John J. Tobin, Leslie W. Looney , Zhi-Yun Li , Sarah I. Sadavoy , Michael M. Dunham , Dominique Segura-Cox4 , Kaitlin Kratter8 , Claire J. Chandler9 , Carl Melis10 , Robert J. Harris4 , andLaura Perez11
1

Current address: National Radio Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA 22903, USA; 2
Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks Street, Norman,
OK 73019, USA; 3 Leiden Observatory, Leiden University, P.O. Box 9513, 2300-RA Leiden, The Netherlands; 4 Department of Astronomy, University of Illinois, Urbana, IL 61801; 5 Department of Astronomy, University of Virginia,
Charlottesville, VA 22903; 6 Harvard-Smithsonian Center for Astrophysics, 60 Garden St, MS 78, Cambridge, MA
02138; 7 Department of Physics, State University of New York Fredonia, Fredonia, New York 14063, USA; 8 University of Arizona, Steward Observatory, Tucson, AZ 85721; 9 National Radio Astronomy Observatory, P.O. Box O,
Socorro, NM 87801; 10 Center for Astrophysics and Space Sciences, University of California, San Diego, CA 92093; 11
Departamento de Astronomı́a, Universidad de Chile, Camino El Observatorio 1515, Las Condes, Santiago, Chile

星形成ゼミ・報告 (SFN #310 N.55-58)資料
2018年12⽉7⽇

E-mail contact: jjtobin at gmail.com

古屋玲

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of multiple protostar systems in
the Perseus molecular cloud previously detected by the Karl G. Jansky Very Large Array (VLA). We observed 17
close (<600 AU separation) multiple systems at 1.3 mm in continuum and five molecular lines (i.e., 12 CO, C18 O,(徳島⼤学・教養教育院)
13
CO, H2 CO, SO) to characterize the circum-multiple
environments in which these systems are forming. We detect atleast one component in the continuum for the 17 multiple systems. In three systems, one companion is not detected,
and for two systems the companions are unresolved at our observed resolution. We also detect circum-multiple dust
emission toward 8 out of 9 Class 0 multiples. Circum-multiple dust emission is not detected toward any of the 8 ClassI multiples. Twelve systems are detected in the dense gas tracers toward their disks/inner envelopes. For these 12
systems, we use the dense gas observations to characterize their formation mechanism. The velocity gradients in thecircum-multiple gas are clearly orthogonal to the outflow directions in 8 out of the 12 systems, consistent with disk
fragmentation. Moreover, only two systems with separations <200 AU are inconsistent with disk fragmentation, in
addition to the two widest systems (>500 AU). Our results suggest that disk fragmentation via gravitational instability
is an important formation mechanism for close multiple systems, but further statistics are needed to better determine
the relative fraction formed via this method.

紹介しない論⽂
http://arxiv.org/pdf/1809.06434
Accepted by ApJ

55

EPIC 203868608: A low-mass quadruple star system in the Upper Scorpius OB associationJi Wang1,2 , Trevor J. David1,3 , Lynne Hillenbrand1 , Dimitri Mawet1 , Simon Albrecht4 , and Zibo Liu5
1

Department of Astronomy, California Institute of Technology, MC 249-17, 1200 E. California Blv, Pasadena, CA

ALMA reveals a collision between protostellar outflows in BHR 71

Alma reveals
collision
betweenprotostellar outflows
in BHR 71 , Guido
5 Garay , Satoko Takahashi ,58
Luis A. aZapata, Manuel
Fernández-López, Luis F. Rodrıǵuez
1

