellar companion. We perform a 3D SPH simulation oftraced
a circumbinary
disc themisaligned
bytraced60◦ atwithrespect
at r = 2a0 , whereas
outer disc is
r = 14a0 (see main text).
outer diskとのなす角は最大100
to the binary orbital plane. The inner disc breaks from the outer regions,precessing
as a rigid body, and leading
to a complex evolution. As the inner disc precesses, the misalignment angle between the inner and outer discs
peak of the m◦varies by more than 100 . Diﬀerent snapshots of the evolution are post-processed with a radiative transfer code, in is at t ⇠ 125
order to produce observational diagnostics of the process. Even though the simulation was produced for the specific antiphase. At
case of a circumbinary disc, most of the observational predictions hold for any disc hosting a precessing inner rim. sum of the twSynthetic scattered light observations show strong azimuthal asymmetries, where the pattern depends strongly on the as 110 , andmisalignment angle between inner and outer disc. The asymmetric illumination of the outer disc leads to azimuthal between thisangles canvariations of the temperature structure, in particular in the upper layers, where the cooling time is short. These
precession.
variations are reflected in asymmetric surface brightness maps of optically thick lines, as CO J=3-2. The kinematicalinformation obtained from the gas lines is unique in determining the disc structure. The combination of scattered
light images and (sub-)mm lines can distinguish between radial inflow and misaligned inner disc scenarios.

Accepted by MNRAS
https://arxiv.org/pdf/1709.08369
Figure 2. Snapshots of the hydrodynamical simulation, with the vertical axis of the image being z, i.e. the initial direction of the binary
angular momentum. The time in the top right corner is expressed in units of the initial binary period Tb .

3

RADIAT

In order to m
3D radiativea grid-based
step towards

Radiation transfer : 散乱光

Observational signatures of broken discs 7
S. Facchini,
14 S.とouter
Facchini, A.でなす角74
Juhász and G. Lodato
30 A. Juhász and G. Lodato
innerCase ABroken disc

Broken disc

0.0
0.5

0.5
0.0
0.5

i
Dec offset [arcsec]

0.0
0.5

i=45

Broken disc

0.5

0.5
0.0
0.5

i=0

i=0

i

0.5
0.0
0.5

i=45

角度が小さい時、outer disk がinner disk に隠され非軸対象が顕著になる

Case A

e

0.0

i

0.5

Case A

0.5

i=0

30
a

e
Dec offset [arcsec]

0.5

i=0

Dec offset [arcsec]

Case Ae
Dec offset [arcsec]

Dec offset [arcsec]ea

Dec offset [arcsec]

Broken disca

Dec offset [arcsec]

a

i

0.5

Dec offset [arcsec]

inner とouter でなす角74 8

Radiation transfer : CO 3-2 のmoment 1

0.0
0.5

i=45

0.5
0.0
0.5

i=45

inner disk の回転の向きがouter disk とずれている
様子が見える２. Interferometric view of the circumstellar envelopes of northern FU Orionis-type stars
O. Fehér1,2 , Ágnes Kóspál1,3 , P. Ábrahám1 , M. R. Hogerheijde3 and C. Brinch4
1

Observatory, Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, H-1121
FUKonkoly
Ori 型星：急激に増光するYSO
Budapest, Konkoly Thege Miklós út 15-17, Hungary
2
増光の起源はinfalling envelope？
Eötvös Loránd
University, Departmentof Astronomy, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
3Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany
8個のFU
Ori
型星のenvelope（〜数千au）をsub-mm
で観測。13CO,
C180のJ=1-0
4
Niels Bohr International Academy, The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100
Copenhagen Ø, Denmark