2

1

3

4

Chin-Fei Lee5 , and Antonio Hernández-Gómez1,61Instituto de Radioastronomı́a y Astrofı́sica, Universidad Nacional Autónoma
de México, P.O. Box 3-72, 58090,
要旨
Morelia, Michoacán, México; 2 Instituto Argentino de Radioastronomı́a (CCT-La Plata, CONICET; CICPBA), C.C.
No. 5, 1894, Villa Elisa, Buenos Aires, Argentina; 3 Departamento de Astronomı́a,
Universidad de Chile, Camino el
1. 分⼦流と分⼦流が相互作⽤する系(345Almareveals a collision
between Chile;
protostellar
in BHR 71
5
Observatorio
1515, Santiago,
Joint outflows
ALMA Observatory,
Alonsode Cordova
3108,
Vitacura,
Santiago,
Chile;例⽬)をALMAでは初めて⾒つけた.
Academia Sinica Institute of Astronomy and Astrophysics, P.O. Box 23-141, Taipei 106, Taiwan; 6 IRAP, Université
BHR71
de Toulouse, CNRS, UPS, CNES, Toulouse, France
2.【中⼼星のひとつ；BHR71 IRS1】
E-mail contact: lzapata@irya.unam.mx• Lbol13.5+/-(the1.0separation
Lsun
For a binary protostellar outflow system in which its members are located close
to =
each
other
being
BHR71

smaller than the addition of the widths of the flows) and with large opening •angles,
collision seems unavoidable
Mdustythe
envelope = 0.215 +/- 0.003
Deflection
regardlessof the orientation of the outflows. This is in contrast to the current observational evidence of just a few
Msun(ALMA),
19M
sun(ハーシェル衛regions with indications of colliding outflows, which could also suggests that the average
distance
betweenprotostars is
IRS1星) Large Millimeter/Submillimeter
larger than the width of the flows. Here, using sensitive observations of the Atacama
Deflection
IRS2
Array (ALMA), we report resolved images of carbon monoxide (CO) towards the binary flows associated with the• 分⼦流の⼒学年齢の下限値は,
IRS1
BHR 71 protostellar system.
These images reveal for the first time solid evidence that their flows are partially colliding,
GREG> say '200*30*au|(25e5)|yr'
IRS2
increasing the brightness of the CO, the dispersion of the velocities in the interaction
zone, and changing part of the
1.1384E+03年くらい, second collapse後orientation in one of the flows. Additionally, this impact opened the possibility ofknowing the 3D geometry of the
それほど時間は経っていないか？
system, revealing that one of its components (IRS 2) should be closer to us.
Accepted by The Astronomical Journal

Colliding zone

Colliding zone

https://arxiv.org/pdf/1804.00625

輝線強度で重み付け平均した視線速度マップ(モーメント計算時の速度範囲は-25 < V-Vsys (km/s) < 20)

Figure 2. ALMA 12 CO(2-1) intensity-weighted velocity (moment one) (color-scale), 12 CO(2-1) integrated
intensity (black contours), and 1.3 mm continuum (grey contours) images of BHR 71. The half-power
12 CO(2-1)
beamsize is shownin the bottom left corner.
The radial
velocity scale-bar
is shown in the 12
right.
e synthesized
2. ALMA
intensity-weighted
velocity(momentone) (color-scale),CO(2-1) integrated
black contours
are startingfrom mm
10% to80% in steps (greyof 10% contours)of the intensity
peak. The
CO intensity
ityThe(blackcontours),and −11.3
continuum
imagesof BHR
71. The half-power−1
peak is 13.9 Jy Beam Km s . The grey contours are starting from 2% to 90% in steps of 2% of theesized
beam
size
is1.3
shown
in the bottom
The −1
radialvelocity scale-bar is shown in the right.
intensity
peak.
The
mm continuum
intensity left
peakcorner.
is 0.4 Jy Beam.

BHR71IRS1
IRS2Colliding zone

輝線強度で重み付け平均した視線速度の速度幅マップ(モーメント計算時の速度範囲は-25 < V-Vsys (km/s) < 20)

Figure 3. ALMA 12 CO(2-1) intensity-weighted square root velocity (moment two) (color-scale), 12 CO(2-1)
integrated intensity (black contours), and 1.3 mm continuum (brown contours) images of BHR 71. The
half-power synthesized beam size is shown in the bottom left corner. The radial velocity scale-bar is shownin the right. The black contours are starting from 10% to 80% in steps of 10% of the intensity peak. The
CO intensity peak is 13.9 Jy Beam−1 Km s−1 . The brown contours are starting from 2% to 90% in steps of
2% of the intensity peak. The 1.3 mm continuum intensity peak is 0.4 Jy Beam−1 .

On the origin of magnetic fields in stars

57

James Wurster1 , Matthew R Bate1 and Daniel J Price2

要旨

On the origin of magnetic field

School of Physics and Astronomy, University of Exeter, Stocker Rd, Exeter EX4 4QL, UK; 2 Monash Centre for1. 【着眼点】若い星[⽂脈から前主系列星
106 Astrophysics and School of Physics and Astronomy, Monash University, Vic 3800, AustraliaIdeal MHD-104(PMS)？]で観測されるkGオーダーの磁場強度
Ideal MHD: Central = Maximum
ρmax=10105 E-mail contact: j.wurster at exeter.ac.uk-910ρmax=10Non-ideal MHD: Centralは原始星形成時にあったものか、それともPMS
理想MHD-84 Are the kG-strength magnetic fields observed in young stars a fossil field left over from
3 their formation or are they
ρ
=10
max
10
10 generated
Non-ideal
MHD: Maximum
進化におけるダイナモで増幅されたものか？
-4-3
by a dynamo?
We use radiation non-ideal magnetohydrodynamics
simulations of the gravitational collapse
⾮理想MHDρmax=10 g cm ;orders of magnitude in density, past the first hydrostatic coredts
103 of a rotating, magnetized molecular cloud core over 17(最⼤値)22.【⼿法】⾮理想MHD効果(双極性拡散,オーム
10
to the formation of the second, stellar core, to examine the fossil field hypothesis. Whereas in previous work we found2
10 that magnetic fields in excess of 10 kG can be implanted in stars at birth,
thisホール効果)＋回転を考慮し,assumed ideal magnetohydrodynamics
損失,
分⼦雲コア
原始星形成後6ヶ⽉
1
non-ideal MHD
calculations
which include
10
1 (MHD), i.e. that the gas is coupled to the magnetic field. Here we present(初期にR=0.013pc,
等温, 回転と重⼒のエネ
10Ohmic resistivity, ambipolar diﬀusion and the Hall eﬀect. For realistic cosmic ray ionization rates, we find that
⾮理想MHD
ルギー⽐=0.005,
臨界値に対する質量磁束⽐kGareimplanted in the stellar core at birth,ruling out 10
a 0strong
fossil field. While these
100 magnetic field strengths of <∼(中⼼部)
results remain sensitive to resolution, they cautiously provide evidence μ=5,適切な宇宙線電離度ζ=1e-17
against a fossil field origin for stellar magnetic
1/sec)から
10-1 fields, suggesting instead that magnetic fields in stars originate in a dynamo process. -1

10
10
10

-2

Accepted by MNRAS

原始星形成-3 http://adsabs.harvard.edu/pdf/2018MNRAS.481.2450W
ファースト
第2
-4

http://arxiv.org/pdf/1809.01234
コア期
collapse期

10-18 10-16 10-14 10-12 10-10 10-8 10-6 10-4 10-2
100
ρmax [g cm-3] 系中⼼部の密度(ほぼ時間軸)

原始星形成直後までを計算.
10-17 -1

3.【結論】

410

Non-ideal MHD: ζcr=10s(i)理想MHD(磁場と物質がカップル)では観測
3
10
事実(?)を説明できない.
210(ii)誕⽣直後の原始星はr~1-3AUの“magnetic
wall”(図2参照)で囲まれており、壁での最⼤110
磁場強度は~900G, 中⼼星を含めた壁内部で0は~240G以下.
10

µ(r)

B [G]

µ(r)

1

Figure 1. Evolution of the magnetic field strength against maximum density, which is a proxy for time. The vertical grey line indicates the formation
density of the stellar core, and the black circles are placed 6 months after
the formation of the stellar core for each model (i.e. dtsc = 0.541yr). For(iii)つまり, PMSで観測されるkGオーダーの磁
both models, the maximum density is coincident with the centre of the sys-1
10tem (i.e. ρmax = ρcen ). In the ideal MHD model, the maximum and central
場はPMS進化中に増幅されたものだろう.
-4
-3
-2
-1
0
1
10
10
10
10
10
10
magnetic field strength are the same for the entire simulation. In the nonr [au]ideal MHD model, the central and maximum magnetic field strengths are【この論⽂と直接⽐較されている先⾏研究】
no longer coincident near the end of the first core phase, and at stellar core
Figure 3. The mass-to-flux ratio in units of the critic
Tsukamoto+15a,
15b, epochs
17
formation, are a few orders of magnitude lower than the values in the idealof radius at six different
for the ideal (top) an
MHD model.
MHD models. The horizontal grey line represents th