5つの天体にCOclump が付随
質量~0.02-0.5Msun
E-mail contact: feher.orsolya
at csfk.mta.hu! FU Orionis-type objects are pre-main sequence, low-mass stars with large outbursts in visible light that last for several

years
or decades.
They are thought to represent an evolutionary
phase during the life of every young star whenCO
clump
が付随しない場合でも、周囲に別のCO
clump がある場合がある。
accretion from the circumstellar disk is enhanced during recurring time periods. These outbursts are able to rapidly!
build up the star while aﬀecting the physical conditions inside the circumstellar disk and thus the ongoing or future
3天体でoutﬂow
planet formation. が見つかる
In many models infall from a circumstellar envelope seems to be necessary to trigger the outbursts.
! We characterize the morphology and the physical parameters of the circumstellar material around FU Orionis-type
stars
using
the
emissionofmillimeter
wavelength
molecular
tracers.
The
highspatialresolution
study
gives
insight
これまでClass II とされていても、massive なenvelope が見つかった天体がある。
into the evolutionary state of the objects, the distribution of parameters in the envelopes and the physical processesFU
Ori 型星はClassI - IIofに分布している。
forming
the environment
these stars.
We observed the J=1−0 rotational transition of 13 CO and C18 O towards eight northern FU Orionis-type stars(V1057 Cyg, V1515 Cyg, V2492 Cyg, V2493 Cyg, V1735 Cyg, V733 Cep, RNO 1B and RNO 1C) and determine thespatial and velocity structure of the circumstellar gas on the scale of a few thousands of AU. We derive temperaturesand envelope masses and discuss the kinematics of the circumstellar material. We detected extended CO emission
associated with all our targets. Smaller scale CO clumps were found to be associated with five objects with radii of
2000−5000 AU and masses of 0.02−0.5 M ; these are clearly heated by the central stars. Three of these envelopes are

(a)13CO moment 0(b)C18O moment 0(c)13CO moment 1(d) C18O moment 1(e) C18O column density(f) temperature

A&A proofs: manuscript no. FUor_CO_v2
Fig. 8. Moment and physical parameter maps of V1735 Cyg. The panels are the same as in Fig. 3, the position of the star and the clumps marked
the same. int = 0.23 Jybeam 1 kms 1 and n = 3, 4, ..., 13 on (a) and int = 0.025 Jybeam 1 kms 1 and n = 3, 5, ..., 15 on (b). The pixels with C18 O
peak values less than 18 are coloured grey on panel (d), (e) and (f).

channel maps at low velocities there is only significant emisIntegrating the 13 CO emission in the line wings between
12.9 and 10.7, then 7.4 and 6 kms 1 (see Fig. 11) the blue
sion in the southwestern corner, then an elongated structure appears in the northeast-southwest direction, between 10.2 and wing shows emission mostly to the southwest and the red wing
9.77 kms 1 . Clump A appears around 9.77 kms 1 and it is sig- to the southeast, in a somewhat clumpy structure. If this indeed
nificant until 8.08 kms 1 , somewhat changing its position and indicates an outflow, the source that drives it should be locatedsize. Clump B is present in these channels as well. Other small around 2000 to the south of the center, rather than V733 Cep itclumps appear further northeast, to the south and to the south- self.
west. At 8.71 kms 1 there are only three strong clumps andabove 7.86 kms 1 there is no significant emission in the center.
However, even at 6 kms 1 there is emission in the southeastern 4.7. V710 Cas
regionthe map.
Therearoundis no clear
the line
Fig. 11.of
OutflowfeaturesV1735systematicCyg, V733change
Cep andinV710
Cas. The greyscale shows the integrated intensity of the line similarly as on theoutﬂow features
V1735 は扁平な13COの構造に
垂直にoutﬂow が見える。

TheLopez,
wind
and
the
magnetosphericaccretion
onto
the
T
Tauri
star
S
Coronae
Australis
3. Garcia
R. et al.: Tracing the wind and the magnetospheric accretion of S CrA at sub-au resolution
at sub-au resolution

1. ObservationR.
log ofthe VLTI/GRAVITY(R 3⇠4000)
of SGaratti
CrA North1,2andSouthLazareﬀ
conducted3with
UTs.
GarciaLopez1,2 ,high-resolution
K. Perraut, A. observations
Caratti o, B.
, J.theSanchez-Bermudez
, M.

e

-20
-16

Benisty3,4 and et al.1

Tot. Int. 1
S CrA N Tot. Int. S CrA S
DITa
NDITb
Proj. baselines
PAc
Calibrator
UD diameterd
for Astronomy,
Knigstuhl
17, Heidelberg,[s] Max Planck[s]Institute [s]#[m][ ] Germany, D-69117
[mas]
2
2100
600
60
5 Studies,
42,CrA
52,31
60,Fitzwilliam
81,
93, 11553,
38, 130,
100, XF86
45, 76 Dublin,
HD 188787Ireland
0.252 ± 0.018
DublinInstitutefor
Advanced
Place,
D02
T
Tauri
binary
S
CrA
N
and
S
S
1200
1200
60
5
47, 56, 59, 87, 102, 130
31, 18, 100, 70, 24, 50
HD 176047
0.309 ± 0.021
3

Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France
4 Near-infrared interferometricobservation(VLTI-GRAVITY)a)(b)(c)Astronoma
UnidadMixta
Internacional
Franco-Chilena
de
(CNRS
UMI
Detector integration time per interferogram. Number of interferograms. Baseline position
angle fromthe3386),
shortest Departamento
to longest baseline. de Astronoma, Unicalibrator uniform-disk(UD)diameterCamino(K band) was
taken from Lafrasseet al.Las(2010).
versidaddeの円盤の構造を見る。（Brγとcontinuum）
Chile,El Observatorio
1515,
Condes,Santiago, Chile
sub-auE-mail contact: rgarcia at cp.dias.ie
To investigate the inner regions of protoplanetary discs, we performed near-infrared interferometric observations of
inverseP-Cygni
proﬁlesthe classical T Tauri binary system S CrA. We present the first VLTI-GRAVITY high spectral
resolution(R ∼ 4000)
observations of a classical T Tauri binary, S CrA (composed of S CrA N and S CrA S and separated by ∼1.4”), combining
red 側で吸収が見える。
the four 8m telescopes in dual-field mode. Our observations in the near-infrared K-band continuum reveal a disc aroundoinfallの兆候
each binary component, with similar half-flux radii of about 0.1 au at d∼130 pc, inclinations (i=28±3
and i =22±6o),

14Fittingno.の結果
ofs: manuscript
rebecaA&A proofs: manuscript no. rebeca

i,continuum
PAがNとSで似ている
同一円盤が起源m datacontinuum
Table
for both
2. Parameters
S CrA components
derived星近傍の円盤
from(see Fig.
the best
2). Seefit oftext
thefor
FTparameter
definition.
data for both S CrA components (seeFig. 2). See text for parameter definition.

4
2

SCrA
fh
0.06±0.01
North
0.10±0.01
South

Sp. fc T e↵
Type
[K]

ik s
[]

PAa kc
[]

a
fs
[mas]

a fh
[au]

0.64±0.04
G05920 28±31.35 -3.73±1.27
0±6
0.83±0.04
0.30±0.04
0.108±0.005
0.06±0.01
0.38±0.02
K05280 22±61.25 -2±12-4.03±0.74
0.70±0.04
0.52±0.02
0.090±0.005
0.10±0.01

fc
0.64±0.04
0.38±0.02連星は円盤分裂で形成
i
PAa
a
a
[]
[]
[mas]
[au]
（？）
28±3
22±6

0±6
-2±12

0.83±0.04
0.70±0.04

0.108±0.00
0.090±0.00

2(a)1.35 forNotes.
the North
The reduced
and South
valuescomponent,of therespectively.
best fit modelare
The1.71
PA andcorresponds
1.35 for to
the North and South component, respectively. (a) The PA corresponds to
Lopez,
et al.:axis
Tracingwind
the magnetosphericaccretion
theR.majorof thethedisk
withandNorth
up and East to theleft. of S CrA at sub-au resolution