原始星
誕⽣直後

中⼼部が卓越

5

-5

磁⼒線の壁

105
104

10

103
B [G]

102

-1

Ideal MHD: Central = Maximum
時 Central
Non-ideal 始
MHD:開Non-idealseMHD: Maximum
p
la
ol
c
2
第

初期

10
0.01
AU~2Rsun(原始星半径；図4から)

10

1

100

10

10

0

-1

10

x [AU]

tio µ(r)also decreases in this region. Outside of this central re-1
10gion, µ(r) > 5 since the cloud
collapses faster along the mag-17 -1
Non-ideal
MHD:perpendicularζcr=10 s
netic10field
lines
than
to them, increasing the mass
4
as a greater rate than the flux. During this phase in the non-ideal
MHD
3model, µnon-ideal (r) > µideal (r), indicating that the non-ideal
10
processes are diffusing the magnetic field, with significant diffu-

-2

10-8
ρmax [g cm-3]

2

3

0

s

原始星 -410 -18
誕⽣直後
10
10-16 10-14 10-12 10-10

10

log d

0

10

10-3

3

1

t = 0 slices throughFigure 2. Density(top) and magnetic field strength (bottom)
Ideal MHD
-10
-3
4
ρmax
=10 gaxis
cm for the ideal (left)
10 hydrostatic core perpendicular to thethe first
rotation-9-3
max=10 g cm
and non-ideal (right) MHD models once theρmaximum
density
has reached
-8
-3
ρmax
=10 phase).
g cm The initial magρmax10≈3 10−8 g cm−3 (near the end of the first
core
-4
-3
ρmax=10cm critical; dtsc=0 mass-to-flux ranetic field strength in both models is fivetimesg thedt
sc=0.5yr2tio. The
10 density slices are qualitatively similar. The magnetic field strength
follows the density profile in the ideal MHD model, while the maximum
magnetic
1 field strength in the non-ideal MHD model is in a structured torus
10
at 1-3 au from the centre of the core.

-17 -1-1
Non-ideal10MHD:
ζcr=10

4

-12
5

-5

106

0

0
x [AU]

µ(r)

1

10-6

10-4

10-2

100

2

10

M/Φ

μ = (M/Φ )MNRAS 000, 1–8 (2018)B=M(r)πr 2 B(r)≃Figure 1. Evolution of the magnetic field strength against maximum den1
10sity, which is a proxy for time. The vertical grey line indicates the formationc1
5
B critdensity of the stellar core,時and the black circles are placed 6 months after
0
始
10
G
3π
開
the formation of the stellar
core for each model (i.e. dtsc = 0.5 yr). Forepsboth models, the maximum
density is coincident with the centre of the sys-1
lal
10 say ‘Msun|(pi*(0.013*pc)**2*163e-6)|((.53|(3*pi)*sqrt(5|G)))’
o
GREG>
初期
c
tem (i.e. ρmax =2 ρcen ). In the ideal MHD model, the maximum and central
-3
-2
-1
0
1
2
3
4.987 10-4
10
10
10
10
10
10
10
第
magnetic field strength are the same for the entire simulation. In the nonr [au]ideal MHD model, the central and maximum magnetic field strengths are
no longer coincident near the end of the first core phase, and at stellar core
Figure 3. The mass-to-flux ratio in units of the critical value as a function
formation, are a few orders of magnitude lower than the values in the idealof radius at six different epochs for the ideal (top) and non-ideal (bottom)
MHD model.
MHD models. The horizontal grey line represents the initial mass-to-flux

1

10

0

10

-1

10

-4

10

-3

10

-2

5

-1

10

0

10 Ideal MHD 10=10 g cmr [au]
max

-8

]

µ(r)

0
x [AU]x [AU]

10M/ΦBµ(r) ≡,(M/ΦB )crit-5

⾮理想MHDOn theoriginof magnetic
fieldsin 5stars
-5
0
5
-5
0

µ(r)

µ(r)

2

10

5

理想MHD

-11

log |B| [G]

y [A

3

10

-5

y [AU]

4

10

1

2

10
10
Non-ideal MHD

3

10

-3

-9

nsity [g/cm3]

図3

図2: ファーストコア期最終盤での磁場構造

t=0
-10
-3
ρmax=10 g cm
-9-3
ρmax=10 g cm
-8-3
ρmax=10 g cm
-4-3
ρmax=10 g cm ; dtsc=0
dtsc=0.5yr

Ideal MHD

-100ratio, µ0 = 5. At t = 0, µ(r) = µ0 = 5 at r = Rc . The non-ideal MHD
processes diffuse the magnetic field even by ρmax ≈ 10−10 g cm−3 , yielding µnon-ideal (r) > µideal (r). There is significant diffusion of the magnetic
field for r ! 10 au in the non-ideal MHD model.

y [AU]

56

0Hall eﬀect-driven formation of gravitationally unstable discs in magnetized molecular
cloud cores-17 -1
s
cr=10

1

1

Hall effect-driven disc formation

James Wurster , Matthew R Bate and Daniel J Price2

3-50 Anti-aligned
-10
-8
-3
-3
50 1 Schoolcm-3 and=10-9g cm-3 University
g cm=10-1.1Rd,
g cmExeter
Physics
Exeter,
Stocker
EX4 4QL, UK; 2 要旨
Monash Centre formax =10of g
maxAstronomy,
max =10 ofmax
50

Astrophysics and School of Physics and Astronomy, Monash University, Vic 3800, Australia

1. 55番論⽂の結果のうち、不安定な円盤の形成に焦点

yy
[AU]
[AU]

y y[AU][AU]

図1 We demonstrate
ファーストコア
the formation of gravitationally第⼆コラプス期
unstable discs in magnetized molecular cloud cores with initial mass0 E-mail contact: j.wurster at exeter.ac.uk

0

to-flux ratios
of five times the critical value, eﬀectively−8−3 solving the magnetic braking catastrophe. We model the-17−10-1g cm−3
ρHydro
=
10
ρ
=
10
g
cm
=10
s
max
max
2.【新しさ】⾮理想MHD効果
cr-50 gravitational
collapse through to the formation of the stellar core, using Ohmic resistivity, ambipolar
diﬀusion and-50 Aligned
magnetic field分⼦雲コアかand
50 the Hall eﬀect, and using the canonical cosmic ray ionization rate of ζCR = 10−17⃗ s−1 . ⃗ When the3つを⼊れて,
J
B
50
不安定円盤
rotation axis are initially aligned, a <are anti-aligned,∼ 1 au disc forms after the first core phase, whereas when they
ら前主系列段階(のうち,ごa gravitationally unstable 25 au disc forms during the first core phase. The aligned model launches a 3 km s−1 firstく)最初まで,0 core outflow, while the anti-aligned model launches only a weak < 0.3 km s−1 first core outflow. Qualitatively,
we⾓運動量ベク
find∼0that models with ζCR = 10−17 s−1 are similar to purely hydrodynamical models if the rotation axis
and magnetic field
トルJと磁場ベクトルBが平-17 -1s anti-aligned, whereas they are qualitatively similar to ideal magnetohydrodynamical models if initiallyarecr=10
initially-16 -1
⾏と反平⾏の場合を解いた.
=10sAnti-aligned
cr-50 aligned.
Anti-aligned-50
50
Astronomical Society
50 Accepted by Monthly Notices of the Royal
Hall効果で円盤形成されず

y [AU]y [AU]

http://adsabs.harvard.edu/pdf/2018MNRAS.480.4434W
0 http://arxiv.org/pdf/1808.04376

J ⃗ B⃗(i)図1の部分でr~25AUの円盤形成されるので、所
謂, 磁気制動catastropheの問題を解決.