an fitting:pure Brline visibilities.
Brγ
blue
shift 成分 がred shift成分より広がっている（marginally detected ）of thetherefore
is worse
twobecause
flux fractionsof the larger
amongnumber
fs , fh , fof
free parameters
the sum of(meanthe is worse because of the larger number of free parameters (meanc (since2
ingfractions
thatSingle-parameter
the three-parameter-fit
value
does
notcircumstellar
decreasefit
signif-ing that the three-parameter-fit 2 value does not decrease signif
stellarthreeequals 1), thefitspectral
indexThree-parameterof theblue:wind
a K change
2 thea i,bybjectedenvironment
icantly). 2No
kc oversignificant
theband, theininclination
channelthechannelprojected
size oficantly).
No significant change in the channel by channel size o
RV
a
a
i
PA
r
r
North[km/s]
angle
thePA
Br (withline respectemittingtoregionthemajor
withinaxis
theofbluethedisk,
andred-shifted
witho NorthBr theo Br line emitting region within the blue- and red-shifted Br
[mas]
[mas]
[ ]
[]
red:
magnetosphericof theup-71
andline East
components
totheleft),
isobserved.
and
a,
the
However,angularsize
the(HWHM)
values
of
the
of
the
PA
in
line
components
isobserved.
However,thevalues
of
the
PA
in
+7
1.96 0.49 ± 0.04 2.51 0.63 ± 0.16 32 9 162 ± 19
circumstellar
the three-parameter
environment
fit dofor givea Gaussian
some hintradialof profile.
di↵erent structures
the three-parameteraccretion
fit do give some hint of di↵erent structures+7-35
2.03 0.51 ± 0.03 2.09 0.66 ± 0.14 31 7 168 ± 15
theBr lineemitting
regionbetweenthe blue andredwingsof the Br line emitting region between the blue and red wings
e sum- 3ofThe
results
of
the
best
fit
for
each
S
CrA
component
are
sum+4
1.45
0.54
±
0.03
2.54
0.54
±
0.07
40
153
±
44
6
of theinline.
Presumably,
thebestgeometry
is morecomplexthan ourof the line. Presumably, the geometry is more complex than ou
urce ismarised
Table
2,
and
the
fit
model
for
each
source+7 is39simple0.60
0.48
±our
0.03
0.92
0.47
± 0.04 38
77 simple± 48 models, and our results should be considered as an incen
9
models,andresults
shouldbeconsideredasanincennclina-overplotted in Fig. 2. Both components present the same inclina+1275tive to 2.12
0.46
±observations
0.04 2.92with0.46± 0.0532 1685± 31to perform new observations with a better coverage of the uv
perform
newabettercoverage
of
the
uv
tive
North-tions (very close to face-on) and the same PAs (along the North+12
112
2.38
0.47
±
0.06
3.39
0.47
±
0.07
29
77
±
36
plane,
allowing
morecomplexmodelstobetested.
plane,
allowing more complex models to be tested.
17o et al.South direction). Considering a distance of 130 pc as Prato et al.
whensizes
averagingvisibilitiesof thered- andblueNotably,
when
averagingthevisibilitiesoftheredandblue
e into(2003),Notably,
the angularof thethebest
fit modeltranslate
into
(a)
(b)

arameter fit of pure Br line visibilities at di↵erent radial velocities (RV).

Size of the semimajor axis.

Position4. E↵ect of Angular Momentum Alignment and Strong Magnetic
Fields on the Formation of Protostellar Disks
1?

2,3

3,4

WilliamJ.
Gray,
Christopher
F.
McKee,
andRichard
I.
Klein,
1 CLASP, College of Engineering, University of Michigan, 2455 Hayward St., Ann Arbor, Michigan 48109, USA
2 Department of Physics, University of California, Berkeley, Berkeley, CA 94720
6
William
J.
Gray
et
al.
磁気制動によって円盤形成は阻害されるか？
3

350v2 [astro-ph.GA] 21 Sep 2017

Department of Astronomy, University of California, Berkeley, Berkeley, CA 94720
4 Lawrence Livermore National Laboratory, P.O. Box 808, L-023, Livermore, CA 94550

6TableWilliam
J.
Gray
et
al.
「乱流なら円盤ができる」や
1. Simulation Runs
Accepted 2017 September 13 . Received 2017 September 13 ; in original form 2017 June 29「角運動量と磁場がmisalignしていれば円盤ができる」という説がある。
Table 1. Simulation Runs
ERot
6 William
J.
Gray
et
al.
Name
Mass
µ
✓
x
↵
M
M
N
A
star
`
vir
obs
max
E
乱流とmisalignのどちらが重要か？
KE
ABSTRACTStar forming molecular clouds are observed to be both highly magnetized and turbulent. ConEon
Rotthe complex
sequently
theformationofprotostellardisks
islargelydependent
interaction
AT0
300
2.0
0.0
2.50
0.595
0.071
0.0212
2.8
0.3
0
Name
Mass
µ
✓
x
↵
M
M
N
align している乱流状態を初期条件として検証
A
star
`
vir
obs
max
E
Table between
1. Simulation
Runs
KEgravity, magnetic fields, and turbulence. Studies of non-turbulent protostellar disk