0-17 -1s
cr=10-16 -1s
Alignedcr=10-50 On the origin of magnetic fields in stars-50 Aligned
11
2
50 James Wurster , Matthew R Bate and Daniel J Price
50 1

y [AU]y [AU]y [AU]

57

3.【結果】

School of Physics and Astronomy, University
Exeter, Stocker Rd, Exeter EX4 4QL, UK; 2 Monash Centre for
所謂,of磁気制動catastrophe
Astrophysics and School of Physics and Astronomy, Monash University, Vic 3800, Australia (ii)ファーストコア段階で分0
0 E-mail contact: j.wurster at exeter.ac.uk

理想MHD

⼦流が駆動される.

s-1
Arecr=10
the -16
kG-strength
magnetic fields observed in young stars a fossil field left over from their formationor are they
• 反平⾏のとき低速(<0.3Anti-aligned-50 generated by a dynamo? We use radiation non-ideal magnetohydrodynamics simulations of the gravitational collapse-50 Ideal MHD
50 of a rotating, magnetized molecular cloud core over 17 orders of magnitude in density, past the firstkm/s)分⼦流
hydrostatic core-50
050
0 stellar
50 -50050
0 hypothesis.
50
to the formationof -50the second,core, to examine
the-50fossil field
Whereas in previous
work we found• 平⾏のとき⾼速(>3km/s)
x [AU]x [AU]x [AU]x [AU]
that magnetic fields in excess of 10 kG can be implanted in stars at birth, this assumed ideal magnetohydrodynamics
分⼦流
0 (MHD), i.e. that the gas is coupled to the magnetic field. Here we present non-ideal MHD calculations
which include
Ohmic resistivity, ambipolar diﬀusion and the Hall eﬀect. For realistic cosmic ray ionization rates, we find that02
4
-16 -1s<cr=10 fieldmagnetic
strengths ofkG
areimplanted
in
2the stellar core at birth, ruling out a strong fossil field. While these∼log column density [ g/cm ]-50 Aligned

4

図2

4

53

6

10

53

10

円盤が不安定になる

52

51 10

51

10

2 -1

Lfc [g cm s ]

10

52

10

51

50

10

50

10

50

10

49

51

Hydro

10

-17 -1Anti-aligned: ζcr=10 Hydros
Hydro-17-17-1 -1-1 Hydro-17
Aligned: ζcrζζ=10sAnti-aligned:=10ss
Anti-aligned:=10-17 -1cr
cr
Anti-aligned:-16-17-1 ζ-1cr=10 s
Anti-aligned:
ζcrζ=10
Aligned:=10 s-17
s -1 -17 -1
cr
Aligned:ζcr=10s
Aligned:-16-16-1 ζ-1cr=10 s
Aligned: Anti-aligned:
ζcrζ=10Anti-aligned:s -1 -16 -1
cr=10 s-16
Anti-aligned:
ζcr=10-16 ζ-1scr=10-16s-1
Ideal
MHDsζ =10 s
Aligned:ζcr=10
Aligned:-16 cr-1
Aligned:ζ=10s
cr MHDIdeal-10-9-8 Ideal MHD -7
10
10
10
10
-3 -10 -9 Ideal -9MHD
-10
-8
-7
-11
-8
-7
ρ10
] 10
10
10 10
10 10
10
max [g cm 10
-3
-3-9
-10 ρ
-8
-7
ρmax
[g cm ]
[g
cm
]
max
10
10
10
10

50

10

0

50

-7

g cm-3[AU]

max=100

max=102

0-7

g cm-3

0

2

0

-2
-2

回転曲線

2

回転曲線

00

-2

-2
Aligned: ζcr=10-17 s-1-17 -1
Aligned:ζcr-17=10
Aligned:ζcr=10
s-1 s

6

6

6

4

4

4

2

6

J ⃗ B⃗

Aligned: ζcr=10-17 s-1
イオンの
回転曲線

24

2

0

vKep
vφ
vKep
vφ,ionvvKepφvrvφ
vφ,ionvr,ionvφ,ionvr
vr,ionvr
ケプラー回転vr,ion

イオンの

4

2

-1
v [km
-1 s ]v [km s ]

10
フ
49
49
10
49
10
ァ 10
48
ー
10 -12
-11
1048
1048
10
10 -11
ス
-12
-12
10
10
48
10
ト 10 -12
-11
10
10
コ
-3
ρ
[g
cm
max
ア Figure 2. Evolution of the angular momentum] in系中⼼部の密度(ほぼ時間軸)
the first hydrostatic core
Figure2.
Evolutionoftheangularmomentumthe first hydrostatic−12−3
Figureas2.theEvolution
the10
angularg cm
momentumthefirstinrepresent
hydrostatic
core coregas with of
ρ≥
).
Thein
triangleswhen
内 (defined−12−3(defined as the gas withρ ≥ 10−3 g cm ). The triangles represent whenas thegas
with ρ ≥ 10−12g cm The). Thetriangles
representthe(defineddiscs becomes
gravitationallyunstable.
angularmomentumin whenthe
⾓
8 becomes
Wurster, Bate
& Pricethe discs
gravitationallyunstable. The angular momentum in theate & Pricediscs
becomesgravitationallyunstable.
Theinangularmomentumin thecore
Figure2.theEvolutionofangularmomentumthe first
hydrostaticcore
is larger
forthemodelswith lower
ionization
rates,
andwithinitially
運 firstfirst core is larger for models with lower ionization rates, and with initially
−3
first
core
is
largerformodelswithgfieldlower
ionization
rates, andrepresent
with initiallyanti-aligned
magnetic
field
and−12
rotation
vectors.
(defined
as
the
gas
with
ρ
≥
10
cm
). The vectors.
triangles
whenanti-aligned
magneticandrotation動anti-aligned magnetic field and rotation vectors.
the
量 discs becomes gravitationally unstable. The angular momentum in thefirst coreis larger formodelswithlower
ionization
rates,−− and with initially⃗⃗⃗⃗angular momentum.
Thisisbecauseinζ
themagnetic
field sup-field supangularmomentum.
Thisisbecauseinζ
the magnetic
17
17
J
B
J
B
−
anti-aligned
magnetic
fieldrotationangularmomentum.
Thisisbecausein ζ17magnetic
field supports
the andcloud
againstgravityanddelaysthe collapse,
extending
ports
the
cloud
againstgravityand vectors.
delaysthethecollapse,
extending44sAnti-aligned: ζcr=10-17 s-1
円盤全体の

6

4

]

2 -1

Lfc [g cm s ]2 -1
Lfc [g cm s ]2 -1

Lfc [g cm s ]10Anti-aligned: ζcr=10

6

-1
v [km
-1 s ]v [km s ]

52
52
10 10

⃗ B
Anti-aligned:
s-1 ⃗
J -17
Anti-aligned:ζcr=10-17 s-1 ζcr=106-17 -1

Wurster, Bate & Price

-1

53

10

vv[km
s-1]s
[km

10

Wurster, Bate & Pricev [km s-1] v [km s-1]

53

円盤全体の
回転曲線

0

イオンが速く回るので,
0
2
ports
the
cloud
againstgravityanddelaysthecollapse,
extending
Bate & Pricethe lifetime oftheof the first corehydrostatic
thelifetime
first hydrostatic
phase.core phase.
磁場は回転より速く回る.
理想MHD
In
all
simulations,
total
angularmomentumisconserved
theInlifetimeof the first hydrostatic
coremomentum
phase.
-2
all simulations,
total angularis conserved-2−
within1 percentduringtheζentire
gravitational
collapsethroughallcent
simulations,
total
angularmomentumis conserved
angularmomentum.
This
isthe
becauseinfield sup-2
within1Inperduringentiregravitational
collapsethrough
17 the magnetic
tostellardensities.
The
initialangularmomentuminoursimula0
1 per
centTheduringtheandentiregravitational
collapse throughstellardensities.
initialmomentumports tothewithin
cloud
againstgravitydelaysthecollapse,
extending−in our simula53angular
2 −1
0
5
10
15
20
25
30
35
persimulacent of this istions53is 2.26
10cm s −momentum, and, in ζ17 , ∼6.5
2×initial−1 gangulartostellardensities.
The
in
our
0
5
10
15
20
25
30
35
per
cent of this istions is 2.26
×contained
10
ghydrostaticcm
s2 hydrostatic, and, in ζcorer [au]
17 ,−∼6.5
the lifetime
of
the
first
incm
first
after
itsperformation.
53−1 core phase.
0
5
10
15
25
30
35
,
∼6.5
cent
of
this
is
tions
is
2.26
×
10
g
s
,
and,
in
ζ
r [au]20
17
containedin
firsthydrostatic
core
after
its
formation.
In contained
all simulations,
total angularmomentumr [au]
より顕著なトロイダル Figure
in first hydrostatic
core after its
formation. is conserved-23. Azimuthally averaged single-fluid
and ion velocities within 20◦
y roAnti-aligne