Ndisk

0
Ndisk
AT10
300
0.0shown that
2.50these fields
0.232
0.302
0.03505.7
0.6
10formation with realistic
magnetic2.0
fields haveare efficient
in removing
AT0300the forming
2.0 disks,0.595 However,0.071 once0.0567
0.0212
2.8
0.3
0
AT50
300
2.0
0.0preventing
2.50their formation.
0.103
1.101
11.0
1.1
40
angular momentum fromturERot although the precise
bulenceisincluded,
disks
can
form
in
even
highlymagnetizedclouds,
AT10
300
2.0
0.232
0.302
0.0350
5.7
0.6
1star
0disk
AT100
300
2.0
0.0
2.50
0.074
2.074
0.0765
15.0
1.6
16
Name
Mass
µ
✓
x
↵
M
M
N
N
A
`
vir
obs
max
E
mechanism remains uncertain. Here we present several high resolution
simulations of turKE
AT50
300
2.0
0.0
2.50
0.103
1.101
0.0567 15.0
11.0
1.1
0
AT100L8
300
2.0
1.25
0.074
2.074
0.0765
1.6
64
bulent, realistically magnetized,
high-mass
molecular
clouds withboth aligned
and random
turbulence to study therole that2.0
turbulence,magnetic fields
have onthealign 乱流
AT100
300
2.0
0.074
2.074
0.0765160
00
AT100NR
0.0misalignment,
2.50
2.072
0.0524
15.0
1.6
12
AT0
300
2.50 and0.051
0.595
0.071
0.02122.8
0.3
formation of protostellar disks. We find that when the turbulence is artificially aligned so that
AT100L8
300
2.0
1.25
0.074
2.074
0.076561
010
RT100TH37
2.0
37.0
2.50
1.6
10
AT10
300
0.0 uniform
2.50
0.232
0.302
0.0350 15.0
5.7
0.6
misalign 乱流
the angular momentum
is parallelto the initial
field, no0.051
rotationally2.090
supported 0.0524
disks
are formed, regardless300
of the initial
We conclude
that turbulenceandtheAT100NR300
2.0 turbulent
0.051
2.072
0.052412010
RT100TH0
2.0
0.0 energy.
2.50
0.013
2.071
0.0139
15.0
1.6
34
AT50
2.50
0.103
1.101
0.056711.0
1.1
misalign 乱流
associated misalignment between the angular momentum and the magnetic field are crucial in
RT100TH37
300 disks
37.0
0.051
10
10
AT100
300
2.0
0.0 of 2.50
0.074fields.2.090
2.074 0.0524
0.0765 15.0
15.0 1.6
1.6
16
theformationofprotostellar
inthepresence
realisticmagnetic
RT10M5
5
2.0
44.0
1.75
0.012
0.177
0.00060.9
0.5（コア全体ではalign） AT100L8
RT100TH0
300
2.0
0.0
2.50
0.013
2.071
0.0139
15.0
1.6
3
1
300
1.25
0.074 2.074
0.0765 15.0
1.6
60
Key words: stars:formation
RT10M5MU5
5 - accretion
5.0 discs
44.0- turbulence
1.75 - MHD
0.012
0.177
0.00060.9
1.2
AT100NR
300
2.0
0.0
2.50
0.051 2.072
0.0524 でのみ円盤が形成
15.0
1.6
12
0
misalign
RT10M5
2.0 44.0
1.75
0.012 0.177 0.0006
0.9
0.5
RT10M5L8
55
2.0
0.87
RT100TH37
300
2.0
37.0
2.50
0.051 2.090
0.0524 15.0
1.6
101
RT10M5MU5
5.0 44.0
1.75
0.012 0.187
0.177 0.0002
0.0006
0.9
1.2
AT10M5
55
2.0
0.0
0.004
0.5
RT100TH0
300
2.0
0.0
2.50
0.013 2.071
0.0139 15.0
1.6
3
1
1 INTRODUCTION
ally supported
to be an ubiquitousof star formaRT10M5L8
52.0
44.0disk seems
0.87
0.012 feature
0.177
0.00060.9
0.5-