0

050

cr=10

Anti-Aligne

s-1

cr=10

s

ealy roAligneg cm-3

cr=10

cr=10

-1

Anti-Aligne

s-1

cr=10

-17 -1Anti-aligne

s

cr=10

-1

50

-7

00

050

y ro
-50
Anti-aligne-17 -1[AU]

max=10-1s

0-50Anti-aligne
eal Aligne-1 -1 -17s-1
Anti-Aligne
Alignescr=10cr=10-17 -1s-1=10-1-17ss-1-1
cr=10
cr

Aligne

cr=10

-1

s-1

eal

−
+
◦
of Azimuthally
the midplane at
ρmax ≈ single-fluid
10−7 g cm−3
ζ17
(top)
and20
ζ17
Figure 3.
averaged
andforionmodelsvelocities
within磁場をつくる.
within 1 per cent4.2.1
duringentiregravitational collapse throughIon theand bulk
velocities◦− Thewithin+
Figure3. Azimuthally
andmodelsion
velocities−7single-fluid−3 for(bottom).
Theρmax
gas averagedis≈rotating
atg sub-Keplerianvelocities.
ionsareζ20roof
themidplane
at
10
cm
ζ
(top)
and
17
17
−
+
to stellar
The
initialangular momentuminoursimula4.2.1 densities.
Ion and bulk
velocities−7 g cm−3 for models−of the tating
midplane
atisthanρrotating
10sub-Keplerian
ζ17
(top)
ζromaxthe≈bulk
slowerrotational flow invelocities.
ζ17, decreasing
the andmagnetic
Fig.
3
shows
the
azimuthally
averagedradialandazimuthalveloc17(bottom).
The
gas
at
The
ions
are
4.2.1 Ion andbulkvelocities
−
53
2 −1
0 promoting
5 disc10
1520The ions 25−(bottom).
Thegas
is bulk
rotating
at formation.
sub-Keplerianvelocities.
are ro, ∼6.5
perofsingle-fluid
this is tatingtions Fig.
is 2.26
×
10
g
cm
s
,
and,
in
ζ
braking
andities,v
andv,
respectively,oftheions centand velocthe
17 bothr
φ averaged radialslowerthantherotational
flow in ζ17,
decreasing
the magnetic
3 shows the azimuthally
andazimuthal−± tating slower than the bulk rotational flow in ζ , decreasing◦ averaged radial and azimuthal−7
Fig.in3 firstshowshydrostatic
the azimuthally
velocr [au] the magnetic
motionwithin20
ofthemidplane
at
ρ
≈
10
for
modelsζ.
17
contained
core
after
its
formation.
max
brakingand promoting disc formation.
17
vr and vφ , respectively, of both the ions and the single-fluid
図9:ities,
分⼦流速度の視線成分

50

-50
-50

0
0
x [AU]x [AU]

2

50
50

-2

-50

0
x [AU]

0vr [ m ]

50

-50

-50

0
0
x [AU]x [AU]

2

50

-2

50

-50

0
x [AU]

0vr [ m ]

50

-50

0
x [AU]

50

2

r0
is vr = 0. There are no first core outflows in the purely
Figure9. Radialvelocity
in a0.slice
throughcore
for eachcalculations. The white contour is vr = 0. There are no first core outflows in the purely
y in a slice
The white
contour
is vr =
There
are nothe
firstfirstcore
outflows
in ofthethepurely− through the first core for each of the calculations.
all of ζ17.
−there are narrow, slow outflows embedded in the centre of the diagonal infall of ζ − .
and there are narrow, slow outflows embedded in the centrehydrodynamics
of the diagonal model,
infall ofandζ17.
17