計算はAMRでideal MHD, sink size 10au, resolution 2.5au
14速度を見ると円盤ができていそうだが、William J. Gray et al.
回転サポートの構造はできないらしい

large scale の構造
Protostellar
Disk Formation Aligned Turbulenalign 乱流ではﬁlament
ができる
他でできないのは初期条件が丸いせい？

align 乱流

misalign 乱流

misalign 乱流（コア全体ではalign）
面密度
面密度
回転速度
Figure 7. Density projections for the largest star formed in Top Panel: AT100, Middle Panel: RT100TH0, and Bottom Panel: RT100TH37. The left column
shows the face-on density projection while the middle column shows the edge-on density projection. The black arrows represent the velocity vectors. The rightcolumn shows the（facevelocity profile for on）
the disk. The red (solid)line is the analytic Keplerian
angularvelocity using the stellar mass. The black points represent
（edge
on）
（赤線がケプラー）
the mean angular velocity as a function of the cylindrical radius R . The green region represents regions within the star particle’s accretion zone and showsz

where the accretion zone alters the gas properties. The left and middle columns include only gas denser than 109 cm 3 (Criterion 5). The final stellar mass isgiven above the face-on images for each model. Note that disks are formed in both RT100TH0 and RT100TH37 but not in AT100.

5. Fragmentation of Filamentary Cloud Permeated by Perpendicular Magnetic Field
Tomoyuki Hanawa1 , Takahiro Kudoh2 and Kohji Tomisaka3
1

Chiba University, Inage-ku, Chiba 263-8522, Japan
2
Nagasaki University, 1-14 Bunkyo-machii, Nagasaki 852-8521, Japan
3
National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan

磁場に貫かれたフィラメントの重力不安定性の線形解析
B =const

x

0 hanawa at faculty.chiba-u.jp
E-mail contact:

境界条件で振る舞いが変わる
固定端：z軸上β<1.67で安定
自由端：任意の強さの磁場に対して不安定となる

We examine the linear stability of an isothermal filamentary cloud permeated by a perpendicular magnetic field.
Our model cloud is assumed to be supported by gas pressure against the self-gravity in the unperturbed state. For
simplicity, the density distribution is assumed to be symmetric around the axis. Also for simplicity, the initial magnetic
field is assumed to be uniform and turbulence is not taken into account. The perturbation equation is formulated to
be an eigenvalue problem. The growth rate is obtained as a function of the wavenumber for fragmentation along theaxis and the magnetic field strength. The growth rate depends critically on the outer boundary. If the displacement
vanishes in the region very far from the cloud axis (fixed boundary), cloud fragmentation
is suppressed by a moderate
65magnetic field, which means the plasma beta is below 1.67 on the cloud axis. If the displacement is constant along themagnetic field in the region very far from the cloud, the cloud is unstable even when the0.12
magnetic field is infinitely
0.4
strong. The cloud is deformed by circulation in the plane perpendicular to the magnetic field.
Theunstable
mode
is
0.10

z,k

固定端

B0=0

σ/(4πGρc)1/2

0.3

β=40

0.2

β=4

0.1

0.0
0.0

成長率のβ依存性（k固定）

β=2
β=1.74
0.1

0.2

0.3
kH

0.4

0.5

0.6

kH=0.250.08
σ2/4πGρc

分散関係
B 大 で 最大成長の
k
小
15

0.06
0.04 kH=0.35
kH=0.150.02
0.00 kH=0.05
0.0

0.2

0.4
1/β

0.6

center, x = y = 0.

自由端

6

分散関係
B 大 で 最大成長の k 小σ2/4πGρc

σ2/4πGρc

σ/(4πGρc)1/2

The growth rate σ∞ (k) is evaluated by a spline fit to
the growth rate in the range 0.2 ≤ β ≤ 1. The value 0.12
of
0.12
0.4
σ∞ (k) is shown by the dashed curve in Figure ??.
0.10
0.10
When kH is smaller, the growth rate is close to the
B0=0
kH=0.25kH=0.25
0.3
asymptotic value for a weaker magnetic field. This reβ=40
0.08
0.08
sult implies that the magnetic field is bent or compressed
little by the unstable perturbation when the initial magβ=4
0.06
0.06
0.2
β=2
netic field is strong. Otherwise, the distorted magnetic
field would induce a strong force acting on the gas. At
0.04 kH0.04
kH=0.15=0.35 the same time, the displacement should be appreciable0.1
β=1
kH=0.15kH=0.35even in the region very far from the cloud center. Oth0.02
0.02
β=0erwise, the growth rate would be independent of the kH=0.05
0.0
0.00 kH=0.05boundary condition in the x-direction. We confirm this
0.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6 0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
expectation1/βin the next subsection.
kH
1/β
The wavenumber of the most unstable mode is smaller
8 Figure 3. Same as Fig. 1 except for8the freeFigure
boundary.
for a larger
B0 . The
wavenumber
is kH ≃Figure0.29 4for
2. Growth squared
as a functionof 1/βfor a given. Growth squared as a function of 1/β for a give
kH, where β denotes
plasmabeta
the cloudkH forfield
the free boundary.
B0the= 0initial
and kH≃ 0.16
for ata smallβ. The magnetic
center, x = y = 0. decreases the growth rate and increases the wavelength
δρ/ρ0
δρ/ρ
δρ/ρ0
The growth rate shows a diﬀerent dependence
on0 they/hでz方向の変位の δρ/ρ0
The0.3growth rate σ∞ (k) is evaluated by a0.3spline fit tof a typical perturbation.
0.3
0.3
15
15
magnetic20field strength when we apply the free20boundary
thegrowth
rate
in
the
range
0.2
≤
β
≤
1.
The
value
o
The
filamentary
cloudisstablefor
anyperturbation
0.4
except for向きが変わる（コントア）
condition. Figure 3 is the same as Figure 1 0.2
0.2 −1
0.2
having a wavenumber0.2larger than k > kcr = σ
0.565∞ (k)His shown by the dashed curve in Figure ??.
the free boundary.
Each curve in Figure 3 denotes
the
15
15
When
when B0 = 0. When the free boundary is applied,
thekH is smaller, the growth rate is close to thB0=0
密度が増加する場所で
0.1
0.1
0.1
0.1
10
growth rate as a function of kH for a given β whose value
10
−1
0.3
critical wavenumber
is slightly reduced, i.e., k≃ value for a weaker magnetic field. This re-0.1
asymptotic
cr H
-0.1
β=40
is designated by the same color. The dashed line denotesy方向に広がる
10
0.51 for a large B0 . The
critical wavenumber issult
evaluated
implies that the magnetic field is bent orcompresse
0.0
0.0
10
0.0
0.0
the growth rate when β = 0, and the value is obtained byfrom β=4
the high resolution computation of ∆xlittle
= ∆y
=
by
the
unstable
perturbation
when
theinitialmag
0.
51extrapolation. As the magnetic field strength-0.1
increases,
-00.2
.1
5
-0.1
β=2
0.3H
and
n
=
n
=
80.
x
y
-0.1
-0.1 magneti
netic
field
is
strong.
Otherwise,
thedistorted
5
磁場を曲げずにyz面をガスが回転
the growth rate0decreases
but remains positive5for kH ≤
.1
0.1
0.3
0.04
field
would 0induce
a strong force
acting on the gas. A
.04
0
0
.3
0
4
.5
.
0
0
.
0.525, and therefore
the
cloud
is
unstable
even
when
the
4
0
-0.2
-0.2
3.2.
Eigenmode
0.5
0.7
-0.2
-0.2appreciabl
0
.
7
the
same
time,
the
displacement
shouldbe
0.1
0 が集まることで重いﬂux tube
magnetic 0field is infinitely strong.
β=1
0
0the
First,
basedon
our
stability
analysis,
wereview-0.3-0.3
0 shown
5 in Figure
10
15
20to contradict the01015even in 0the region
very farfrom thecloud-0.3
center. Oth-0.35
3 seems
The result
0
5
10
15
20
5
10
15
x/H
z/H absence of the magnetic
unstable
perturbationinthe
重力エネルギーを解放
β=0
erwise, the growth z/Hrate would be independent of thx/Hnaive expectation that a subcritical cloud is stable (see,0.0field. When B0 = 0, both the growth rate and the eigen-

成長率のβ依存性
（k固定）

y/H

y/H

σ/(4πGρc)

1/2

y/H

y/H

固有モード（kH=0.2, β=4）